Tying and Bundling in Two-Sided Markets
- Why Tying WMP and the Windows OS Increases Total Welfare -
Tilburg University Master Thesis
Author: Pauline Luise Affeldt
ANR: 285505
Supervisor: Prof. Lapo Filistrucchi
Program: MSc Economics
Department: Department of Economics
Date of Completion: November 28, 2011
Date of Defense: December 13, 2011
Abstract
Recently, the European Commission seems to closely scrutinize the high-tech and software
sector as the investigations into Intel, IBM, Qualcomm, Rambus, Apple, SAP and Google over the
last years show. In these cases, the Commission is mainly concerned about exclusionary behavior
by dominant firms. Tying and bundling practices are part of these behaviors and have traditionally
been seen as anti-competitive and adopted to foreclose competition.
Nevertheless, especially software markets are not only highly dynamic, they are also in many
instances characterized by two-sidedness. The literature on two-sided markets has shown that
the traditional models and procedures used in antitrust analysis often deliver incorrect results if
applied unaltered to two-sided markets.
Given the recent focus of the European Commission on the high-tech sector, this thesis investigates whether tying and bundling practices in two-sided markets can be judged in the same way
as these practices in one-sided markets or whether the economics of two-sided markets imply that
tying and bundling can be profit-maximizing strategies that potentially increase both total welfare
and consumer surplus.
The literature on tying and bundling in two-sided markets is therefore reviewed and factors
determining the likely welfare implications of tying and bundling in two-sided markets are identified.
The concepts emerging from the literature are then applied to the decision by the European
Commission against Microsoft. In this case, the European Commission found Microsoft guilty
of abusing its dominant position in the operating system market by tying its Windows Media
Player to the Windows Operating System. Since streaming media players are two-sided platforms,
the Microsoft EU case allows applying the findings from the literature to a high profile abuse of
dominance decision.
Lastly, since one of the crucial factors determining the likely welfare implications of tying in
two-sided markets is multi-homing, a game theoretic model of tying in a two-sided market with
horizontally differentiated products in which both groups of consumers multi-home is developed
based on Choi (2010). In order to make the model fit closer to the Microsoft EU case, two groups
of users are distinguished, who differ in their transportation costs. While mainstream users have
relatively high transportation costs, tech-savvy users have low transportation costs. The model
further investigates whether tying will lead to foreclosure of the rival in the media player market
if absent tying the market is covered and content providers as well as high and low transportation
cost users multi-home.
i
Acknowledgements
There are several people who played an important role in the completion of this thesis.
Firstly, I would like to thank my supervisor, Prof. Lapo Filistrucchi, not only for valuable comments
on my thesis and his time, but also for making the last year at Tilburg University a unique, challenging
and rewarding experience.
Secondly, I thank the second reader, Prof. Jan Boone, for useful comments on the model.
Thirdly, I thank Christoph Schottmüller for his precious help. Without him I would not have been
able to complete the model.
Fourthly, I would like to thank my boyfriend, Falk, for his love, patience and support not only over
the period of writing this thesis but during my whole time at Tilburg University.
Lastly, I thank my parents for always supporting me in every possible way over the entire course of
my studies.
ii
Contents
1 Introduction
1
2 Literature Review
3
2.1
2.2
2.3
Tying and Bundling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.1.1
Definitions of Tying and Bundling . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.1.2
Traditional One-Sided Explanations . . . . . . . . . . . . . . . . . . . . . . . . .
6
Two-Sided Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1
Definition of Two-Sided Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2
Types of Two-Sided Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3
Pricing in Two-Sided Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4
Single- versus Multi-Homing
2.2.5
Platform Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.6
Implications for Competition Policy . . . . . . . . . . . . . . . . . . . . . . . . . 15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Tying and Bundling in Two-Sided Markets . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1
Review of the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2
Factors Determining Likely Effects . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3
Implications for Tying and Bundling Antitrust Cases in Two-Sided Markets . . . 29
3 Microsoft EU Case Discussion
3.1
3.2
3.3
31
Summary of the Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1
Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.2
Considered Abuses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.3
Structure of the Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Economic Analysis of the Microsoft EU Case . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1
Are the Tying Good and the Tied Good Two Separate Products? . . . . . . . . . 35
3.2.2
Does Microsoft’s Tie Foreclose Competition? . . . . . . . . . . . . . . . . . . . . 36
3.2.3
Are There Arguments Justifying Microsoft’s Tie? . . . . . . . . . . . . . . . . . . 38
3.2.4
Dynamic Aspect of Microsoft’s Tying . . . . . . . . . . . . . . . . . . . . . . . . 42
Conclusion on Microsoft EU Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
iii
4 A Model of Tying in a Two-Sided Market with Multi-Homing on Both Sides
4.1
46
Model Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1.1
Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.2
Content Providers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2
Market Equilibrium in Two-Sided Market with Multi-Homing and No Tying . . . . . . . 49
4.3
Market Equilibrium in Two-Sided Market with Multi-Homing and Tying . . . . . . . . . 52
4.3.1
No Tying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.2
Tying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.3
Incentives to Tie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4
Welfare Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5
Potential Other Tying Equilibrium: Tying with No Multi-Homing by Users . . . . . . . 60
4.6
Significance for Microsoft EU Case and Limitations . . . . . . . . . . . . . . . . . . . . . 63
5 Conclusion
67
References
69
A Appendix
72
A.1 Profit Maximization on User Side with Multi-Homing and No Tying . . . . . . . . . . . 72
A.2 Derivation of Assumption A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
A.3 Derivation of Assumption A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.4 Assumption on v in Choi (2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A.4.1 No Tying with Covered Market and Multi-Homing . . . . . . . . . . . . . . . . . 75
A.4.2 No Tying with Not Fully Covered Market and No Multi-Homing . . . . . . . . . 75
A.4.3 Tying with Covered Market and Multi-Homing . . . . . . . . . . . . . . . . . . . 81
A.4.4 Tying with No Multi-Homing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
A.5 Derivation of Covered Market Condition under No Tying . . . . . . . . . . . . . . . . . 84
A.6 Derivation of Covered Market Condition under Tying
. . . . . . . . . . . . . . . . . . . 90
A.7 Profit Maximization of Platform B under Tying . . . . . . . . . . . . . . . . . . . . . . . 91
A.8 Profit Comparison of Platform A under Tying and No Tying . . . . . . . . . . . . . . . 92
A.9 Profit Comparison of Platform B under Tying and No Tying . . . . . . . . . . . . . . . 93
A.10 Change in Number of Multi-Homing Users due to Tying . . . . . . . . . . . . . . . . . . 94
A.11 Change in Total Welfare due to Tying . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
A.12 Change in User Surplus due to Tying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
A.13 Change in Content Provider Surplus due to Tying . . . . . . . . . . . . . . . . . . . . . 98
A.14 Profit Maximization of Platform A under Tying with No Multi-Homing . . . . . . . . . 100
iv
List of Figures
1
Two-Sided Market With Multi-Homing on Both Sides . . . . . . . . . . . . . . . . . . . 48
2
User Choices for Type θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3
Two-Sided Market with Tying by A and Multi-Homing . . . . . . . . . . . . . . . . . . . 55
4
Two-Sided Market with Tying by A and No Multi-Homing . . . . . . . . . . . . . . . . . 61
v
1
Introduction
Tying and bundling have traditionally been seen as anti-competitive by competition authorities. According to standard economic theory, tying and bundling have welfare enhancing as well as welfare
decreasing effects. On one hand, tying and bundling can often lead to efficiencies, which are welfare
enhancing. On the other hand, these strategies can be used as a tool to price discriminate and hence
extract consumer surplus more efficiently. Lastly, tying and bundling can be used strategically to
foreclose competitors and entrants both in the tied and the tying good’s market.
This thesis’ goal is to investigate whether these results of standard economic theory also hold in a twosided market context. Over the last ten years, an extensive literature about the economics of two-sided
markets has developed. This literature shows that many of the economic results that hold in traditional
one-sided markets do not hold in two-sided markets. Hence, a thorough assessment of antitrust cases
in two-sided markets requires taking into account the specifics of two-sided markets. While the issues
of for example defining a relevant market, establishing dominance or evaluating the effects of mergers
in two-sided markets have been discussed in the literature, there exists no comprehensive review of the
literature about tying and bundling in two-sided markets.
In my thesis I hence address the question of whether the effects of tying and bundling in two-sided
markets can be assessed in the same way as in a one-sided market context or whether in a two-sided
market tying and bundling can be profit-maximizing strategies rather than instruments to foreclose
competitors and entrants. I furthermore try to answer the question under which circumstances tying
and bundling in two-sided markets can increase total welfare and potentially also consumer surplus.
In order to answer these questions, I first review the existing literature on tying and bundling in onesided markets as well as in two-sided markets and draw conclusions about which factors determine
the likely economic effects of tying and bundling in two-sided markets. After having defined these
factors, I apply them to the Microsoft EU case in which Microsoft was found guilty of abusing its
dominant position in the Operating System (OS) market by tying its Windows Media Player (WMP)
to its Windows OS. Even though the case was already decided in 2004, the case is still relevant today.
Especially software markets are characterized by two-sidedness in many cases, where the two sides
of the market are typically content or software providers on one side and users on the other side.
Furthermore, in recent years, the European Commission seems to have looked especially closely at
the high-tech sector as the recent investigations into Intel, IBM, Qualcomm, Rambus, Apple, SAP
and Google show.1 Since the high-tech sector is seen as an important driver of economic growth, the
European Commission is especially concerned with exclusionary conduct by incumbents and keeping
the sector competitive. As many of the high-tech markets are characterized by two-sidedness, the
recent European Commission’s focus on this sector warrants a thorough assessment of the impact
of two-sidedness on the economic outcomes of practices that have traditionally been seen as anticompetitive.
Lastly, after having concluded that one important factor determining the likely outcomes of tying and
bundling in two-sided markets is multi-homing and that this factor is also extremely relevant in the
Microsoft EU case, I develop a game theoretic model of tying in a two-sided market with multi-homing
on both sides and two groups of users. In this model, which is based on Choi (2010), I investigate
1 The European Commission fined Intel in 2009 for conditional rebates, dropped an investigation of Qualcomm’s
licenses in 2009, accepted Rambus’ commitments regarding royalty licenses in 2009, accepted Microsoft’s commitment
about unbundling Windows and Internet Explorer in 2009, initiated an investigation into IBM’s practices in 2010, closed
an investigation into Apple in 2010 and currently investigates SAP and Google (Coppi, 2011).
1
whether tying can be a profit-maximizing strategy, whether it is able to foreclose the competitor in
the tied good market and the outcomes for total welfare as well as consumer surplus.
The thesis proceeds as follows. In section 2, I present the relevant literature on traditional onesided explanations of tying and bundling, the economics of two-sided markets in general and tying and
bundling in two-sided markets. I conclude by defining the factors determining the likely effects of tying
and bundling in a two-sided market context. Following the literature review, I discuss the Microsoft
EU case in section 3. In order to investigate the likely outcomes of Microsoft’s tying practice in terms
of profits, consumer surplus and total welfare, I lay out a model of tying in a two-sided market with
multi-homing on both sides and two types of users in section 4. I conclude in section 5.
2
2
Literature Review
In traditional one-sided markets, tying and bundling have often been seen as anti-competitive. These
strategies were seen as being adopted either for price discrimination or foreclosure reasons. Nevertheless, these results do not necessarily hold in two-sided markets. Two-sided markets are markets
characterized by two distinct groups of consumers who are linked by indirect network externalitites.
In these markets, tying and bundling can be profit-maximizing strategies rather than means to price
discriminate or foreclose competitors. This result is due to the indirect network externalities and there
are circumstances under which tying and bundling not only increase profits but also consumer surplus.
These results in turn have important policy implications and rather than per se prohibiting tying
practices, a rule of reason standard should be adopted.
Reviewing the literature on tying and bundling in two-sided markets, I conclude that there are three
main factors determining whether tying or bundling is welfare enhancing. Firstly, the higher the
magnitude of the indirect network externalities, the more likely tying or bundling increases total
welfare as well as consumer surplus. Secondly, the symmetry between network externalities matters.
The more asymmetric the indirect network externalities across sides, the more likely it is that tying
or bundling on the low externality side is welfare and consumer surplus enhancing. In these cases
bundling or tying can be a means to subsidize participation on the low externality side which in turn
benefits the high externality side. Lastly, if consumers do not face too high costs of multi-homing,
tying or bundling is less likely to be welfare detrimental. Competition authorities should hence assess
these factors when analyzing cases of tying or bundling in two-sided markets.
In this section, I first define tying and bundling and give an overview of traditional one-sided explanations of tying and bundling in section 2.1. Section 2.2 explains two-sided markets. In section 2.3,
I review the existing literature on tying and bundling in two-sided markets and derive competition
policy conclusions for antitrust cases involving two-sided markets.
2.1
Tying and Bundling
In this section I will firstly discuss the definitions of tying and bundling (section 2.1.1) and then review
the traditional explanations for tying and bundling in one-sided markets that have been identified in
the literature (section 2.1.2).
2.1.1
Definitions of Tying and Bundling
Tying and bundling means that two distinct2 products are sold together. When trying to further
identify different possible modes of selling products together, tying, pure bundling and mixed bundling
can be distinguished. While there seems to be consensus on the definition of bundling, there is no
consistent definition of tying. At least two different types of definitions can be distinguished.
Motta (2004) defines bundling (or also package tie-in) as instances where goods are sold together in
fixed proportions. Shoes, for example, are always sold together with one pair of laces. He further
2 The definition of what can be considered “distinct” products is not very clear. According to Tirole (2005), legally
products are considered to be distinct if consumers would buy them separately absent any tying or bundling. The author
remarks in this respect that this definition seems rather vague as a purchasing decision depends on “pricing, delivery,
guarantee, and assembly offerings” (Tirole, 2005, p.8).
3
distinguishes between pure bundling and mixed bundling. Pure bundling means that products are
only available as a bundle and cannot be purchased separately, while mixed bundling means that
the bundled goods can be purchased individually or together. Motta (2004) gives the example of a
restaurant which offers dishes à la carte or bundled together in a fixed menu.
Tying, according to Motta’s (2004) definition, means that a consumer not only buys a certain good
but is required to also buy all the subsequent units of another good that he or she wants to purchase.
Hence, the two goods are offered together in variable proportions. He also refers to this mode of
selling as requirements tying. An example are photocopiers and toner cartridges, where buyers have to
contractually agree to purchasing all future toner cartridges from the photocopying company.
Tirole (2005) defines tying and bundling slightly differently. As explained in his paper, tying refers to
a situation where one product (the tying good) is sold conditional on the purchase of the other product
(the tied good).
Bundling means that two products are sold together. If the products are only available as a bundle,
the bundling is said to be pure, if the products can either be purchased separately or as a bundle, the
bundling is called mixed. Under mixed bundling, the price of the bundle is lower than the sum of the
stand-alone prices of the two goods. Hence, Tirole’s (2005) definitions of pure and mixed bundling are
consistent with Motta’s (2004) definitions of the same concepts.
Tirole’s (2005) definition of tying differs however from Motta’s (2004) definition.
The difference between pure bundling and tying, according to Tirole (2005), is that under tying the
tied good is also available on a stand-alone basis. The difference between mixed bundling and tying
is that under mixed bundling both goods are also available on a stand-alone basis while under tying
only the tied good is available separately but not the tying good.
Consider as an example the tying or bundling of the Microsoft operating system (OS) with the Windows
Media Player3 (WMP). Under tying, the operating system is the tying good while the Windows Media
Player is the tied good. Thus, the operating system is only available in combination with WMP while
WMP is also available on a stand-alone basis. In the case of pure bundling, the operating system
and WMP would only be available as a bundle and neither of the two goods would be available on a
stand-alone basis. Under mixed bundling, the operating system and WMP would both be available on
a stand-alone basis as well as in a bundle where the bundle price would be lower than the sum of the
two stand-alone prices.
Tirole (2005) mentions however that in the case where the tied good is valueless without the tying
good, the distinction between tying and pure bundling becomes irrelevant as nobody would ever buy
the tied good without the tying good. Also here tying Microsoft’s operating system to WMP is an
example as the media player is useless without an operating system.
Other authors giving definitions of tying, pure bundling and mixed bundling include Carlton and
Waldman (2002), Schmalensee (1984) and Whinston (1990).
Schmalensee (1984) defines pure bundling as the practice of selling one unit of each good together,
where the two goods are not available separately. Under mixed bundling both goods are available
separately as well as in a bundle.
3 The Windows Media Player is a streaming media player which allows to play media files. See section 3 for the
Microsoft EU case discussion.
4
Both Whinston (1990) and Carlton and Waldman (2002) essentially define tying as the practice of
refusing to sell the tying good to a consumer unless she also purchases the tied good.
Hence, while the definitions of pure and mixed bundling are the same across authors, the definitions
of tying differ between authors. I understand the definitions of tying by Whinston (1990) and Carlton
and Waldman (2002) to be the same as Tirole’s (2005) definition. None of these three definitions
mentions the variable proportions Motta (2004) uses to distinguish between bundling and tying.
In the following, I will stick to the definition of tying as stated by Tirole (2005).
According to the definitions of pure bundling, mixed bundling and tying I adopt, some of the papers
I discuss in section 2.3, have to be reclassified. Tirole (2005) examines tying in two-sided markets,
Amelio and Jullien (2007) analyze tying and bundling, Chao and Derdenger (2010) consider mixed
bundling and Chen (2009) looks at pure and mixed bundling. These papers follow the definitions
above.
However, Li (2009) calls “tying” what should actually be “pure bundling”. The paper examines bundling
of a magazine and a CD, where one of the firms is a monopolist for the CD. The author states that
under tying, the platform needs to make sales of magazines in order to profitably sell CDs. The paper
states that a consumer only has the choice between purchasing the bundle of the magazine and the
CD or the competing magazine alone. Hence, if the bundling platform fails to attract one reader, it
also loses the opportunity to make sales of a profitable CD. I infer from these statements, that the CD
will no longer be available on a standalone basis, which means that the paper actually considers pure
bundling and not tying.
Also Choi (2010) speaks of tying but then mentions that the price of the “bundle” is set so that
everybody purchases the bundle. He further assumes that the tied good is necessary for participating
in the two-sided market. However, if the price is set so that everybody buys the bundle, one could
consider this as pure bundling rather than tying. Following Tirole (2005), I argue however that in
this special case the distinction between tying and pure bundling becomes irrelevant. As stated above,
Tirole (2005) argues that the distinction between tying and pure bundling is irrelevant in cases where
the tied good is valueless without the tying good as nobody would ever buy the tied good without
the tying good. This situation fits Choi’s (2010) model since he assumes that the product M (which
would be the OS in the Windows OS and WMP example) is essential for participating in the two-sided
market (which are two competing media players in the paper). Since one of the two platforms is a
monopolist in offering product M, nobody would ever purchase one of the two competing media players
without also purchasing M as a media player without an OS is useless. In that case, I would argue
that it makes no difference which of the two goods is the tying good and which is the tied as there is
no difference to pure bundling. This result however crucially depends on the firm offering M being a
monopolist so that consumers have no alternative to using product M.
Lastly, Rochet and Tirole (2008) analyze the so-called honor-all-cards (HAC) rule in the payment card
industry. They speak of tying a credit and a debit card on the merchant side of the market: a merchant
who accepts the credit card also needs to accept the debit card of that network. However, this can
only be considered as tying if the merchant can also decide only to accept the debit card and not the
credit card. Otherwise, if the merchant always has to accept both, it is pure bundling.
Concluding, while the definitions of pure and mixed bundling are consistent across authors, there
seem to be different definitions of tying. In the remainder of this thesis, I will stick to Tirole’s (2005)
definition of tying. According to Tirole (2005), under tying, consumers can purchase the tying and the
5
tied good together as well as the tied good separately. The tying good is however not available on a
stand-alone basis.
After having defined bundling and tying, I will now turn to the traditional, one-sided explanations of
bundling and tying given in the literature.
2.1.2
Traditional One-Sided Explanations
There are three main effects of tying and bundling, which have been widely discussed in the literature
on tying in a traditional, one-sided context. The first effect is that tying and bundling can lead to
efficiencies and thus can increase welfare. Nevertheless, the two other possible explanations for tying
and bundling, which are price discrimination and foreclosure of competitors, have the potential to
decrease welfare and can thus have anti-competitive effects. I will discuss each of these traditional
explanations in turn.
Efficiency Reasons One of the reasons for why tying and bundling (of complementary goods) are
so widespread are efficiency reasons. These are welfare enhancing and thus pro-competitive.
Tying and bundling can reduce production costs. Often it is much more efficient to sell components
together due to economies of scale and the principle of division of labor (Motta, 2004). It is, for
example, much more efficient to sell cars as a bundle rather than selling all the different components
separately and let consumers assemble them.
Additionally, tying and bundling can decrease transaction costs (Tirole, 2005). Consider once again
the example of selling the Windows OS and WMP together. In that case, consumers do not need to
acquire an OS and a streaming media player separately but receive both goods in a single transaction.
Furthermore, tying and bundling might also reduce distribution costs (Tirole, 2005). Rather than
distributing WMP either separately on disk or offering it for download via Internet, WMP is shipped
together with the Windows OS to original equipment manufacturers (OEMs).
Also, tying and bundling might ensure perfect compatibility between products or components. In
that case, selling the products or components together ensures the best performance of the products
(and thus consumers receive the highest possible product quality) but also helps to preserve a firm’s
or brand’s reputation (Motta, 2004). In that sense, tying and bundling might be means to overcome
asymmetric information problems.
Nevertheless, as Motta (2004) notes, when assessing the possible efficiency gains of tying and bundling,
one needs to also look at whether these efficiency gains could be realized through means other than
tying or bundling.
Price Discrimination Another explanation for why firms adopt tying and bundling so frequently
is that these strategies can serve as price discrimination tools and thus help firms to extract more
consumer surplus and increase profits (Motta, 2004).
Pure bundling is a means to extract consumer surplus and increase profits if consumer valuations
are heterogenous and the valuations of the two products are negatively (or at least not too strongly
positively) correlated. The reason is that selling the products together decreases consumer heterogeneity because the standard deviation of the bundle valuation is smaller than the sum of the standard
6
deviations of the valuations for the two products separately. The decreased consumer heterogeneity
allows the firm to extract more of consumers’ surplus (see for example Adams and Yellen (1976) or
Schmalensee (1984)).
According to Schmalensee (1984), mixed bundling combines the advantages of pure bundling and
independent selling. It allows on one hand to reduce consumer heterogeneity for consumers with high
valuations for both products while still allowing the firm to sell products separately at a high price to
those consumers who only highly value one of the goods.
Tying can be a profit-maximizing strategy for firms also where it helps to measure consumers’ intensity
of use. Consider again the example of the photocopier and the toner cartridges. Depending on how
much consumers use a photocopier, their willingness-to-pay for it differs. However, by requiring people
to buy toner cartridges from the same firm, the firm can use the sale of toner to measure the intensity
of demand from different consumers. It might then be profit-maximizing to sell the photocopier at a
relatively low price in order to also attract consumers with a low willingness-to-pay and increase the
price of the complementary toner cartridges in order to extract more surplus from those consumers
with a high willingness-to-pay (see for example Motta (2004) or Tirole (2005)).
The welfare effects of bundling and tying as a price discrimination tool are ambiguous. They clearly
increase producer surplus as they are adopted as a profit-maximizing strategy. The effects on consumer
surplus are not à priori clear though. Motta (2004) states that if all consumers who buy without
bundling or tying also buy when products are bundled or tied together, then total welfare decreases
under bundling/tying.4 Nevertheless, tying might allow to attract consumers who would not have
bought without the tie (those for whom the initial price of the photocopier was too high because they
did not intend to use it much), which has a positive effect on welfare. Hence, the negative and positive
effects need to be weighed against each other in order to determine the overall effect on total welfare.
Foreclosing Competition Tying and bundling tends to hurt rivals. Hence, the last explanation
for the widespread use of tying and bundling practices relates to the leverage theory. There are
basically two rationales for engaging in tying and bundling for anti-competitive reasons: The first is
to monopolize the competitive segment (market B), the second is to protect the monopoly segment
(market A) (Tirole, 2005).
I first turn to the mechanism that allows to monopolize market B by leveraging monopoly power from
market A.
Whinston (1990) argued that tying5 is a means to leverage monopoly power from one market into
another, competitive market, in order to foreclose sales and thus monopolize this second market. This
is the so-called leverage theory. Even though the leverage theory emerged as an informal concept in the
law literature, it has been used as an argument in several court decisions. Choi and Stefanadis (2001)
cite for example Terminal Railroad Association (1912), IBM (1936), Standard Oil (1949) and Civil
Aeronautics Board hearings (1983).6 The basic argument is as follows: Assume there is a monopolist
in market A who is also active in market B, where it faces one competitor. Demands for product A
4 More consumer surplus is extracted by firms. This is merely a transfer from consumers to producers. However, there
is also a deadweight loss.
5 Even though Whinston speaks of tying, according to the definition I adopted above, he actually analyzes pure
bundling, that is selling the two products only together.
6 United States v. Terminal Railroad Association of St. Lewis, 224 U.S. 383 (1912); International Business Machines
v. United States, 298 U.S. 131 (1936); Standard Oil v. United States, 337 U.S. 293 (1949); Civil Aeronautics Board,
Hearings for Proposed Rulemaking – Airline Computer Reservation Systems, EDR – 466 (1983).
7
and product B are independent. The fact of selling product A and B together acts as a commitment
to be aggressive in the tied good market (market B). Hence, the optimal effective price for good B is
lower under bundling than when A and B are sold independently. This is because on every lost sale
of product B, the monopolist now also looses a sale of product A. Since the firm is a monopolist in
market A, margins in this market are high. Loosing sales of good A is thus costly for the monopolist.
Consequently, it will price very aggressively to attract a significant number of consumers to buy its
version of product B (and thus also A) rather than the competitor’s product. This aggressive behavior
obviously hurts the competitor in the tied good market relative to the case where the monopolist does
not bundle its products and, if the competitor is no longer able to cover fixed costs, will force it to
leave the market. Whinston (1990) calls this mechanism “strategic foreclosure”.
The leverage theory, which relies on products A and B being independent, has been heavily criticized
by the Chicago school following its application in case decisions.7 The main argument is that, in the
case of complementary products, where tying and bundling occur most, a monopolist will not want
to use tying and bundling to foreclose competitors in the competitive market as this is not profitable.
Hence, if a monopolist uses tying, then it must be for either efficiency or price discrimination reasons.
Consider once again a monopolist in market A who is also active in market B, where it faces several
competitors (see Whinston (2001)). Products A and B are perfect complements, which means that
they are consumed in fixed proportions and generate a system value of v. Market B is characterized
by perfect competition. Assume for the moment that product B is homogenous, hence, the price of B
will be equal to marginal production costs cB . For simplicity, production costs of good A are assumed
to be zero. When the monopolist decides to bundle8 A and B together, it becomes the only supplier of
product B and can charge a price equal to the valuation v for the system of A and B. Its profits (per
bundle sold) are then equal v − cB . If, on the contrary, the monopolist decides not to bundle, the price
of product B will be equal to its marginal costs cB . Hence, consumers are willing to pay v − cB for
product A. The monopolist’s profits per product A sold are then equal to v − cB no matter whether
consumers buy its own product B or competitors’ product B. Consequently, since the monopolist’s
profits are the same under unbundling and bundling, the monopolist is indifferent between bundling
A and B or selling them separately. Whatever profits the monopolist reaps are due to its monopoly
in market A. Furthermore, the monopolist will not want to foreclose competitors in market B because
it can only profit form their presence. Assume for example that the competitors’ marginal costs for
producing product B are lower or that their product is of superior quality compared to the monopolist’s
product B so that consumers attach higher value to a system composed of A and competitors’ product
B. In these cases, while the competitors’ product B is still sold at marginal costs9 , the monopolist
can extract additional profits from charging a higher price for product A, since the difference between
system valuation v and marginal production costs cB is now higher (either because cB is lower or v is
higher). The monopolist can thus extract all consumer surplus.
Concluding, if goods are perfect complements, the monopolist will not find it profitable to bundle.
In cases where either the marginal costs of the competitors are lower (so they are more efficient) or
the value of the competitors’ good is higher than the value of the monopolist’s own product B, the
monopolist even obtains higher profits under separate selling than under bundling. The reason is that
the monopolist can extract the extra surplus generated by the competitors’ more efficient or superior
7 See
for example Bork (1978); Bowman (1957); Director and Levi (1956); Posner (1976).
Tirole’s (2005) comment applies: Since A and B are perfect complements, nobody will purchase the tied good
B without the tying good A. Hence, the distinction between tying and pure bundling is irrelevant.
9 The monopolist now no longer sells any product B.
8 Here
8
product B by charging a higher price for good A.
Whinston (1990) points out though that the Chicago school argument relies on the products being
complements as well as the complementary good market being perfectly competitive and characterized
by constant returns-to-scale. Consequently, Whinston (1990) departs from these assumptions in his
paper and argues that under different assumptions, tying can be successful in foreclosing competitors
in market B.
Firstly, he shows that in the case of independent goods A and B and with uniform valuation by consumers of good A, tying can be profitable for the monopolist because of its exclusionary effect explained
above. This holds only if the monopolist can credibly commit to tie. Absent this commitment, it will
always have an incentive to sell the monopolistic good A also to those consumers who chose not to
purchase the bundle and gain additional profits. Nevertheless, the tying strategy is only profitable for
the monopolist if it leads the competitor to exit the market. This is true because under bundling, the
monopolist looses some sales of product A (those consumers who decide not to purchase the bundle)
and lowers its effective price of product B. If the competitor stays in the market under bundling, this
strategy leads to lower profits than independent pricing. Additionally, Whinston (1990) notes that
even if bundling drives the competitor out of the market, it is not necessarily profitable for the monopolist. Since the monopolist has to credibly commit to only sell product A and B together, it will
have to sell only the bundle even after the competitor left the market. If there is a large number of
consumers who had a strong preference for the competitor’s product B over the monopolist’s product
or who do not attach high value to product A, bundling might not be a profitable strategy even if it
leads to foreclosure.
Secondly, Whinston (1990) alters the assumption of homogenous preferences for good A. He shows
that with heterogenous consumer preferences for the monopolistic good, bundling does not necessarily
foreclose the competitor in market B because if a significant number of consumers do not attach high
value to good A (so they have valuations below costs), they will continue to purchase product B from
the competitor rather than the product bundle from the monopolist. If a lot of consumers dislike
product A or if there is a lot of dispersion of the valuations for good A and the competing products
B are not very differentiated, bundling can even increase the profits of the competitor. Nevertheless,
tying can be a profitable strategy for the monopolist even absent the ability to commit. This is the
case if the monopolist can sell a bundle of product A and B as well as A independently.
Thirdly, Whinston (1990) re-examines the case of complementary goods, consumed in fixed proportions.
Even though he introduces scale economies in the differentiated tied good market B as well as an
oligopolistic instead of competitive market structure, he finds that the Chicago argument still holds:
tying is not a profitable strategy for the monopolist. Since product A is essential for using product
B, the monopolist always benefits from competition in the tied good market and selling more units
of its monopolistic good A. The monopolist’s profits are even higher if a competitor is present in
market B than if there is none since the monopolist can extract the additional surplus generated
by the competitor. This result breaks down as soon as one introduces the presence of an inferior,
competitively supplied good A or an alternative use of product B, for which A is no longer essential.
Under these circumstances tying can once again emerge as a profitable strategy to reduce competition
in market B.
Whinston (1990) states that when tying leads to foreclosure, the effect on welfare is ambiguous. Consumers often loose due to less product variety being available and higher prices once the competitor
is forced to exit the market. The overall effect on welfare however depends also on the effects of
9
price discrimination and efficiencies resulting from fewer firms being active in industries with scale
economies.
Note that most of these exclusionary bundling and tying strategies depend on the monopolist being
able to credibly commit to tie or bundle, for example by implementing a technological tie (Whinston,
1990). Otherwise it will usually be profitable to divert and offer product A also for those purchasing
B from the competitor.
The second rationale for exclusionary tying is to protect the monopoly in market A. This theory relies
on complementary products and dynamic models where the incumbent firm faces potential entry in
both the primary and the complementary market in the future.
Choi and Stefanadis (2001) analyze how tying10 can protect the incumbent’s position in both markets
in the presence of risky R&D investment necessary to enter.
In their model, the incumbent is a monopolist in both goods’ markets in the first period but faces a
potential entrant in each of the markets in the second period. Each potential entrant can enter the
market only if it has a successful innovation where the probability of success depends on its initial
R&D investment. If it is successful, its technology is superior to the incumbent’s technology. Since
products are complements, under tying by the incumbent, an entrant in one market can only make
profits if there is also successful entry in the complementary market. If the incumbent decides to tie
its products together, it thus lowers the incentives for investment and innovation of potential entrants.
The incumbent faces a trade-off. If there is successful entry only in one of the two markets, this is
profitable for the monopolist as it can use its monopoly power in the complementary product market
to engage in a “price squeeze” and capture part of the surplus created by the innovation. If however
both entrants are successful, the incumbent is driven out of the market since the superior innovations
replace the incumbent’s products. Hence, if the risk of both entrants succeeding is high compared to
the additional profits the incumbent could capture if only one entrant succeeds, the incumbent will
find it profitable to engage in tying in order to decrease the incentives of potential entrants to invest
in innovation. These results however only hold if the incumbent can irreversibly commit to the tie.
Otherwise, if only one entrant succeeds, the incumbent will always find it profitable to unbundle its
products ex post.
Carlton and Waldman (2002) also analyze tying11 of complementary products in a dynamic setting.
Similarly to Choi and Stefanadis (2001), they show how a firm which is currently a monopolist in its
primary market can use tying with the complementary product to prevent future entry in the primary
market or newly emerging markets. This theory relies however on economies of scope between entry
decisions, where the entrant can enter in both markets at some cost, rather than one entrant entering
each market with a certain success probability as in Choi and Stefanadis’ (2001) model.
In Carlton and Waldman’s (2002) model, the firm is a monopolist in the primary market in the first
period but faces an entrant into the primary market in the second period. This alternative producer
can also enter the complementary market either in the first or the second period. Entry entails costs
for the alternative producer in each market. While the primary products are assumed to be equivalent,
the complementary good of the alternative producer is superior. In this model, Carlton and Waldman
(2002) find that the monopolist can deter entry by strategically tying its primary and complementary
10 While the authors speak of tying, what they analyze is actually pure bundling. Once again, following Tirole (2005),
this distinction is irrelevant since products are complements.
11 Also Carlton and Waldman (2002) speak of tying while actually analyzing pure bundling. Nevertheless, the distinction is once again irrelevant due to complementarity between products (Tirole, 2005).
10
products. Since tying eliminates the profits of the alternative producer from selling its complementary
product in the first period, he will not enter the complementary market as he will not be able to
recover the entry costs in only one period. Secondly, if the alternative producer does not enter the
complementary market in the first period because of the tie, he will also not enter the primary market
in the second period. This is due to the fact that the return to entering the primary market is related
to being able to capture the surplus from its superior complementary good. The authors conclude that
this type of strategic tying is most likely to occur in industries which are characterized by innovation
and short product lifetimes. If product lifetimes were long, tying would be less likely to deter entry in
the complementary market as the alternative supplier could profit from entering the primary market
and selling its superior complementary product for a long time period. Hence, it would be easier to
recover fixed entry costs. Carlton and Waldman (2002) further find that the results derived in the
first model also hold if the market for the complementary good is characterized by direct network
externalities rather than entry costs.
Similarly to this first model, the authors further find that tying can also deter a potential entrant
from entering a newly emerging market by decreasing the return to entry. The newly emerging market
is assumed to replace the primary market but is associated with the same complementary product.
Also in this model, the cost of entry in the complementary market reduces the return to entry in the
emerging market under tying. Direct network externalities in the complementary market lead to the
same conclusions as costly entry.
Conclusion on Traditional One-Sided Explanations of Tying and Bundling Concluding,
there are three main, one-sided effects or explanations of tying and bundling practices. Firstly, selling
products together can lead to efficiencies. Secondly, bundling and tying can act as a profit enhancing
price discrimination tool. Thirdly, under certain assumptions, tying and bundling can be used to
protect a monopolistic market or to monopolize a second market by driving competitors out of the
market or foreclosing potential entrants. Nevertheless, exclusionary tying is less likely if products are
complements.12
Traditionally, tying and bundling have been seen as anti-competitive. However, the welfare effects of
price discrimination and exclusionary tying are ambiguous. And even when anti-competitive effects can
be clearly identified, these should be weighed against potentially offsetting pro-competitive efficiencies.
In the next section, I turn to the definition and description of two-sided markets.
2.2
2.2.1
Two-Sided Markets
Definition of Two-Sided Markets
Evans (2003) gives three necessary conditions for a market to be two-sided. Firstly, there are two
or more distinct groups of consumers. Secondly, the market is characterized by indirect network
externalities. Thirdly, an intermediary is necessary to internalize these indirect network externalities.
12 Somehow the conclusion I derive that tying and bundling is less likely to be exclusionary in two-sided markets than
in one-sided markets is similar to the complementarity argument. While in the case of complementary products one
consumer buys two related goods, in the case of two-sided markets, there are two different consumers purchasing a good.
Nevertheless, these cases are similar in the sense that tying in a two-sided market is less likely to be welfare detrimental
because it can be a means to get both sides of the market on board.
11
A two-sided market is thus a market in which a firm, called platform, serves two distinct groups of
consumers. The Windows Media Player, for example, serves both users and content providers. The
platform tries to get both sides “on board” with its pricing strategy and provides a space where both
groups of consumers can “meet” and interact (Rochet and Tirole, 2006).
A two-sided market is further characterized by indirect network externalities between the two sides of
the market. This means that the value obtained by a customer of one type depends on the number of
consumers of the other type present on the platform (Evans, 2003). Sticking to the WMP example,
users care about how much content is available on the WMP platform. Hence, their valuation of WMP
or their utility from joining the platform increases with the number of content providers present on the
platform. The same holds the other way round: the more users are present on the platform, the more
valuable the platform becomes for content providers since they derive benefits from each additional
user their content reaches. These network externalities are not internalized by the two consumer groups
(Rochet and Tirole, 2006).
The indirect network externalities need not always be positive. Consider the case of television, for
example, where the two sides of the market are viewers and advertisers. While advertisers clearly care
about the number of viewers their advertisements reach, viewers might be annoyed by advertising.
Hence, viewers would be better off and attach a higher value to a given channel, all else equal, the
fewer advertisements the channel broadcasts. Also, one indirect network externality is enough for the
market to be two-sided. It is often assumed for example, that readers are indifferent to advertising in
newspapers. Nevertheless, since advertisers care about how many readers their advertisement reaches,
a newspaper is a two-sided platform. Note however that a two-sided market with two negative indirect
network externalities is not possible as in that case neither of the two groups of consumers wants to
interact with the other group, i.e. join the platform.
The third condition for the market to be two-sided is that the two groups of consumers are not able
to internalize the externalities they exert on each other. Hence, it is less likely that they will reach
an efficient outcome by avoiding the platform and bargaining bilaterally. This is generally due to
prohibitively high transaction costs between the two customer groups (Evans and Schmalensee, 2007)
or constraints on pricing between customer groups imposed by the platform13 (Rochet and Tirole,
2006).
Concluding, the main task of the platform is to decrease transaction costs and to allow the two sides
to benefit from trading or interacting with each other. It does so by pricing so as to get both customer
groups to join the platform and internalize the externalities that both groups exert on each other
(Evans and Schmalensee, 2007).
2.2.2
Types of Two-Sided Markets
There are two different types of two-sided markets. Filistrucchi (2008) speaks of two-sided markets of
the “media type” and the “payment cards type”, Armstrong (2006) proposes a membership model versus
the usage model of Rochet and Tirole (2003; 2006). These different terminologies mean essentially the
same distinction. Two-sided markets of the “payment cards type” are characterized by a transaction
between the two different customer groups. Hence, they correspond to Rochet and Tirole’s usage model.
Examples include credit card schemes, where a transaction between merchants and buyers takes place,
13 In
case of an actual transaction taking place between the two sides of the market.
12
or virtual market places such as Ebay. Since these markets are characterized by a transaction between
the two consumer groups, it is possible to charge customers per transaction. Two-sided markets of the
“media type”, on the contrary, are characterized by the absence of a direct transaction between the
two customer groups. This corresponds to Armstrong’s (2006) membership model. Examples include
newspapers or television where no direct transaction between a reader or viewer and an advertiser
takes place. Since there are no direct transactions between the customer groups, platforms can only
charge a fixed membership fee but no transaction fee.
2.2.3
Pricing in Two-Sided Markets
Since a two-sided platform faces two consumer groups and hence two demand curves, where each
depends not only on the price charged but also the quantity purchased by the other consumer group,
the platform has to determine two prices, one on each side (Evans, 2003). Rochet and Tirole (2006)
argue in this respect, that one of the defining criteria of a two-sided market is that not only the overall
price level (the sum of the prices charged to both sides) but also the pricing structure (roughly the
ratio between the two prices charged to the different sides) matters for the volume of transactions and
hence profits and welfare. This means that charging less to one side and increasing the price paid by
the other side by the same amount matters for the volume of transactions.
This is due to the feedback loop between the two sides created by the indirect network externalities.
An increase of the price on one side leads to a drop in demand on that side. This decreases demand on
the other side which decreases demand further on side 1 and so on. Once all feedbacks are taken into
account, the increase in price on one side has a direct effect of decreasing demand on side 1 and an
indirect effect of decreasing demand further on both sides due to the indirect network externalities.14
The higher the indirect network externalities are, the larger the effect of a price change even if the
consumers on the side where the price is changed are not very price sensitive (Evans and Schmalensee,
2007).
The key inside for understanding pricing in two-sided markets is that the Lerner equation does not
hold for the individual prices and that the profit-maximizing prices hence do not directly change with
marginal costs. Furthermore, the allocation of costs to a particular side of the market is often arbitrary
because the platform provides a joint service to the two sides (Evans, 2003). The implication of these
results is that pricing below marginal costs cannot be seen as predation. Furthermore, platforms often
adopt very skewed pricing structures. In general, the side with the lower externality is likely to receive
relatively low prices in order to stimulate its demand. A higher price is then charged to the other side
of the market. Hence, it can be profit-maximizing to charge a price below marginal costs or even a
negative price to consumers on the low externality side in order to subsidize their participation to the
platform (Evans, 2003). Caillaud and Jullien (2003) call this a “divide-and-conquer” strategy. As a
result, platforms often make most of their profits only on one side of the market (Rochet and Tirole,
2006).
Lastly, prices do not only depend on the magnitude of the indirect network externalities but also on
whether consumers single- or multi-home (Armstrong, 2006).
14 In
cases where both indirect network externalities are positive.
13
2.2.4
Single- versus Multi-Homing
In the two-sided market literature, single-homing refers to a situation where consumers only participate
in one platform. Multi-homing means that consumers engage in multiple platforms.
Multi-homing affects the price level as well as the price structure. In general, prices will be lower
when consumers multi-home on both sides of the market compared to a situation where both sides
single-home since the presence of substitute platforms means that competition between platforms is
fiercer (Evans, 2003). In situations where one side of the market single-homes while the other side
multi-homes however, a platform provides monopoly access to its single-homing users. Hence, the
platform acts as a “competitive bottleneck”. This means that the price charged to single-homing users
will usually be low in order to attract them, while the platform charges high prices to multi-homing
users on the other side for getting access to single-homing users (Armstrong, 2006).
2.2.5
Platform Size
Evans and Schmalensee (2007) identify five factors which influence the size of two-sided platforms: indirect network externalities, economies of scale, congestion, platform differentiation and multi-homing.
Firstly, indirect network externalities promote fewer and larger platforms.15 Taking again the example
of WMP, the more end-users adopt WMP, that is join the platform WMP, the more content providers
want to join WMP as they derive additional utility from each potential end-user their content reaches.
Given that more content will thus be available encoded in WMP format, end-users will prefer to join
WMP all else equal and so on. These feedback-loop effects might make the media player market tip
in favor of WMP.
Secondly, also economies of scale promote large platforms. In industries characterized by high fixed
costs and very low marginal costs, such as for example the software industry, which incurs high R&D
costs but almost no marginal costs, average costs decrease as production increases. This promotes
fewer but larger players.
Nevertheless, there are also factors offsetting the factors favoring tipping of the market. These are
congestion, differentiation and multi-homing.
Congestion can arise if, for a given physical size or capacity of the platform, increasing the number of
customers is costly, for example by increasing search and transaction costs. Congestion thus limits the
growth of platforms.
Two-sided platforms can also be differentiated. This can be vertical differentiation (different quality
levels) or horizontal differentiation (different features). Platform differentiation decreases the tendency
of two-sided markets to tip in favor of one platform.
Lastly, the fact that platforms are differentiated will lead consumers to multi-home, if costs of multihoming are not prohibitively high. Multi-homing decreases the tendency of two-sided markets to tip
in favor of one platform.
15 Indirect network externalities need not be linear though. For example, readers might value advertising in magazines.
Nevertheless, when there is too much advertising compared to content, readers might start to be annoyed. Hence, the
indirect network externality might become negative after a certain point. See Sokullu (2010) for an empirical two-sided
market model of the German magazine industry that finds non-linear indirect network effects.
14
2.2.6
Implications for Competition Policy
The particularities of two-sided markets compared to one-sided markets lead to important competition
policy issues (see for example Evans (2003) or Wright (2004)).
Questions arise, for example, about how to define a relevant antitrust market. How is the SSNIP test
for defining the relevant market to be implemented in a two-sided market context, given that platforms
charge two prices, one on each side? And which price should be raised in the SSNIP test, i.e. the price
level or the price on one side of the market?
Also, the assessment of market power in a two-sided market context raises questions. Are market
shares a relevant indicator for market power? And market shares on which side of the market should
be considered? Furthermore, a price, which is significantly higher than marginal costs, is not necessarily
an indication of market power. As discussed in section 2.2.3, it is quite common to charge a price below
marginal costs on one side of the market while charging a price above marginal costs on the other.
Lastly, a number of behaviors that were traditionally considered to be anti-competitive, do not follow
the same rationales in two-sided markets. An example is predation which is usually defined as pricing
below marginal costs. Nevertheless, in two-sided markets, in can be a profit-maximizing strategy to
price below marginal costs on one side of the market. Also tying and bundling strategies have been
close to a per se prohibition as they were seen as foreclosure strategies. How the assessment of tying
and bundling changes in a two-sided market context will be discussed in the following section.
2.3
Tying and Bundling in Two-Sided Markets
As explained in section 2.1.2, tying and bundling have traditionally been seen as anti-competitive
practices and mainly as predation. The main argument is that tying and bundling are usually not a
profit-maximizing strategy but adopted in order to drive competitors out of the market or foreclose
potential entrants. For potentially higher future profits, the tying firm would even sacrifice short-term
profits.
These arguments do not necessarily hold in two-sided markets characterized by indirect network externalities. Tying is not necessarily predation but can be a profit-maximizing strategy and pure bundling
can dominate mixed bundling in certain instances. The existing literature shows circumstances in a
two-sided market context in which tying is actually a profit-maximizing strategy rather than a strategy
to drive competitors out of the market. This result is due to the indirect network externalities. Thus,
giving for example an implicit subsidy to one side of the market in the form of a tie increases not
only participation on that side but also on the other side of the market. Consequently, tying might be
profit enhancing and even welfare increasing in a two-sided market context. These results in turn have
important policy implications. Competition authorities should start assessing whether the market is
one-sided or two-sided when considering tying and bundling cases. In case the tying or bundling takes
place in a two-sided market context, it should be assessed whether tying is a profit-maximizing strategy
and what the effects on total welfare and consumer surplus are.
In this section, I first review the literature on tying and bundling in a two-sided market context (section
2.3.1) and secondly, look at aspects determining whether bundling or tying is a profit-maximizing
strategy and what the likely implications on total welfare and consumer welfare are (section 2.3.2).
Lastly, I analyze the implications for the assessment of bundling and tying in antitrust cases (section
2.3.3).
15
2.3.1
Review of the Literature
There are numerous theoretical and a few empirical papers discussing tying and bundling in two-sided
markets. I will briefly discuss these in turn.
Tirole (2005) analyzes the factors influencing the impact of tying on rivals and consumers and argues
that tying should not be seen as a separate offense but should be considered as one possible form of
predation. He argues that the assessment of tying should follow a three step procedure. In the first
step one has to find out whether tying is likely to reduce competition in the tied market. If this is true,
one should assess in the second step whether consumers are likely to be hurt. If this is also the case, the
third step should try to find appropriate remedies. While Tirole’s paper is not specifically concerned
with tying in two-sided markets, the author mentions two-sidedness as one aspect influencing the effect
of tying on competition.
Tirole (2005) argues that in two-sided markets, tying may take place on one side of the market but not
on the other. An example are payment systems such as Visa or American Express where merchants
are forced to accept all cards issued by the system (e.g. credit and debit cards) but where no tie is
imposed on the consumer side (e.g. it is possible to own a debit card without owning a credit card
and vice versa). In this setting, competitors might have a higher ability to withstand the tie. Even if
they are unable to differentiate their product on the side of the market where the tying takes place,
they might be able to sign exclusive deals or successfully differentiate themselves on the other side
of the market. Since consumers on the tying side of the market care about consumers on the other
side, they might be induced to purchase both the tied product and the one from competitors, thus to
multi-home, even though they do not consider the products to be differentiated apart from the network
effect. Consequently, if the cost of multi-homing on the tying side of the market is relatively small,
tying might not be able to preclude competitors.
Li (2009) considers pure bundling16 of independent goods17 in two-sided markets. While in one-sided
markets pure bundling leads to losses both for the bundling as well as the rival firm and will thus
only be adopted if it helps to drive the rival out of the market, these results do not necessarily hold
in a two-sided market context. Li (2009) adopts a model in which bundling a magazine and a CD can
be a profit-maximizing strategy for a platform competing with another one on the magazine market
but being a monopolist on the CD market. Readers are assumed to single-home and are indifferent to
the size of advertisements. Advertisers are allowed to multi-home and their valuation of the magazine
increases with the number of readers. The magazine market is assumed to be covered so that every
consumer buys one of the magazines. The CD market is not assumed to be covered.
Li finds that in this model bundling the magazine and the CD can be a profit-maximizing strategy for
the platform. If the positive externality that readers exert on advertisers is large, prices are strategic
substitutes. This means that the competing platform reacts to the more aggressive pricing behavior of
the bundling platform by increasing its magazine price in order to limit its losses per reader. In this
setting, the bundling platform may benefit from selling the CD and the magazine as a package. While
losses on the CD market are inevitable, these may be offset by gains in the magazine market: the higher
price of the competing platform attracts more readers to the bundling platform and consequently more
advertising revenues.
16 While Li (2009) speaks of tying in the model, what is actually analyzed is pure bundling as has been discussed in
section 2.1.1.
17 Li (2009) analyses tying of a magazine with a CD.
16
In the model, the decision of whether to bundle or not is purely driven by profit maximization as
fixed costs are assumed to be zero and thus competitors cannot be driven out of the market. Hence, a
platform will only adopt a bundling strategy if it is profitable to do so. This crucially depends on the
magnitude of the network externality which can turn prices into strategic substitutes. Further, pure
bundling can actually be welfare enhancing: Bundling leads to a more asymmetric market structure
which is preferred due to the network effect. This positive effect can potentially offset the negative
welfare effects caused by the bundle.
Similarly to Li (2009), also Amelio and Jullien (2007) investigate the effects of tying and bundling of
independent goods in two-sided markets. Differently from Li’s (2009) model though, Amelio and Jullien
(2007) assume that both indirect network externalities are positive and that both groups of consumers
single-home. They analyze the rationale for tying and bundling in the monopoly and duopoly context
when platforms are constrained to set non-negative prices. The paper illustrates second-degree price
discrimination implemented through tying.
As in two-sided markets there is a need to coordinate consumers on an efficient allocation, some
consumers might need to be subsidized. If platforms are constrained to set non-negative prices, tying
and bundling the sales of another good with the access to the platform can be a strategy to implicitly
relax the non-negativity constraint.
In the monopoly context, tying is a way to achieve negative prices implicitly on the low externality
side of the market by offering discounts. The platform can sell another good18 that can be bundled
to the service of the platform. Further, only consumers on side 119 value this good. In this model the
platform is found to prefer tying to no bundling. This is due to the fact that tying allows subsidizing
participation to the platform while avoiding selling the good to non-interested consumers. If consumers
all have the same valuation of the good, the only effect of tying is to relax the non-negativity constraint
without additional costs. Participation will be higher on both sides than under no bundling, consumer
surplus as well as profits increase relative to the no bundling case.
In the duopoly case analyzed by Amelio and Jullien (2007), one platform (A) can tie a good to the
platform service on side 1, this again relaxes the non-negativity constraint, while the other platform
(B) is constraint and thus sets the price for the service equal to zero. The market is assumed to be
covered.
There are two effects of the de facto negative subscription price to the platform under tying: Firstly,
demand on side 1 shifts towards platform A which also makes platform A more attractive to side 220
(demand shifting effect). Secondly, A now incurs higher losses per customer on side 1 than under a zero
price. Thus, it has less to gain by cutting prices on side 2 and raising demand. Consequently, platform
A tends to set higher prices on side 2 (competition softening effect). While the demand shifting effect
is detrimental for platform B, the competition softening effect is beneficial. The combination of these
two effects determines the optimal pricing strategy on side 2. The impact of tying on platforms’ profits
depends on the relative levels of externalities on side 1 and 2.
The consumer surplus under tying of platform A is found always to be higher on side 1. The effect
on side 2 is ambiguous. The demand shift on side 1 towards platform A raises the perceived quality
of platform A but reduces the one of platform B, the overall effect is thus ambiguous. Further, the
18 The
platform is not necessarily a monopolist in this market. The tied good market could also be competitive.
side 1 to be the side where the tying takes place.
20 So side 2 is the side of the market where no tying takes place.
19 Consider
17
competition softening effect implies higher prices on side 2. The overall effect on consumer surplus
depends on the degree of asymmetry. Total consumer surplus increases in case of high asymmetry in
the network externalities between side 1 and 2. In case of symmetric network externalities, profits
increase for both platforms under tying of A while total consumer surplus as well as total welfare
decrease. In case of no network externality on side 1, consumer surplus increases under tying. If the
network externality on side 2 is large, then profits of A and total welfare increase, if it is small, B’s
profit increases while total welfare decreases.
Choi (2010) also reaches the conclusion that tying can be a profit-maximizing strategy in two-sided
markets. Contrary to Li (2009) and Amelio and Jullien (2007) he analyses tying21 of complementary
rather than independent goods in two-sided markets and its effects on competition and social welfare.
Furthermore, he allows consumers on both sides of the market to multi-home, which also differs from
both Li (2009) and Amelio and Jullien (2007). The paper is motivated by the antitrust cases concerning
Microsoft and its practice of tying the Windows operating system with WMP (see section 3 for the
Microsoft EU case discussion).
Choi’s model contains three types of agents. There are two groups of consumers on each side of the
market: content providers and final consumers. Both groups are allowed to multi-home22 , that is,
content providers offer content in more than one format and final consumers have more than one
media player. Two intermediaries, A and B, provide platforms to make these two consumer groups
meet and they compete in market shares for both groups. The market is characterized by positive
indirect network effects on both sides of the market, which is different from Li (2009), where there
is one positive and one zero network externality. Consumers only have an incentive to multi-home
if there is different content across platforms. Thus, content providers deliver two types of content:
either exclusive content for platform A or B respectively or non-exclusive content which is available
on both platforms.23 The existence of exclusive content on each platform A and B creates incentives
for consumers to multi-home.
In the case of tying, Choi (2010) assumes that platform A is also a monopolist in the related market
for the product M which is essential for participating in the two-sided market. If A bundles the two
products and sets its price so that every consumer will purchase the bundle, every consumer has access
to the content on platform A. Thus, there no longer is an incentive for non-exclusive content providers
to provide this content also to platform B. Multi-homing on the consumer side then only takes place if
there is exclusive content available on platform B. In equilibrium the number of consumers who multihome and thus have access to the exclusive content of platform B increases relative to the no-tying
equilibrium. Given that A sets its price of the bundle so that every consumer will purchase the bundle,
platform A’s profits increase while platform B’s profits decrease under tying.
In this model, Choi finds that total welfare increases under tying compared to the no tying case. Tying
leads all consumers to have access to exclusive and non-exclusive content on platform A and more
consumers to have access to exclusive content on platform B than under no tying. The fact that more
consumers multi-home makes platform-specific content available to more consumers. This in turn is
beneficial for content providers. Further, Choi concludes that tying reduces consumer welfare.24 The
21 As has been discussed in section 2.1.1, the author actually analyses pure bundling rather than tying but since the
goods are complements, the distinction is irrelevant following Tirole (2005).
22 But they can choose to single-home.
23 Note that the amount of exclusive and non-exclusive content is exogenously given in the model and does not change
following the tie.
24 However, he considers consumer welfare to be the welfare of consumers only. While Choi (2010) includes both
18
fact that product M is necessary to participate in the two-sided market makes it easy for the monopolist
to extract all consumer surplus from multi-homing consumers. As more consumers multi-home under
tying, consumer surplus decreases and only single-homing consumers receive positive surplus.
Even though Chao and Derdenger (2010) also consider complementary products, they investigate
mixed bundling, rather than tying or pure bundling as in Li (2009) and Choi (2010), in the two-sided
market of portable video games and consoles where the console is a monopolist. Similarly to Amelio
and Jullien (2007) and Choi (2010), the market is characterized by two positive network externalities.
In the portable video game console market a bundle consists of selling a game and a console together
for a single price. There are two different types of video game developers in the market. First-party
games are produced by the console’s own in house design studio. Third-party games on the contrary
are games produced by independent firms which are not associated with the producing console. Thus,
the console can sell both portable consoles and first-party video games independently as well as bundles
of a portable console and a first-party game.
The existence of third-party game developers makes this market two-sided. In the absence of thirdparty games, the monopolist would just sell perfect complements (the console and the first-party game)
and the market would be one-sided. Once third-party games are introduced, the console and the firstparty game are still complements but no longer perfect complements. Consumers now have the option
to purchase the console without the first-party game from the monopolist and then buy compatible
third-party games. Hence, this market can be considered a two-sided market as consumers and game
developers interact with each other through the intermediary console. That is, indirect network effects
emerge since the number of third-party games available for a given console depends on the number of
console owners and vice versa.
This implies three classes of players within the console market: the console (platform), consumers and
game developers. There are two groups of consumers whose total size is normalized to one. Group 1 is
the installed base, which is a pre-existing group who already purchased the console from the platform
but has yet to purchase the first-party game. Group 2 consumers have yet to purchase the platform’s
console. Consumers pay a fixed fee for the console and a fixed fee for a video game. Game developers
pay the console a royalty rate for the rights to the code which is necessary to make the game compatible
with the console. This fee is not a fixed one-time fee but the developer has to pay a royalty rate for
each copy of the game bought by a consumer.
The theoretical model developed in the paper shows that it is a dominant strategy for a monopolistic
two-sided platform to offer a mixed bundle of console and video game rather than a pure bundle or
no bundle. Under mixed bundling, both the standalone console price on the consumer side as well as
the royalty rate on the game developer side decrease compared to a no bundling equilibrium. Mixed
bundling acts as a price discrimination tool used to segment the market more efficiently. The standalone
price of the first-party game is specifically targeted at the installed base and will consequently be set
equal to the reservation value of the installed base. It is important to note that if the installed base
was to be removed from the model, there would be no need for the bundle.
When analyzing the welfare effects of mixed bundling compared to independent pricing, Chao and
Derdenger (2010) find that the effects differ depending on whether the royalty rate charged to thirdparty game developers is endogenously or exogenously determined. Under exogenously determined
consumers as well as content providers in the calculation of total welfare, he does not include content providers in
the computation of consumer surplus. Nevertheless, both consumers as well as content providers are consumers of the
two-sided platform and should hence be accounted for in consumer welfare.
19
royalty rates, total surplus under mixed bundling is higher than under independent pricing if and
only if there is more participation on both sides in equilibrium. Under endogenously determined
royalty rates, total surplus is higher under mixed bundling than under independent pricing. While all
consumer surplus from the installed base is extracted, this is only a transfer to the platform. However,
new gamers are strictly better off under mixed bundling since all prices are lower and more third-party
game developers join the platform. Further, also the profits of the platform are higher under mixed
bundling as the decreases in marginal revenue from the decline in console price and royalty rate are
more than offset by the increases in consumers’ and game developers’ demand.
Derdenger’s (2010) empirical paper fits the theoretical paper by Chao and Derdenger (2010) and
analyses technological tying25 in the video game industry and its effects on console prices and consumer
surplus. The paper concludes, in line with Chao and Derdenger (2010), that technological tying
increases console price competition, i.e. console prices decrease under tying (or rather increase under
untying). This is due to console producers subsidizing consumers in order to increase video game sales
(and particularly of their tied games) where the greatest part of profits is made in the video game
industry. Hence, console makers’ profits increase under technological tying.
According to Derdenger (2010), there are two effects at play in technological tying. Firstly, in order to
play a first-party game, a consumer first has to purchase the respective game console, which increases
the console manufacturer’s market power. This effect gives an incentive to raise prices due to the
relative increase in utility given that rival consoles have fewer available games under technological
tying. Secondly, integration leads to a further profit stream for the firm from designing, producing
and selling its own video game. Thus, integration generates incentives for console manufacturers to
lower the console price because lower prices lead to increased demand for consoles which leads to
greater demand for video games. Hence, there is a trade-off between higher hardware and software
profits. Derdenger (2010) concludes that the second effects dominates where tying actually leads to
lower console prices and increases new console owner welfare.
The paper assumes a nested logit model for console demand as well as a multinomial logit model for
video game demand to account for differentiated video games. Console and video game demand are
linked since at the stage where a consumer decides to buy a console, she takes into account the expected
maximum utility generated from the set of available video games. This is the indirect network effect.
It is the expectation of software utility which is equal to the expected maximum utility from choosing
from a set of available and compatible video games for console j at time t. Console, first-party and
third-party video game supply is determined by maximizing profits with respect to prices. Console
manufacturers as well as third-party game developers take into account the effect of video game prices
on console demand when determining their prices.
Console and video game demand and supply models are jointly estimated with simulated methods
of moments using quantity and revenue data from the 128-bit video industry26 in the US between
2002 and 2004 as well as consumer level demographic and ownership data of consoles in 2005. Prices
are considered as endogenous27 and are instrumented for with proxies for marginal costs.28 Also, the
25 Technological
tying means that a console manufacturer produces software which is incompatible with rivals’ hardware.
GameCube, Sony PlayStation 2 and Microsoft Xbox and all their compatible video games.
27 Prices are endogenous because the error term contains unobserved product characteristics. These unobserved product
characteristics might then be correlated with prices.
28 For console price, the instrument used is the one month lag of the Japanese to US exchange rate, since most consoles
are produced in Japan according to the author, and a one month lag of the producer price index for computers. For
video games, the software producer price index is used as an instrument.
26 Nintendo
20
predicted mark-up and predicted market share are used as supply-side instruments for mark-up and
market share, as consoles or games with higher unobserved quality might be more costly to produce.
Derdenger (2010) considers two counterfactuals in order to compare technological tying of first-party
games to the console with a situation where no tying occurs. The first counterfactual considers what
happens if all first-party games are eliminated. The second counterfactual investigates forced compatibility. This means that all produced first-party games need to be compatible with each console. In
this counterfactual, the console’s profit function changes: the console can make additional profits buy
selling its first-party game for use on competing consoles but has to pay royalty fees for each game sold
on a competing console and incurs a fixed cost of five hundred thousand dollars to port each game to
a competing console. Thus, when the console firm is forced to untie, it additionally needs to consider
the effect of sales of video games on competing consoles in its profit maximization problem.
Chen (2009) reaches a conclusion contradicting the results of Chao and Derdenger (2010) even though
both analyze a monopolistic platform. While Chao and Derdenger (2010) find that in their model
mixed bundling dominates pure bundling and no bundling, Chen (2009) concludes in his model of
bundling and à-la-carte regulation in the TV industry that, while mixed bundling is a weakly dominated
strategy for a monopolist in a one-sided market, in a two-sided market setting pure bundling can strictly
dominate mixed bundling for the monopolist. One of the relevant differences between the two models is
that Chen (2009) assumes viewers dislike advertising. Hence, contrary to Chao and Derdenger’s (2010)
model, Chen’s model is characterized by one positive and one negative indirect network externality.
His result that pure bundling can be the monopolist’s profit-maximizing strategy is then due to the
fact that pure bundling can lead to less advertising and hence higher consumer utility. The impact
of advertising on consumer utility is also important for the assessment of à-la-carte regulation. While
in a one-sided market an à-la-carte regulation benefits consumers, it might actually harm them in a
two-sided context because advertising increases.
The paper examines the TV industry. According to Chen (2009), the TV industry is a two-sided market
where operators try to attract both viewers and advertisers.29 The higher the number of viewers, the
more attractive the network is to advertisers. As mentioned before, the paper further assumes that on
the other hand advertisements impose a negative externality on viewers.
The model used in the paper contains four types of agents: viewers, a monopolist downstream cable
operator, two competing upstream TV networks and advertisers. The TV networks sell their programs
to the cable operator by charging a license fee and their advertising slots to advertisers. The monopolist
cable operator buys the TV programs from the stations and sells them to viewers. Absent à-la-carte
regulation, the cable operator can choose to offer each channel separately (no bundling), each channel
separately as well as a bundle of the two (mixed bundling) or only the bundle of the two channels (pure
bundling). There are three types of viewers: Those who only demand one of the two channels a or b
(called single demand viewers) and those demanding both channels (called multiple demand viewers).
29 I include the two theoretical papers investigating bundling in the TV industry by Chen (2009) and Adilov (2011) in
this section in order to give a complete overview of the theoretical literature on tying and bundling in two-sided markets.
Nevertheless, I will not discuss the empirical literature of the TV industry here. The reason is that the business model
of the TV industry is particular and does not fit the Microsoft EU case I will analyze in the following. The TV business
model involves not only a TV channel as a platform and viewers and advertisers as the two sides of the market, but
program networks and cable operators who negotiate the license fee the program network obtains from the cable operator
for each subscriber as well as the number of advertising minutes the cable operator retains. It is not even clear whether
this industry structure actually fits a two-sided market model. Chen (2009) and Adilov (2011) consider the cable TV
industry to be a two-sided market though. I refer the reader interested in empirical papers analyzing bundling and
à-la-carte pricing in the TV industry to Byzalov (2008), Crawford (2008), Crawford and Cullen (2007), Crawford and
Yurukoglu (2010), Rennhoff and Serfes (2008) and Yurukoglu (2008).
21
In a one-sided model (that is with no advertising) mixed bundling is the optimal pricing strategy: it
allows the monopolist to price discriminate. Multiple demand viewers pay a lower per-channel price
than single demand viewers. In contrast, in the two-sided model described above, the author finds two
types of equilibria: one pure bundling equilibrium and one mixed bundling equilibrium. For relatively
low values of the maximum willingness to pay of multiple demand viewers, the monopolistic cable
operator offers a pure bundle while for higher values of the maximum willingness to pay of multiple
demand viewers, it is more profitable to offer a mixed bundle. Thus, contrary to the one-sided model,
pure bundling can strictly dominate mixed bundling in the two-sided context.
The model shows that the inverse demand curves for advertisements on the TV channels are steeper
under pure bundling than under mixed bundling, which implies higher advertising fees and less advertising under pure bundling than under mixed bundling. The author calls this the slope effect resulting
from a change from mixed bundling to pure bundling but forcing the inverse demand curves to pass
through the equilibrium under mixed bundling.
The second effect is the location effect which allows the location of the equilibrium to adjust when
switching from mixed to pure bundling. The slope effect shows that there will be less advertising on
both channels as the monopolist switches from mixed to pure bundling. Less advertising on a rival
channel increases viewer utility and thus demand. Consequently, the monopolist will increase the
subscription fee. However, given the constraint of only being able to offer one bundle to all types of
viewers, the price increase will not completely offset the advertising benefit. This leads to an increase in
the demand from multiple demand viewers leading in turn to an increase in the demand for advertising.
This effect shifts the inverse advertising demand curve out implying higher advertising fees and higher
levels of advertising. In the model, the slope effect dominates the location effect under pure bundling.
Thus there is less advertising in equilibrium under pure bundling than under mixed bundling.
Consumer surplus is lower under mixed bundling than under pure bundling. There are two reasons for
this. Firstly, as stated above, mixed bundling allows the monopolist to price discriminate and extract
more consumer surplus than pure bundling. Secondly, there are fewer advertisements under pure
bundling than under mixed bundling which further increases consumer surplus under pure bundling.
Nevertheless, it seems that Chen (2009) only considers surplus of viewers in consumer surplus and
neglects the effects of mixed and pure bundling on advertisers’ surplus.
Further, Chen (2009) finds that while imposing à-la-carte pricing regulation increases consumer welfare
when replacing mixed bundling, it might actually harm consumers when replacing pure bundling. This
is because advertisement levels are higher under à-la-carte pricing than under pure bundling which
makes viewers worse off. However, the monopolist will react by decreasing subscription fees. Which
effect dominates is unclear.
Adilov (2011) also develops a theoretical model of product bundling in the cable TV industry in order to
investigate whether consumers would profit from unbundling. Differently from Chen (2009), he includes
endogenous quality choice in his model but looks only at à-la-carte pricing versus pure bundling, while
Chen (2009) also analyzes mixed bundling. Adilov (2011) considers thus not only differences in price
between bundled channels and à-la-carte but also differences in quality of the programming that might
arise from unbundling.
He finds that the average price of a product might not be a reliable indicator of consumer surplus if
higher prices correspond to higher product quality. This implies in turn that à-la-carte pricing could
reduce consumer surplus even if the average price decreases. He finds in his model that bundling
22
increases consumer surplus and product quality even when it raises the average price per channel.
Further, heavy reliance on advertising revenues decreases programming prices but it also leads to less
investment in product quality and could thus make consumers worse off. In the model both a cable
operator’s and a program network’s profits decrease under unbundling.
The model includes three goods: Product 1, Product 2 and an Outside Good M. Consumer utility
of purchasing Product 1 or Product 2 is a function of the consumer’s preferences and the quality of
the product. Marginal costs of selling a product to an additional consumer are zero. There are fixed
costs related to the quality of the product produced. The quality of a product is a function of the
investment in quality. Extra investment in quality increases the quality of a product at a decreasing
rate.
Firstly, Adilov (2011) compares à-la-carte pricing of the two goods to a bundle of Products 1 and
2 without taking into account advertising. Thus, the monopolist maximizes profits by setting the
optimal prices for Product 1 and 2 (the bundle of both) under à-la-carte pricing (under bundling) as
well as the optimal investment in quality of Product 1 and 2. When solving the profit maximization
problem of the firm, Adilov (2011) finds that product quality is higher under bundling than under
à-la-carte pricing. This is due to the fact that under à-la-carte pricing, the quality of one product is
independent of the quality of the other product. Under bundling, the quality levels of the products
are complements where the firm’s marginal benefit form increasing the quality of one product is higher
when the quality of the other product is higher. The per product price can be either higher or lower
under à-la-carte pricing. When the marginal benefit of quality improvement is high (that is the quality
of the product improves relatively much by additional investment in quality), the firm increases the
quality of the products under bundling and increases the price of its products. However, if the marginal
benefit of quality improvement is low, even though the quality of the products is still increased under
bundling, the average price of the products decreases. Since both price and quality change under
à-la-carte pricing, Adilov (2011) compares price-adjusted quality (investment in quality divided by
price of a product) between bundling and à-la-carte pricing and finds that price-adjusted quality is
higher under bundling. He further finds that the firm’s profits, consumer surplus and total welfare are
higher under bundling than under à-la-carte. Thus, an à-la-carte regulation would hurt both consumers
and producers. Even if the price per product decreases under à-la-carte, consumer surplus decreases
because the price-adjusted quality level is lower.
Secondly, Adilov (2011) extends the model to also include advertising revenues in the firm’s maximization problem. He assumes that advertising revenues depend on the number of products sold. While
the profit formula thus includes that advertising revenues depend on the quantity of the product sold
(that is the number of subscriptions), it does not incorporate that in turn the number of products
sold might depend on the advertising level. Adilov (2011) does also not use any two-sided terminology. Hence, the model does not seem to fully incorporate the two-sided nature of the TV industry
and will only be correct if viewers are indifferent to advertising. In comparison, Chen (2009) assumes
that viewers dislike advertising. Once again, the firm maximizes profits by setting the optimal prices
for the products separately or the bundle under respectively à-la-carte and pure bundling as well as
the optimal investment in quality of Product 1 and 2 taking into account the effects on advertising
revenues. Adilov runs simulations to investigate the effects of advertising. He finds that prices under
both regimes decrease when the advertising revenue parameter increases. This is because the firm has
stronger incentives to cut prices and attract more viewers when a larger share of the revenues is derived
from advertising. When the advertising revenue parameter is large enough, the optimal price decreases
23
to zero and all revenues are derived from selling advertising. However, the price approaches zero under
à-la-carte pricing first because under bundling, the firm can extract more consumer surplus and is less
likely to give up sales revenues to attract consumers by decreasing prices. Again, per product prices
can be higher or lower under à-la-carte pricing compared to bundling. Product quality decreases under
both à-la-carte and bundling as the advertising revenue parameter increases. When larger portions of
the firm’s profits are derived from advertising, it has less incentive to invest in quality and to increase
its sales revenues. It is more profitable for the firm to reduce the price to attract viewers. Product
quality reaches zero faster under à-la-carte pricing than under bundling. This is again due to the fact
that under bundling, the firm can extract more consumer surplus and is less likely to give up sales
revenues. Consumer surplus is still higher under bundling than under à-la-carte pricing. As prices drop
to zero under both regimes, consumer surplus decreases sharply. Thus, consumers do not necessarily
benefit from lower prices because product quality is low as well. Note however, that Adilov (2011),
similarly to Chen (2009), seems to only consider viewers in the computation of consumer surplus and
neglects advertisers.
Lastly, Adilov (2011) incorporates bargaining between a cable operator and a program network into the
model. The cable operator buys programs from the program network and resells them to consumers.
Adilov models a three-stage game where in the first stage the program network chooses the quality
levels of its programs to maximize its expected profits. In the second stage, the program network and
the cable operator negotiate the transfer payment the cable operator pays to the program network as
well as the share of the advertising revenues which is kept by the cable operator. In the third stage, the
cable operator chooses the prices (for the two products separately under à-la-carte or the bundle price
under bundling) that maximize its profits. Adilov simulates the model setting the share of advertising
revenues kept by the cable operator to 15%30 . He finds once again that program quality as well as
consumer surplus are higher under bundling. As before, the average product price can be higher or
lower under à-la-carte pricing. Both the cable operator’s as well as the program network’s profits are
higher under bundling.
Concluding, the paper shows how product quality can be affected by bundling. It concludes that
even when product prices are reduced under à-la-carte pricing, consumer surplus does not necessarily
increase as product quality decreases. Bundling increases consumer surplus even when the average
product price increases relative to à-la-carte pricing. This is due to increased product quality. The
main results are robust to adding advertising revenues to the model. However, product quality and
prices fall under both regimes when the firm relies more on advertising revenues.
Rochet and Tirole (2008) investigate the effects of tying in the two-sided market of payment cards.
Under the HAC rule, merchants accepting credit cards offered by a card network need to also accept
the debit cards offered by the same network, which corresponds to tying credit and debit card on the
merchant side. However, the market for payment cards is different from the markets considered in the
other papers discussed so far, as it is a four-party system. There are the two types of agents on the
two sides of the market: the cardholders (buyers) and the merchants (sellers). Furthermore, there is
not simply one platform but the payment service is provided jointly by the issuer (customer’s bank)
and the acquirer (merchant’s bank). These banks are members of a not-for-profit association run by
their members. Rochet and Tirole’s model assumes competition between two networks, one offering
only a debit card, the other offering both a debit and a credit card.
30 Adilov (2011) states that according to the Federal Communications Commission, the cable operator collects about
2 minutes of advertising time revenues out of 12 to 14 minutes available advertising time slots per hour.
24
The assumption that the associations are not-for-profit implies that the associations can only adjust
the price structure across the two sides of the market but not the price level. This also means that
networks do not want to maximize profits but aim at maximizing network volume. This fact as well
as the four-party system make this model different from the other models considered so far.
In the simplest version of the model, there are two independent markets, one for “credit” goods and one
for “debit” goods and substitution between credit and debit cards is not possible. Further, total demand
for final goods is assumed to be inelastic so that the total number of debit and credit transactions is
fixed.
Under these assumptions, the authors find that in a payment card market with competition, tying
the credit and the debit card (thus imposing the HAC rule) improves total welfare. This is because
under the HAC rule, the network has more freedom as it can choose a combination of debit and credit
cardholder fees maximizing its members’ total profit subject only to the constraint that the total user
surplus provided by the two cards is bigger than the one provided by the debit card of the competing
network alone. The rebalancing of the interchange fee31 structure across the credit and debit card
leads to an increase in total user surplus and total volume (and thus total welfare) relative to the no
HAC case.
Concluding, the HAC rule can be beneficial. In the absence of tying, the platform needs to get the
merchants “on board” who have attractive bypassing opportunities. This is to the detriment of the
other side (cardholders). The tie allows a platform to rebalance its rates: rates go up for the good
facing the most intense competitive pressure (here the debit card) while they go done for the other
(credit card).
Lastly, Gao (2009) investigates bundling in so-called mixed two-sided markets. He defines mixed
two-sided markets as two-sided markets where the consumer can appear on both sides of the market;
specifically she can be a buyer and a seller where each agent’s surplus from using either service increases
with the number of agents on the other side of the market. Examples of mixed two-sided markets
include telecommunications networks, stock exchanges or online auctioning platforms such as Ebay.
Gao (2009) argues further that since some consumers want to use the services the platform provides
on both sides, the platform can use multi-product pricing strategies that are irrelevant in standard
two-sided markets. Particularly, it can bundle its selling and buying services and provide them to
all potential users. Thus, this paper studies a new kind of bundling, which Gao (2009) calls “hybrid
bundling”. It consist of two parts: firstly, a bundled membership fee which gives access to both selling
and buying services and secondly, two separate transaction fees which apply to the two parties involved
in a transaction. Under hybrid bundling, every user can make multiple transactions on either side of
the market. Since the paper’s setting is different from the other theoretical papers discussed so far,
the results are not comparable.
The model adopted by Gao (2009) is characterized by one monopoly platform and a continuum of
agents. Agents can trade a certain good only by using the buying and selling services of the platform.
Seller-buyers are of special importance to the platform in a mixed two-sided market. Firstly because
they act as both sellers and buyers and thus bring in double revenues and secondly, because they are
potentially more cost-effective as the model allows for scope economies in the fixed costs of serving
users. Gao (2009) defines the degree of mixedness of the mixed two-sided market as the proportion of
31 Rochet
and Tirole (2008) define the interchange fee as “the payment made by the merchant’s bank (the acquirer) to
the cardholder’s bank (the issuer)” (p.1334).
25
seller-buyers among all users. This degree of mixedness is strictly increasing in the bundled membership
fee if there exists a positive number of seller-buyers and the market is not fully mixed.
Gao (2009) derives conditions under which hybrid bundling dominates unbundled sales. Firstly, raising
the bundled membership fee will generally save costs for the platform as seller-buyers are potentially
more cost-effective. However, this effect only exists if there are economies of scope in the fixed costs
of serving users. Secondly, increasing the membership fee has three first-order effects on revenues. It
decreases the number of users paying membership fees, it thus reduces the total volume of transactions
between sellers and buyers leading to less total transaction fees paid and it increases membership
revenues per user due to the higher membership fee. The overall impact of hybrid bundling on revenues
can be positive or negative depending on the distribution of valuations (determining how many users
drop out).
If the valuations of buying and selling are independent, Gao (2009) finds that hybrid bundling strictly
dominates unbundled sales. Negatively correlated valuations also tend to favor hybrid bundling under
certain conditions. In the case of positively correlated valuations however, it cannot be concluded for
all kinds of distributions what the net impact of hybrid bundling on profits will be. This is due to the
fact that unbundled sales already do well in capturing people with high valuations for both services.
However, the cost saving effect of hybrid bundling is always present regardless of the correlation
between valuations.
After having discussed the literature on tying and bundling in two-sided markets, I discuss the factors
coming out of the literature that determine the likely welfare effects of tying and bundling in two-sided
markets in the next section.
2.3.2
Factors Determining Likely Effects
There are two common points emerging from the theoretical literature. Firstly, tying and bundling
in a two-sided market context can actually be profit-maximizing strategies for a player. This means
tying and bundling are adopted to maximize profits and not in order to drive competitors out of the
market. Secondly, these strategies might actually be welfare enhancing. In that case, one still needs
to look at whether this increase in welfare is driven by an increase in profits or whether also consumer
surplus rises. If consumer surplus does not increase, the optimal treatment of tying and bundling in
these markets depends on whether the competition authority has adopted a total welfare or a consumer
surplus standard.
All theoretical papers considered in section 2.3.1 as well as the empirical paper by Derdenger (2010)
have found that tying and bundling can be profit-maximizing strategies in a two-sided market context.
The question is now which factors influence whether tying and bundling are profit-maximizing strategies
and when they are welfare enhancing or less likely to hurt consumers.
One important factor is the magnitude of the indirect network externalities in the two-sided market.
In general, one can say, the larger the network externalities across sides, the more likely it is that
tying or bundling will actually benefit consumers. For example, Chao and Derdenger (2010) conclude
that in their model of mixed bundling between a game console and a video game, the change in total
surplus depends on the welfare impact of mixed bundling on new gamers. This impact is ambiguous
depending on whether the standalone price of the console changes, the number of game developers on
the platform and the magnitude of the indirect network effects. Also Li (2009) finds that if network
26
externalities are large, pure bundling is likely to benefit consumers as it leads to a more asymmetric
market structure. This asymmetric market structure is welfare enhancing due to the indirect network
externalities.
Another important factor is the symmetry between network externalities of the two sides of the market.
Amelio and Jullien (2007) find that tying is a way to relax the non-negativity constraint. When
the monopolistic platform is constraint to set non-negative prices, tying allows subsidizing the low
externality side of the market. This directly boosts participation on that side of the market. However,
there is also an indirect effect of this subsidy: increased participation on the low externality side
will also increase participation on the high externality side of the market due to the indirect network
effects. The magnitude of the effect is further increased by a multiplier effect. Profits and consumer
surplus unambiguously increase compared to independent pricing. In duopoly, the welfare effects of
tying depend on the degree of symmetry between network externalities. In case of symmetric network
externalities, profits increase for both platforms under tying of one platform while total consumer
surplus as well as total welfare decrease. In case of no network externality on side 132 , consumer
surplus increases under tying. If the network externality on side 233 is large, then profits of the
tying platform and total welfare increase, if it is small, the competing platform’s profit increases while
total welfare decreases. So the more asymmetric the network externalities, the more likely it is that
subsidizing the low externality side of the market will benefit consumers on both sides.
Another important aspect when analyzing the effects of tying and bundling in two-sided markets is
whether consumers single-home or multi-home. Tirole (2005) concludes that if the costs of multihoming on the tying side of the market are relatively small, tying might not be able to preclude
competitors. The tie will simply lead more consumers on the tying side of the market to multi-home.
Also Choi (2010) finds that in a model where multi-homing is possible on both sides of the market,
tying is a profit-maximizing strategy. Thus, it is not adopted to drive the competitor out of the market
though it is true that the competitor’s profits decrease. However, he finds that while content providers
(that is one side of the market) profit from the tie, the other side (consumers), where the tying takes
place, loose from the tie. The fact that more consumers multi-home under tying makes platformspecific content available to more consumers. This in turn is beneficial for content providers. On the
consumer side, the fact that the tying good is necessary to participate in the two-sided market makes
it easy for the monopolist to extract all consumer surplus from multi-homing consumers. As more
consumers multi-home under tying, consumer surplus decreases and only single-homing consumers
receive a positive surplus. Thus, Choi (2010) finds in his model that total welfare increases under
tying: Profits of the tying platform increase, profits of the competing platform decrease, consumers
loose. Thus, even if multi-homing takes place, the optimal policy will differ depending on whether
competition authorities adopt a total welfare or a consumer surplus standard. In the former case, as
tying with multi-homing increases welfare, tying should not be seen as anti-competitive. In the latter
case, as consumer surplus decreases, tying should be judged as anti-competitive behavior. However,
one has to notice that Choi (2010) considers only consumers when calculating the effects on consumer
surplus. However, content providers should also be regarded as consumers of the two-sided platform
and thus their surplus should be included in the computation of consumer surplus.34
32 I
consider side 1 to be the side where the tying takes place.
side 2 is the side of the market where no tying takes place.
34 As stated above, Choi (2010) argues that content providers benefit from the tying on the user side since more users
have access to platform specific content under tying. I argue, however, that the fact that content providers do not
multi-home in Choi’s model allows platforms to extract more content provider surplus. Choi (2010) however ignores
content provider surplus in his computations of consumer surplus.
33 So
27
Most theoretical papers summarized above analyze the case where the two-sided market is characterized
by two positive externalities. As has been discussed above, according to Amelio and Jullien (2007) the
degree of asymmetry between the two positive network externalities determines whether tying increases
or decreases welfare. The more asymmetric the network externalities are, the more likely total welfare
and consumer surplus will increase under tying where it is used to subsidize the low externality side.
Also Choi (2010) finds that with two positive network externalities total welfare increases. However,
in his model consumer surplus35 decreases under tying as it allows extracting all consumer surplus
from multi-homing consumers. Lastly, also Chao and Derdenger’s (2010) model is characterized by
two positive network externalities and they find that the effect on total welfare depends on whether
the royalty rate the platform charges to game developers is endogenously or exogenously determined.
Nevertheless, total welfare always increases if participation on both sides increases due to the tie.
Li’s (2009) model is characterized by only one positive network externality and he finds that tying is
welfare enhancing if network externalities are large. Also Amelio and Jullien (2007) state that if the
network externalities are zero on side 1 and positive on side 2, consumer surplus increases under tying
as participation on the side without externality is subsidized. Whether total welfare increases then
depends on the effect of tying on profits which itself depends positively on the magnitude of the network
externality on side 2. Lastly, also Adilov’s (2011) model is characterized by only one positive network
externality where advertisers care about viewers. Adilov (2011) finds that in his model, total welfare
as well as consumer surplus are higher under pure bundling than à-la-carte pricing. Nevertheless, he
does not include advertisers’ surplus in consumer surplus. Additionally, his result works via quality:
under pure bundling, there is less advertising which gives the platform incentives to invest in higher
quality which in turn increases viewer surplus.
Only the model by Chen (2009) includes one positive and one negative network externality where
viewers are annoyed by TV advertising. He considers no bundling, pure and mixed bundling equilibria
and concludes that consumer welfare is higher under no bundling than under mixed bundling. This
result is similar to Choi’s (2010) result since mixed bundling allows to price discriminate among viewers.
However, Chen (2009) also finds that pure bundling might increase consumer surplus compared to no
bundling and mixed bundling as in the model it leads to less advertising.
Lastly, one should notice that also Rochet and Tirole (2008) and Gao (2009) conclude that tying in
two-sided markets could be beneficial though their models are somewhat different. Rochet and Tirole
(2008) investigate the HAC rule in the payment card market. In their model in the absence of tying,
the platform needs to get the merchants “on board” who have attractive bypassing opportunities. This
is to the detriment of the other side (cardholders). The tie allows a platform to rebalance its rates:
rates go up for the good facing the most intense competitive pressure (here the debit card) while they
go down for the other (credit card). This is similar to Amelio and Jullien’s (2007) subsidy argument
and depends on the magnitude and asymmetry of the network externalities.
Gao (2009) considers what he calls “hybrid bundling” in a market where users can act on both sides
of the market, both as buyers and sellers for example. Hybrid bundling consists of two parts: firstly,
a bundled membership fee which gives access to both selling and buying services and secondly, two
separate transaction fees which apply to the two parties involved in a transaction. In his paper Gao
(2009) argues that the degree of mixedness, which he defines as the proportion of seller-buyers among
all users, is of primary importance. The higher the degree of mixedness of the two-sided markets, the
more profitable hybrid bundling is. Further, whether bundling dominates unbundled sales depends on
35 However,
as noted before, he disregards content providers in the computation of consumer surplus.
28
the correlation between valuations of buying and selling. If the valuations of buying and selling are
independent, Gao finds that hybrid bundling strictly dominates unbundled sales. Negatively correlated
valuations also tend to favor hybrid bundling under certain conditions. In the case of positively
correlated valuations however, it cannot be concluded for all kinds of distributions what the net impact
of hybrid bundling on profits will be.
After having analyzed the factors that determine the likely consequences of tying and bundling in
two-sided markets, I will discuss the implications for tying and bundling antitrust cases in two-sided
markets.
2.3.3
Implications for Tying and Bundling Antitrust Cases in Two-Sided Markets
The results of the literature on tying and bundling in two-sided markets lead to important policy
implications: While in one-sided markets, tying is generally not a profit-maximizing strategy and
will thus only be adopted by a firm if it helps to drive competitors out of the market, tying cannot
automatically be seen as anti-competitive behavior in a two-sided market context. The different
models discussed demonstrate that, if network externalities are large, tying and bundling might be
profit-maximizing strategies regardless of the effect on competitors. Factors determining whether tying
and bundling are profit-maximizing are for example the magnitude and symmetry between network
externalities or whether consumers single- or multi-home.
I think the results of the papers show that competition authorities should not regard tying or bundling
in two-sided markets as anti-competitive per se. Rather, decisions have to be taken on a case by case
basis according to a rule of reason standard.
Competition authorities should first determine whether the tying or bundling takes place in a one-sided
or in a two-sided market context.
If the tying or bundling takes place in a two-sided market, it needs to be assessed whether the tying or
bundling is actually adopted in order to drive competitors out of the market or whether it is a profitmaximizing strategy. In order to do so, one needs to evaluate the magnitude of the network externalities
and the asymmetry between them. The larger the indirect network externalities, the more likely tying
or bundling is actually a profit-maximizing strategy. Also, as seen before, tying and bundling are ways
to relax the non-negativity constraint. If users on side 1 of the market are for example indifferent to
users on side 2 but users on side 2 value users on side 1 very much, subsidizing users on side 1 via a
tie or bundle with another good and recouping on side 2 is likely to be a profit-maximizing strategy
for the platform.
Lastly, if it has been established that tying or bundling is actually a profit-maximizing strategy rather
than anti-competitive behavior, the welfare effects of this strategy have to be examined. Here, it is
also important to assess whether consumers can easily multi-home which tends to reduce the negative
effects of tying and bundling. The models discussed in the theory part show that there are instances
where tying or bundling not only increases total welfare but also consumer surplus. However, there
are also situations in which total welfare and consumer surplus move in opposite directions. As for
example Choi (2010) concluded in his model, even if multi-homing takes place, the optimal policy
will differ depending on whether competition authorities adopt a total welfare or a consumer surplus
standard. In his model tying with multi-homing increases total welfare, thus tying should not be seen
as anti-competitive if a total welfare standard is adopted. However, in his model, consumer surplus
29
decreases under tying which means that tying should then be regarded as anti-competitive if consumer
surplus is the adopted standard.36
A final caveat of the papers discussed has to be noted. Quite a few papers only discuss the welfare
effects of tying and bundling for one group of consumers when talking about consumer surplus. They
hence discuss whether tying or bundling negatively or positively affects viewers/readers/users but
often neglect the effects on advertisers/content providers/game developers. Competition authorities
should be aware that since a two-sided market comprises two groups of consumers, consumer surplus
comparisons should also include both consumer groups.
One high profile tying case involving two-sided platforms is the Microsoft EU case in which Microsoft
was found guilty of abusing its dominant position in the OS market by tying its WMP to the Windows
OS. As noted above, the welfare consequences of tying in two-sided markets depend, among others, on
whether consumers single- or multi-home. Since the media player industry is characterized by multihoming on both sides of the market, this aspect seems especially relevant in the Microsoft EU case. I
thus want to discuss this case, especially focussing on two-sided aspects, in the next section. Building
on the case discussion in section 3 and Choi’s (2010) model of tying in a market with multi-homing
on both sides, I develop a theoretical model of tying in section 4 in order not only to account for
multi-homing but also two different user groups.
36 Though Choi (2010) only includes consumers into the computation of consumer surplus and does not include content
providers who constitute the second consumer group.
30
3
Microsoft EU Case Discussion
In this section I will discuss the investigation of Microsoft by the European Commission (EC) and its
subsequent decision in 2004, which was one of the biggest antitrust cases in the European Union. Microsoft has been accused and found guilty of abusing its dominant position in the Client PC Operating
System market in two ways. The first accuse related to compatibility issues in the work group server
market and the second to Microsoft’s practice of tying its Windows Media Player to the Windows OS.
The European Commission fined Microsoft a record penalty of €497 million for its abuses.
Even though the case was already decided in 2004, the case is still relevant as it raises important
questions about the treatment of tying in the software industry, which is characterized by many twosided markets. Given the recent focus of the European Commission on close scrutiny of the high-tech
sector and its high profile abuse of dominance cases and investigations into for example Intel, IBM,
Apple or Google, a thorough assessment of the impact of two-sidedness on the economic outcomes of
practices that have traditionally been seen as anti-competitive is advisable. Hence, I want to apply
the relevant aspects about tying in two-sided markets, which I identified in the previous section, to the
example of the tying part of the Microsoft EU case and discuss which of these issues might not have
been considered sufficiently in the Microsoft EU decision.37
I find that especially the two-sided nature of the streaming media player market matters for the
economic assessment of Microsoft’s tying practice. The European Commission was concerned in this
respect that exactly this two-sided nature of the media player industry would make the market tip in
favor of WMP under tying. While it is true that indirect network effects as well as economies of scale
promote few large platforms and hence favor tipping of the market, I find that platform differentiation
and multi-homing prevent tipping of the media player market in favor of WMP. Secondly, I argue that
Microsoft’s tying can actually be profit-maximizing for Microsoft rather than a strategy to foreclose
competing media players. As tying is also a means to overcome the coordination problem of getting
both sides of the market “on board” in the two-sided media player industry, it can furthermore increase
total welfare.
I also briefly consider the dynamic aspects of Microsoft’s tying practice. I assess the Commission’s
claims that Microsoft’s tie stifles innovation in the media player market and claim that this conclusion is
wrong but also that the tie enhances innovation in the software industry and thus increases consumer
surplus. Nevertheless, the Commission’s concern that Microsoft uses tying as a strategy to deter
potential entry in the OS market could be justified if media players turned out to develop into general
purpose platforms that could potentially allow entry in the OS market. Hence, while Microsoft’s tie
could be beneficial also from a dynamic efficiency perspective in the media player market it could also
be a means to deter potential entry in the OS market.
37 Even though the Microsoft US case, settled in 2002, which concerned among others the tying of the Internet Explorer
to the Windows Operating System, is also a high profile decision in the software market, I claim that it does not fit
the theory of tying in two-sided markets. This is because web content can be accessed using every available browser.
This implies that users do not need to care about the amount of content available via a given browser (they just care
about the amount of content available on the Internet). The same is true for content providers. Since their content is
accessible with every web browser, they do not care about the number of users on a particular browser but just about
the total number of Internet users. Thus, a web browser is not a two-sided platform. Additionally, the main concern in
the Microsoft US case was not related to leveraging market power from the OS market into the browser market but to
strategic tying in order to protect Microsoft’s market power in the OS market (see for example Whinston (2001)). These
concerns are similar to some of the European Commission’s concerns in the Microsoft EU case. The Commission was
worried that Microsoft used tying as a means to prevent entry in the OS market. I discuss this issue briefly in section
3.2.4.
31
I first give an overview of the investigation and decision in section 3.1, then assess the economic
aspects of Microsoft’s tying strategy in section 3.2 and conclude in section 3.3. All information on the
proceedings is taken from the official Commission Decision38 if not indicated otherwise.
3.1
3.1.1
Summary of the Facts39
Investigation
The investigation of Microsoft Corporation by the European Commission started initially in December
1998 after Sun Microsystems, a US company, had filed complaint against Microsoft for refusal to provide
interface information necessary for Sun in order to develop products compatible with Windows PCs.
In 2000, the Commission decided to investigate Microsoft also for its tying of the Windows Media
Player with the Windows 2000 PC Operating System. After five years of investigation, the case was
decided on the 24th of May 2004.
3.1.2
Considered Abuses
The European Commission accused Microsoft of infringing Article 82 (d) of the EC Treaty40 by making
the purchase of the Windows Client PC OS (tying good) conditional on the acquisition of the WMP
(tied good) from May 1999 till the date of the decision in 2004. The Commission held that Microsoft
used its dominance in the PC OS market to strengthen the position of its WMP in the streaming
media player market, a market in which Microsoft faces competition. According to the European
Commission, this behavior foreclosed competition and was not justified by efficiency reasons.
3.1.3
Structure of the Case
The following structure is adopted in an abuse of dominance case in the EU, such as the one against
Microsoft. Firstly, the relevant market(s) need(s) to be defined. In the Microsoft case, both the
market for the tying good (Microsoft’s OS) and the market for the tied good (WMP) need to be
defined. Secondly, dominance has to be established in the relevant market. In a tying case, dominance
has to be established in the market for the tying good (OSs). Lastly, an abuse of this dominant position
in the relevant market needs to be proven.
This section will shortly lay out the procedure adopted by the European Commission in the Microsoft
tying case.
Relevant Market The relevant product market for operating systems was defined as the PC OS
market by the European Commission. Even though a distinction could be made between “Intelcompatible” and “non-Intel compatible” PC OSs, the Commission stated that the question of whether
the former or the latter was the relevant product market could be left open as the difference did not
change the results of the assessment of Microsoft’s market power.
38 Case COMP/C-3/37.792 Microsoft, available at http://ec.europa.eu/competition/antitrust/cases/dec_docs/
37792/37792_4177_1.pdf
39 This section is based on the Fact Sheet “Summary of Facts: Tying Microsoft Media Player with Windows” which I
wrote jointly with Bart Compen prior to the class presentation of the EU Microsoft case in the Seminar Competition
Policy.
40 which is now Article 102 (d) of the Treaty of the Functioning of the European Union (TFEU).
32
The relevant product market of the WMP was defined as the market for streaming media players. The
core functionality of a streaming media player is to “decode, decompress and play digital audio and
video files downloaded or streamed over the Internet” 41 according to the European Commission. CDs
and DVDs as well as non-streaming media players were considered not to be substitutes for streaming
media players, as they do not offer the full set of functionalities offered by streaming media players.
According to the European Commission, consumers expect media players to be able to play and stream
both audio and video content.42
The relevant geographical market was defined as being global for both OSs and streaming media
players.
Dominant Position As stated above, the relevant market in which dominance has to be established
is the one for the tying good (that is the one for PC OSs in this case). Microsoft has had high market
shares in the market for PC OSs since at least 1996 and market shares above 90% in the more recent
years prior to the decision. Furthermore, the market is characterized by high barriers to entry and by
the presence of indirect network effects. Thus, the more users an OS reaches, the more applications
will be developed for this OS and the more applications are written for a certain OS, the more users
will adopt the OS. Microsoft has acknowledged its dominant position in the PC OS market.
Abuse of Dominance The European Commission found that Microsoft abused its dominant position by tying the WMP to its PC OS. The decision was based on a five step procedure:
1. Microsoft held a dominant position in the PC OS market
2. The tying good (Windows PC OS) and the tied good (WMP) were two separate products
3. Microsoft did not give the choice to consumers to obtain the Windows OS without the WMP
4. Microsoft’s tying foreclosed competition in the streaming media player market
5. Microsoft’s arguments to justify tying were rejected
According to the European Commission all these conditions were satisfied in the Microsoft tying case
and thus an abuse of dominance by Microsoft was established. Concerning point 3, the Commission
considered the fact that costumers do not pay extra for the WMP to be irrelevant as article 82 (d) of the
EC Treaty43 does not state that a supplemental obligation relates to paying. Further, as stated in point
4, the Commission alleged that Microsoft’s tying foreclosed competition in the streaming media player
market. Tying the WMP with the Windows OS ensures WMP’s ubiquity on PCs worldwide. Due to
the indirect network effects in this market as well as additional costs of supporting several technologies,
this gives content providers and developers of software based on media player formats an incentive to
rely primarily on Windows Media technology. Consumers in turn will prefer to use WMP since there
will be more complementary software and content available than for other streaming media players.
Thus, according to the Commission, the tying of WMP with the Windows OS increased WMP’s usage
41 page 110, paragraph 402 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
42 page 113, paragraph 415 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
43 which is now Article 102 (d) of the Treaty of the Functioning of the European Union (TFEU).
33
and shielded Microsoft from effective competition from potentially more efficient media players who
could challenge its position in the media player market. Furthermore, the Commission stated that
the abuse by Microsoft hindered innovation in the streaming media player market and harmed the
competitive process and consumers who ultimately would face less choice. The Commission dismissed
all arguments given by Microsoft during the proceedings of the case potentially justifying the tie.
Remedies and Fines The decision by the European Commission, taken on 24th May 2004, required
Microsoft to offer, within 90 days, a version of its Windows client PC OS without WMP to PC
manufacturers. Nevertheless, Microsoft retained the right to offer a bundle of Windows and WMP.
Furthermore, Windows was fined a total of €497 million. This fine however concerned the two distinct
abuses of refusal to supply (not discussed here) and tying. Microsoft appealed at the Court of First
Instance (CFI). The CFI upheld the Commission decision on Microsoft’s abuse of its dominant position
and confirmed the totality of the fine on 17th September 2007. Furthermore, Microsoft got two
additional fines (one in 2006 and one in 2008) from the Commission for non-compliance with the
remedies imposed regarding the refusal to supply part of the case. These additional fines amount to a
total of €1 179.5 million.44
3.2
Economic Analysis of the Microsoft EU Case
In the following, I want to critically discuss the European Commission’s assessment of the abuse of
dominance by Microsoft.
Coming back to the structure of the case adopted by the European Commission (and discussed in
Section 3.1.3), I will neither discuss the market definition nor the established dominant position of
Microsoft in the PC OS market, as these aspects seem to be less disputed. Rather, I will concentrate
on the steps taken and conditions looked at by the European Commission in order to prove Microsoft’s
abuse of dominance.
Specifically, I want to address the following questions:
• Are the tying good (PC OS) and the tied good (WMP) two separate products?
• Does the tie foreclose competition in the streaming media player market?
• Are there arguments justifying the tie?
These questions address points 2, 4 and 5 in the establishment of abuse of dominance by the Commission
as discussed in Section 3.1.3.
Lastly, I would also like to shortly discuss two dynamic issues. Firstly, the Commission stated that
Microsoft’s tie stifles innovation in the streaming media player market. In response to this statement,
I would like to shortly discuss consequences of Microsoft’s tying for dynamic efficiency. Secondly, the
Commission was concerned that Microsoft uses its tie to prevent future entry in the OS market in
order to protect its near monopoly. Thus, I want to shortly discuss whether this concern is justified.
44 See http://ec.europa.eu/competition/elojade/isef/case_details.cfm?proc_code=1_37792 for an overview of
the follow ups of the decision.
34
3.2.1
Are the Tying Good and the Tied Good Two Separate Products?
One of the disputed points in the Microsoft EU tying decision was whether the Windows OS and WMP
are two separate products.
The European Commission argued that the Windows OS and the WMP are two separate products.
The argument by the European Commission was that firstly, there is separate demand for media players
as there are consumers who download and use a standalone media player (e.g. Real Player). Secondly,
there is not only demand for standalone media players but also supply of them. Thus, there are firms
offering streaming media players on a standalone basis without also offering a PC OS. The example
given in the case is again the RealPlayer offered by RealNetworks. Furthermore, even Microsoft offers
the WMP for download, for example for usage with the Apple OS. Thus, supplying a streaming media
player on a standalone basis must be profitable. Concluding, the Commission stated that since there
is both separate demand and separate supply of streaming media players without an OS, a PC OS and
a streaming media player, such as WMP, are two distinct products.
Microsoft claimed however that this conclusion was wrong. The European Commission only considered
that there needs to be separate demand for the tied good (streaming media player) to prove that an
OS and a media player are distinct. Instead, the Commission should also have looked at whether there
is separate demand for the tying good (the PC OS). Microsoft argued in this respect that this is not
the case as users see media functionalities as an integral part of their OS. Hence, there would be no
demand for a Windows OS without an integrated streaming media player. This result has also been
established in the literature. For example Evans, Padilla, and Polo (2002) state that music players
are nowadays seen as an integrated part of an OS and that they constitute functionality that users
expect from their PC. Thus, consumers would be disappointed and dissatisfied if their OS would not
be capable of playing audio and video content.
Nevertheless, as pointed out by the European Commission, even if users expect media functionalities,
this does not necessarily mean that the media player delivered with the Windows OS has to be WMP.
Thus, if Original Equipment Manufacturers (OEMs) had a choice of which streaming media player to
pre-install on a PC, the Windows OS could be delivered together with a streaming media player other
than WMP. However, that would not make the competing media player a part of the Windows OS.
Another argument made by Microsoft was that the European Commission ignored the commercial
usage criterion. If it is common practice in the industry to sell OSs with integrated streaming media
players, then there must be little demand for the two products separately. Since other software
providers, such as for example Apple also sell their OSs with an integrated media player, OSs and
streaming media players constitute one integrated product. The European Commission countered in
this respect that one should not only look at the behavior of other sellers of the tying good, that is
the OS, but also at other providers of the tied good, that is streaming media players. Since there are
independent providers of streaming media players, Microsoft’s commercial usage criterion argument is
not valid. Furthermore, for example Linux provides an OS that is not bundled with its own media
player but with third party media players. Lastly, none of these competing software suppliers ties its
media player to its OS in the way Microsoft does, since Microsoft’s tie does not allow to remove the
WMP code from a PC.
Concluding, there seems to have been some disagreement between the European Commission and
Microsoft as to whether OSs and streaming media players constitute separate products.45 If they
45 See
also Footnote 2 in section 2.1.1 on the question of when products are considered to be distinct.
35
were only one integrated product, there could not be tying as tying requires the existence of two
distinct products which can be tied together. Even though it might be the case that users nowadays
see media functionalities as an integrated part of their OS, the Commission concluded however that
OEMs could pre-install streaming media players other than WMP on client PCs and hence Microsoft’s
argument that there would be little demand for the Windows OS absent WMP was judged to be
invalid. Furthermore, if the Windows OS would be delivered to users together with a competing media
player, the media player would not automatically become part of the Windows OS. Hence, OSs and
streaming media players constitute separate products according to the European Commission.
3.2.2
Does Microsoft’s Tie Foreclose Competition?
The European Commission further stated in their argumentation that Microsoft’s tying of the WMP
to the Windows OS forecloses competition in the media player market by ensuring WMP’s ubiquity
on PCs worldwide sold through OEMs. The Commission stated that the tie allowed WMP to profit
from a very efficient distribution channel which was not available to other streaming media players.
Due to indirect network effects, the ubiquity of WMP would ensure that content providers as well as
software developers would develop content and software primarily for WMP which in turn would lead
to even more consumers adopting WMP (See Section 3.1.3).
However, in order to be able to judge whether Microsoft actually forecloses competition in the media
player market via its tie, two questions need to be answered: Is Microsoft able to foreclose competition
in the media player market? And even if it is able to foreclose competition, would Microsoft want to
do so? I will discuss both questions in turn.
Is Microsoft Able to Foreclose Competition? I claim that by tying the WMP to its OS, Microsoft is not able to foreclose competition in the media player market. My argument is based on
Larouche (2008) who argues that there are essentially two distinct groups of users of streaming media
players.
The first group are tech-savvy users who want to have the best available media player for their requirements. They are able and willing to download and to install a media player competing with WMP if
they consider this media player to better satisfy their needs.
The second user group are mainstream users who neither have the skills nor the will to play around
with the software on their computer. They expect their OS to be able to handle media files and are
more likely to be satisfied with whichever media player handles the task.
Also the model I develop in section 4 relies on this distinction between two different user groups. This
distinction is further justified by the European Commission’s distinction between mainstream users
and sophisticated users.46
If this distinction between user groups hence holds, then tech-savvy users will look for the best available
media player. For them media players thus compete on performance. Contrary, most mainstream users
will stick with WMP for convenience (if WMP is tied to the OS). Nevertheless, this does not mean that
they are indifferent to performance or do not have a preference for a certain media player. They trade
off convenience and more choice. Should the WMP be a significantly worse product than competing
46 page 230, paragraph 866 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
36
media players, the cost savings of not having to shop around for a different media player would be
defeated by the loss in utility of using a bad quality product. In that case, even the mainstream users
would switch to another media player, given that the costs of switching are relatively low (zero price
of most streaming media players).
Consequently, as long as mainstream users can keep informed about what is happening in the media
player industry with the help of tech-savvy users and as long as the tech-savvy user segment is competitive, Microsoft is under pressure to keep WMP close to the best available media player. This is
necessary to avoid loosing the mainstream users.
Concluding, this means that even though the mainstream user segment might be dominated by only
one media player (WMP) due to tying, this could be efficient and does not foreclose competitors in the
media player market. Tying WMP to the Windows OS delivers convenience benefits to mainstream
users while tech-savvy users obtain the best available media player in the market. Furthermore,
Microsoft is forced to innovate in order to keep WMP close to the best available media player to avoid
losses of mainstream users. Thus, Microsoft is not able to foreclose competition in the media player
market by tying WMP to its OS.
Does Microsoft Want to Foreclose Competition? I just claimed in the previous section that
tying does not enable Microsoft to foreclose competition in the streaming media player market. Assuming, however, for the sake of the argument, that Microsoft would be able to foreclose competition
by tying, the second question which needs to be answered is whether Microsoft would want to do so
absent efficiency reasons. According to the Chicago argument about tying of complementary goods,
discussed in section 2.1.2, the answer to this question is no.
I will illustrate the Chicago argument for the WMP case with a simple example from Ayres and Nalebuff
(2005). Assume Microsoft has a monopoly in Windows and Windows is worth $100 to all consumers.
Windows is an essential product in the sense that a media player without an OS is useless. Assume
further that there are two competing media players in the market: WMP, worth $2 to all consumers,
and RealPlayer, worth $3 to all consumers. Ayres and Nalebuff (2005) further assume zero costs of all
products for simplicity. Assuming zero marginal costs is however a reasonable assumption since the
software industry is characterized by high fixed costs due to initial investment in R&D but very low
if not zero marginal costs (See for example Ponsoldt and David (2007) or the Commission Decision
itself 47 ). Lastly, Ayres and Nalebuff (2005) assume that the media player market is characterized by
Bertrand competition.48
Microsoft can now decide to either tie its WMP to Windows or sell Windows and WMP separately. If
Microsoft decides to tie WMP to Windows, it will be able to charge $102 for the bundle and extract
all consumer surplus. Since Windows is essential for being able to use a media player, no one will buy
RealPlayer and the competitor is thus foreclosed49 . If Microsoft decides however not to bundle, WMP
and RealPlayer will compete in the market for media players. Since this market is characterized by
Bertrand competition, prices will be competed down to marginal costs, that is zero in this example.
47 page 265, paragraph 958 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
48 As discussed in section 2.1.2, Whinston (1990) established that the result about tying of complementary goods being
unprofitable is robust also in case of oligopolistic market structure as well as to the introduction of economies of scale
in the tied good’s market.
49 This assumes however that consumer use only one media player. In the case of multi-homing, even under tying,
Microsoft might not be able to foreclose RealPlayer. Since the media player industry is characterized by multi-homing
on both sides, foreclosure is not likely to happen as I will argue in section 3.2.3.
37
Since RealPlayer is worth $3 to consumers and WMP is worth only $2 to consumers, given a price
of zero, all consumers will buy RealPlayer. However, Windows is an essential product. This means
that Microsoft can extract all consumer surplus by charging a price of $103 for Windows absent tying
as consumers value the package of Windows and a free RealPlayer at $103. All consumers will buy
Windows for $103 and RealPlayer for $0 and Microsoft will extract all consumer surplus.
Concluding, absent efficiency reasons for tying, by tying WMP to Windows, Microsoft would loose
$1 on each OS sold compared to the case where it does not tie and consumers buy the competing
media player RealPlayer. Hence, absent efficiency reasons, it is not profitable for Microsoft to foreclose
competition by tying WMP to its OS. This is due to the fact that an OS is an essential product.
However, this example only considers a one-off game without taking into account future upgrades etc.
3.2.3
Are There Arguments Justifying Microsoft’s Tie?
In the previous section I established that Microsoft is firstly not able to foreclose competition in
the media player market but secondly, even if it would be able to do so, would not want to foreclose
competition absent efficiency reasons. This means that if Microsoft nevertheless adopted tying of WMP
to its OS, this strategy must have been justified by efficiency reasons. The European Commission
dismissed all possible efficiency reasons for tying, partly also for lack of sufficient proof of efficiencies
by Microsoft.
Furthermore, in the previous section, when discussing whether Microsoft would be able to foreclose
competition in the media player market and whether it would even want to do so, I did not take into
account that media players are two-sided platforms. In this section I will thus in turn discuss possible
efficiency reasons for the tie but also how Microsoft’s tie could be a profit-maximizing strategy in light
of the two-sided nature of the media player market rather than a means to foreclose competition.
Efficiency Reasons for Tying There are numerous efficiency reasons for tying which I have presented in section 2.1.2.
As stated before, Tirole (2005) argues that tying can reduce transaction costs. In the case of WMP
this means that consumers do not need to acquire an OS and a streaming media player separately but
receive both goods in a single transaction. The European Commission argued in this respect that even
though it is true that, from the user perspective, a bundle of OS and media player reduces transaction
costs, this does not mean that the bundle necessarily needs to include WMP but could just as well
contain a different media player. Which media player to bundle with the OS would then be the decision
of OEMs, which in turn is driven by user demand, i.e. user preferences.
Furthermore, tying can reduce distribution costs (Tirole, 2005). This also applies in the WMP case as
WMP is shipped together with the Windows OS to OEMs instead of having to be either separately
distributed on disks or downloaded via the Internet.
Also, tying is a means to signal to consumers that WMP is perfectly compatible with the Windows OS.
This in turn helps to preserve Microsoft’s reputation for its OS. If there are for example problems with
a media player installed on a Windows OS, consumers cannot distinguish whether the media player or
the OS causes the problem. Furthermore, since the tie ensures perfect compatibility, it also enhances
the user experience as the bundled software system allows seamless and efficient navigation (see for
example Evans, Padilla, and Polo (2002)).
38
These efficiency reasons for tying hence increase consumer surplus.
Additionally, I argue that the tie also benefits software developers. For example media software
developers need to be sure that their software is compatible with a certain operating system. For this
to be the case, they build their software on so-called application programming interfaces (APIs)50 .
The WMP contains such APIs media software can build on. Due to the tie, software developers know
that the WMP is present on almost all PCs worldwide and thus media functionalities are also present
on these PCs. Consequently, software developers can concentrate on developing new and innovative
applications instead of wasting time and resources to make sure that their software is compatible with
the underlying OS. This in turn leads to a greater variety of software applications being available to
end-users, which increases consumer surplus (see also Evans et al. (2002) for a similar argument).
Furthermore, as discussed before, the European Commission dismissed the commercial usage criterion.
Nevertheless, if the integration of the tying and the tied good is common practice in the industry, this is
strong evidence that the integration creates efficiencies (Hull, 2006). This is the case because basically
a non-dominant firm would have no incentive to tie otherwise. Consider for example Apple, which
also ties its media player to its OS. Given Apple’s small market shares in the PC OS market51 , Apple
cannot believe to be able to foreclose WMP in the media player market due to its tie. Hence, Apple’s
tying strategy must be justified by efficiency reasons.
Lastly, as stated before, the WMP is a two-sided platform. This means that the media player market
is characterized by indirect network effects: the more end-users use a given media player, the more
content providers will provide content for this media player. And the more content is available for
a certain media player, the more users will want to use this specific media player. As I discussed in
detail in section 2.3, in this context, tying can be efficient as it is a means to solve the coordination
problem of getting both sides of the market “on board”. Applying these aspects to the Microsoft EU
case, I will discuss the two-sided nature of the media player market as well as the rationales for tying
WMP to the Windows OS in the next two paragraphs.
Given all discussed efficiency reasons for tying the WMP to the Windows OS, I conclude that tying is
beneficial for total welfare as well as consumer surplus: costs decrease, the user experience is enhanced
and more complementary applications and content will be available.
WMP as a Two-Sided Platform As explained in the previous section, the WMP is a two-sided
platform. This means that it is characterized by indirect positive network externalities as explained
above. These indirect network externalities have been recognized by the European Commission and
they are exactly the reason why the Commission feared that the tie would lead the streaming media
player market to tip in favor of WMP. While it is true that indirect network effects as well as economies
of scale tend to lead to large platforms and concentrated markets, these are not the only factors
influencing whether a market will tip in favor of one platform. I claim thus that the media player
market will not tip in favor of WMP following the tie to the Windows OS.
50 The European Commission defines APIs as “[i]nterfaces used by applications to call upon the services provided by
an operating system” (page 13, paragraph 38 of the European Commission decision, available at http://ec.europa.eu/
competition/antitrust/cases/dec_docs/37792/37792_4177_1.pdf).
51 Apple’s market shares in the Client PC OS market in the years 2000 to 2002 varied between 2.2% and 3.9% depending
on whether units or revenues were looked at according to the decision of the European Commission (Case COMP/C3/37.792 Microsoft, available at http://ec.europa.eu/competition/antitrust/cases/dec_docs/37792/37792_4177_1.
pdf, page 120)
39
As explained in section 2.2, Evans and Schmalensee (2007) identify five factors which influence the size
of a platform: indirect network externalities, economies of scale, congestion, platform differentiation
and multi-homing. Apart from congestion, all these factors are relevant in the WMP case.
Firstly, indirect network externalities promote fewer and larger platform. The European Commission
argued that the tie makes sure that WMP is present on almost all PCs worldwide. In two-sided market
terminology this means that more end-users join the platform WMP. All else equal, this means that
more content providers want to join WMP as they derive additional utility from each potential end-user
their content reaches. Given that more content will thus be available encoded in WMP format, endusers will prefer to join WMP all else equal and so on. These feedback-loop effects might, according
to the European Commission, make the media player market tip in favor of WMP.
Secondly, also economies of scale promote large platforms. The software industry is characterized by
high fixed costs, which are R&D costs in the case of streaming media players, and very low marginal
costs. This means that average costs decrease as production increases. Hence, also economies of scale
in the production of media players favor large platforms.
Nevertheless, in the streaming media player industry, platform differentiation and multi-homing prevent tipping of the market in favor of WMP under Microsoft’s tying.
The media player industry is characterized to a certain extent by platform differentiation. This can
be vertical differentiation (different quality levels) or horizontal differentiation (different features).52
The fact that platforms are differentiated will lead consumers to multi-home. Multi-homing in the
case of end-users of media players means that end-users will own and use several media players, while
multi-homing in the case of content providers means that they will encode their media content in
more than one format (so for more than one media player). Multi-homing decreases the tendency
of two-sided markets to tip in favor of one platform under tying, at least if multi-homing does not
decrease following the tie. The European Commission argued that content providers face high costs in
the streaming media player market to encode in several formats. Nevertheless, the Commission also
admitted that “the majority of content owners and content developers presently still support multiple
formats.” 53 Furthermore, also Evans, Hagiu, and Schmalensee (2006) state that the media player
industry is characterized by multi-homing on both sides, that is by content providers and end-users.
They remark that about 40% of consumers who used media players use two or more each month
according to a Nielsen NetRatings report from January to December 2005. Furthermore, most content
providers supply their media files in more than one format.
Even if multi-homing would be costly for content providers, the question is whether multi-homing is
also costly for end-users. As most (basic versions of) streaming media players are offered for free (for
example WMP’s competitors RealPlayer and QuickTime), the costs of multi-homing for an end-user
are essentially the time and effort required to go to the website of a competing media player, download
the media player and install it on her PC. As I stated before, I think that two different user groups need
to be distinguished who evaluate the costs of multi-homing differently. While mainstream users find
it relatively difficult and costly to find, download and install a media player, tech savvy users consider
the cost of multi-homing to be relatively low. I pursue this argument in my model in section 4. I find in
the model that tying decreases content providers’ incentives to multi-home, which proves the European
Commission’s concern about content provision to be right. Nevertheless, in a two-sided market, less
52 My
model in section 4 considers media players to be horizontally differentiated.
239, paragraph 890 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
53 page
40
multi-homing on one side implies more multi-homing on the other side. This is also true in my model,
in which I find that not only multi-homing by tech-savvy but also by mainstream users increases under
tying.54 Thus, multi-homing by users prevents tipping of the media player market in favor of WMP
under Microsoft’s tying. This conclusion is consistent with the literature on tying in two-sided markets,
discussed in section 2.3 and my finding that tying in two-sided markets characterized by multi-homing
is less likely to be anti-competitive.
Concluding, while it is true that indirect network effects and economies of scale in the streaming media
player market favor large platforms, platform differentiation and multi-homing by end-users make sure
that the market will not tip in favor of WMP due to the tie. This is also one of the reasons why it is
unlikely that tying in this case will have negative effects on total welfare, which I will discuss next.
Tying in The Two-Sided Media Player Market Traditionally, in one-sided markets, tying has
been seen as predation. However, the economics of two-sided markets provide an explanation for why
tying practices are adopted even if they seem to reduce consumer choice and harm consumers.
The following argument is based on Evans and Schmalensee (2007). In a two-sided market context,
the platform provider (in this case Microsoft with its WMP) designs the platform so as to internalize
the indirect network effects, minimize transaction costs between customers on both sides and thus to
maximize the overall value of the platform. The platform provider wants to basically increase the
positive indirect network effect between both sides. And this can for example be done by a tie. This
means that the two-sided platform provider may impose a requirement on side A, lets say end-users,
which does not benefit them directly. In the present context, this would mean tying the WMP to the
Windows OS so that every end-user purchasing a PC with Windows OS automatically also acquires the
WMP. Even if the tie does not benefit end-users directly, the tying of WMP benefits side B (content
providers and software developers) of the platform. All else equal, they prefer joining a platform with
more end-users on the other side, which their content will reach. Thus, demand of content providers
increases (basically, their demand curve shifts outwards). The fact that the number of content providers
joining the platform WMP increases, in turn increases the value placed on the platform on the side of
end-users. This increase in value (due to more content being available on the platform WMP) could
possibly offset the initial negative effect discussed above. Thus, the tie of WMP to the Windows OS
can provide net benefits to side A (end-users) and it certainly benefits side B (content providers).
Hence, tying in a two-sided market context can potentially increase consumer surplus of consumers
on both sides of the market, unless the platform is able to perfectly extract the additional consumer
surplus via appropriate prices.
In section 2.3, I reviewed the theoretical literature analyzing tying in two-sided markets. Especially
the model developed by Choi (2010) fits well the case of Microsoft’s tying of WMP and the Windows
OS. In fact, the paper has been inspired by Microsoft’s practice. Choi’s model analyses tying in a
two-sided market and its effects on competition and social welfare in case consumers on both sides of
the market are allowed to multi-home. Choi (2010) argues that multi-homing is common in digital
media markets and counteracts the tendency towards tipping or lock-in effects in two-sided markets.
This is the same argument as was discussed in Section 3.2.3 following Evans and Schmalensee (2007).
54 Note however that this result relies on exclusive content being present on the competing media player both under
no tying and tying. If, under tying, content providers decided to provide less or no exclusive content to the competing
media player anymore, users would have less or no incentive to multi-home. In that case, the European Commission’s
worry about foreclosure in the media player market would be justified.
41
As explained before, Choi (2010) finds that tying increases the tying platform’s profits compared to
the no-tying case. This is an important result as it shows that tying is thus not adopted to foreclose
competitors but it is instead a profit-maximizing strategy due to the two-sided nature of the market.
It is true though, that the competitor’s profits as well as consumer surplus decrease under tying. Total
welfare, however, increases under tying compared to the no-tying case in the model.
Concluding, Choi’s model on tying in two-sided markets shows that tying can be a profit-maximizing
strategy rather than a means to foreclose competitors. While consumer surplus decreases, total welfare
increases under tying. Hence, if a competition authority adopts a total welfare standard, tying in twosided markets is actually beneficial. Nevertheless, it should be noted that these results crucially depend
on the ability of consumers to multi-home.55 This is however applicable in the WMP case and I thus
claim that the tie increases total welfare, the more so the more consumers multi-home. As for the
decrease in consumer surplus Choi (2010) finds in his model, note that dynamic aspects relating to
innovation not only in the streaming media player industry but also in related software markets are
not taken into account. I will discuss these next.
3.2.4
Dynamic Aspect of Microsoft’s Tying
So far, I have only looked at static efficiency when evaluating Microsoft’s tying practice. I argued
that the tie adopted by Microsoft has efficiency reasons, which lower costs, but also that tying might
actually benefit end-users and that total welfare increases under tying in two-sided markets. In the
following, I shortly want to look at dynamic efficiency as well. Dynamic aspects are especially relevant
in high-tech markets, which are typically very dynamic, in which products are altered frequently and
where the boundaries of markets are constantly changing (Coppi, 2011).
The European Commission claimed that the tie of WMP to the Windows OS would stifle innovation
in the media player market as it gives competitors lower incentives to innovate. Firstly, the relation
between innovation and competition is not so clear and still debated in economics (Schumpeter (1942)
versus Arrow (1962)). Apart from this, it has also been argued that especially in industries characterized by innovation competition, in which market power is a reward for successful innovation and
typically short-lived, the application of traditional antitrust analysis is problematic (see for example
Schmalensee (2000)). This is also related to the fact that once the competition authority will have
analyzed a complex market in detail, the industry will already have moved on. Products, market
boundaries and interconnections will have changed.
Nevertheless, apart from these general criticisms, I also argue that the European Commission’s conclusion that Microsoft’s tie stifled innovation in the media player market is not necessarily true following
the argument of the two distinct consumer groups laid out in Section 3.2.2. Furthermore, one should
not only look at the media player market in isolation.
Instead, one should consider the consequences of the tie on innovation in the software market as a
whole. As I already claimed before and as stated by Evans, Padilla, and Polo (2002), tying the WMP
to the Windows OS benefits software developers. Developers of multimedia applications benefit as
they can count on the presence of multimedia APIs on all machines where the Windows OS (and thus
automatically also WMP) is installed. This will lead software developers to concentrate on innovative
features of new products rather than on adding functionality to an application so as to make sure that
55 Choi (2010) thus notes that in a model where both groups of consumers single-home not only consumer surplus but
also total welfare decreases under tying.
42
it will be compatible with the OS. This ultimately benefits users who will be offered a broader variety
of applications. Thus, tying might actually enhance innovation in the software market.
Additionally, I want to shortly mention a model developed by Choi (2004). The model looks at the
R&D incentives of the tying firm and the rival firm in the tied good market (so in the Microsoft case
this would be the media player market) under tying and no tying.
Choi (2004) abstracts in this model from the issue of entry and exit by the rival firm and considers a
model where tying is not profitable in the absence of R&D competition. In this model Choi finds that
the tying firm’s R&D incentives in the tied good market increase under tying since the firm can spread
out the R&D costs over more units while the rival firm’s incentives to invest in R&D decrease under
tying relative to the no-tying case. Also in this model, tying can be a profit-maximizing strategy even
if it does not foreclose rivals.
In order to answer the question whether tying is then socially beneficial in the presence of R&D
competition, one needs to look at two different aspects of R&D. R&D competition can promote the
diversity of research lines and thus increase the aggregate probability of success if the outcome of
research projects is uncertain. On the other hand, R&D competition can also result in the duplication
of research effort, which is wasteful and costly from a social point of view. Thus, there is a trade-off
between diversity benefits and duplication costs of R&D.
Depending on the level of initial fixed investment needed in R&D in Choi’s model, the cost duplication
effects can outweigh the diversification benefits of R&D. In that case it would be better from a social
welfare perspective to have only one firm invest in R&D. If this is the case, tying can act as a welfare
improving coordination mechanism, as it makes sure that under tying only the tying firm will invest
in R&D.
Apart from dynamic considerations relating to innovation in the media player and software markets,
the European Commission argued that Microsoft also had incentives to tie WMP to the Windows OS
in order to protect its monopolistic position in the OS market. This argument is especially related to
the model of Carlton and Waldman (2002) discussed in section 2.1.2. In this model a monopolist in
the primary market uses tying with the complementary product strategically to prevent future entry
in the primary market or newly emerging markets. The European Commission argued in this respect
that media players, which exhibit APIs, have the potential to be “strategic applications” 56 . APIs allow
software developers to write applications that build on these APIs and hence work on any PC where
the said API is present. As such, the application is then independent of the OS of a particular PC.
The Commission admitted that at the time of the decision, media player APIs did not allow to write
general purpose application programs (but only media applications). As such media players could
not substitute an OS. The Commission claimed however that, should a media player become very
widespread, there would be the incentive to expand the APIs present on it so as to allow to write
also general purpose applications. Secondly, the European Commission claimed that a combination of
a media player and middleware, such as Java, could represent a viable substitute for an OS already
at the time of the decision. Hence, the Commission concluded that Microsoft has the incentive to
strategically tie WMP and the Windows OS so as to foreclose or weaken competitors in the media
player market, which could potentially threaten its dominant position in the OS market. Furthermore,
the Commission alleged that Microsoft has a strong incentive to obtain a strong market position in
the media player market since media players are a “strategic gateway” to a number of related markets,
56 page 270, paragraph 974 of the European Commission decision, available at http://ec.europa.eu/competition/
antitrust/cases/dec_docs/37792/37792_4177_1.pdf
43
such as for example content encoding software, format licensing, Digital Rights Management (DRM)
solutions and online music retailing, where potentially high revenues can be made.
While the model by Carlton and Waldman (2002) supports these kind of dynamic arguments, it remains
to be seen whether indeed media players could develop into general purpose platforms, which could
threaten and substitute an OS.
Concluding, contrary to the claim of the European Commission that Microsoft’s tie stifles innovation
in the media player market, I argue that the tie could promote innovation in the software industry.
This would ultimately offer a greater variety of innovative applications to end-users and thus increase
consumer surplus. Additionally, as shown by Choi (2004), tying can act as a welfare enhancing coordination mechanism in situations where firms compete on R&D investments and where having several
firms invest in R&D in the tied good market would be socially wasteful. Nevertheless, the European
Commission’s concern about Microsoft using tying as a strategy to deter potential entry in the OS
market could be justified if media players turned out to indeed develop into general purpose platforms.
Hence, while Microsoft’s tie could be beneficial also from a dynamic efficiency perspective in the media
player market it could also be a means to deter potential entry in the OS market.
3.3
Conclusion on Microsoft EU Case
In this section, I have critically assessed the European Commission’s arguments why Microsoft’s practice of tying its WMP to its Windows OS constitutes an abuse of dominance. I found that the European
Commission’s arguments were flawed in a number of respects.
Firstly, it is questionable whether the Windows OS and the WMP can be seen as two distinct products.
According to Microsoft, consumers see media player functionalities as an integrated part of an OS. In
that case, selling the Windows OS and WMP together would not even constitute tying. The Commission countered that even though it might be the case that users nowadays see media functionalities
as an integrated part of their OS, OEMs could pre-install streaming media players other than WMP
on client PCs. In case the Windows OS would be delivered to users together with a competing media
player, the media player would not automatically become part of the Windows OS. Hence, OSs and
streaming media players constitute separate products that consequently can be tied together according to the European Commission. This argument also relates to the dynamic aspects of the case as
the definition of products might change over time with changing user expectations especially in the
fast-moving software industry.
Secondly, if one considers the Windows OS and WMP to be distinct products that can be tied together,
I have shown that the tie does not foreclose competition in the streaming media player market contrary
to the claims by the Commission. Microsoft is not only unable to foreclose competition in the media
player market, but even if it could do so, it would not be profitable for Microsoft to tie absent efficiency
reasons.
Thirdly, I discussed numerous efficiency reasons for tying WMP to the Windows OS, which have all
been rejected by the Commission. I discussed the two-sided nature of the media player market and the
effects of tying in this particular two-sided markets. I argued, based on Choi (2010), that Microsoft’s
tying practice is profit-maximizing rather than a strategy to foreclose and that it increases total welfare
as it is a means to overcome the coordination problem in two-sided markets.
44
Lastly, I considered the dynamic aspects of Microsoft’s tying practice. I critically assessed the claims
by the Commission that Microsoft’s tie stifles innovation in the media player market. I not only claim
that this conclusion is wrong but also that the tie enhances innovation in the software industry and
thus increases consumer surplus. Furthermore, I discussed a model by Choi (2004) which finds that
tying can act as a welfare improving coordination mechanism in situations were the duplication of
R&D investments is socially wasteful. Nevertheless, the Commission’s concern that Microsoft uses
tying as a strategy to deter potential entry in the OS market could be justified if media players turned
out to develop into general purpose platforms that could potentially allow entry in the OS market.
Hence, while Microsoft’s tie could be beneficial also from a dynamic efficiency perspective in the media
player market it could also be a means to deter potential entry in the OS market.
Following my argument that there are two distinct user groups, one group of mainstream users and
one group of tech-savvy users, I want to develop a model of tying in a two-sided market characterized
by multi-homing on both sides in the next section. The model is based on Choi (2010). Nevertheless,
the inclusion of two different user groups is relevant for the assessment of the effects of tying WMP to
the Windows OS, as mainstream users are less likely to multi-home than tech-savvy users and multihoming is one of the critical aspects determining the effects of tying in the Microsoft EU case. Since
Choi (2010) does not make this distinction, my extension of the model allows to more realistically
picture the streaming media player industry and to assess whether Choi’s results in terms of consumer
surplus and total welfare are robust to the introduction of two different user groups.
45
4
A Model of Tying in a Two-Sided Market with Multi-Homing
on Both Sides
The model I lay out in this section and in which I analyze tying in a two-sided market is an extension
of the model presented in Choi (2010). As discussed in section 2.3.1, Choi develops a two-sided market
model in which he analyzes the welfare implications of tying when both groups of consumers multihome. His model tries to depict the tying of WMP to the Microsoft OS. As explained in section 3,
the media player industry is characterized by multi-homing by both content providers and users. In
the model in this section, I extend Choi’s analysis by distinguishing two different types of users: one
group of users with high transportation costs and one group of users with low transportation costs.
By assuming two different types of users, I try to capture an important argument made in the EU
Microsoft case discussed in section 3. While two different users might have the same preferences for
one media player or the other, they differ in their evaluation of how costly it is to multi-home. Users
with high transportation costs, i.e. mainstream users, find it relatively costly to search, download and
install a media player, while users with low transportation costs, i.e. tech savvy users, find it relatively
easy and hence not very costly to do so. Maintaining Choi’s assumption of multi-homing by content
providers as well as users absent tying, I analyze the welfare implications of tying.
I find that Choi’s (2010) results are robust to the introduction of two different user groups. While
tying of platform access with the OS is profitable for the monopolist in operating systems, it decreases
the competing platforms profits. Furthermore, also consumer surplus decreases under tying. Total
welfare increases though. This implies that the treatment of tying should differ depending on whether
competition authorities adopt a consumer surplus or total welfare standard.
Choi (2010) assumes the market to be fully covered under no tying as well as tying. In my analysis
I also check whether in a context where absent tying the market is covered and multi-homing occurs
on both sides, tying situations in which the market is no longer covered could occur. I find that if
absent tying the market is covered and both users and content providers multi-home, under tying,
there will also be some users multi-homing and hence the competing platform cannot be foreclosed.
This conclusion is relevant also for the Microsoft EU case where concerns that competing media players
would be driven out of the market by Microsoft’s tying of WMP and the Windows OS were raised.
4.1
Model Set-Up
In this section, I set up the basic framework of the model in which I will analyze tying. As in
Choi (2010), the model comprises three types of agents. There are two consumer groups, content
providers and users, who interact with each other via platforms (i.e. media players). Differently from
Choi, I analyze a case in which users differ in their transportation costs. One group of users incurs
high transportation costs, while the other group incurs low transportation costs. This difference in
transportation costs captures the fact that users evaluate the cost of multi-homing, i.e. downloading
and installing a second media player, differently even if the underlying preferences for one or the other
media player are the same. Content providers and both groups of users are allowed to multi-home, i.e.
participate in more than one platform.
There are two platforms, i = A, B. Platforms compete for market share in each consumer group and
charge prices pi and qi to content providers and users respectively with i = A, B. I further assume
46
that marginal costs of serving another content provider or user are c and d respectively. Lastly, mi is
the number of content providers on platform i, ni is the number of single-homing users on platform i
and Ni is the total number of users participating in platform i.
4.1.1
Users
In order to analyze demand for media players from users, I follow Choi (2010) and adopt a Hotelling
model of horizontal product differentiation. Platforms are located at the endpoints of the Hotelling
line, i.e. platform A is located at 0 and platform B is located at 1.
Differently from Choi (2010), I distinguish two user groups and hence two Hotelling lines. Fraction
α (α ∈ [0, 1]) has high transportation costs tH and is uniformly distributed on the interval [0, 1] with
density α. Fraction (1 − α) of users has low transportation costs tL and is uniformly distributed on the
interval [0, 1] with density (1 − α). High transportation cost users can be interpreted as mainstream
users while low transportation cost users are tech-savvy users. Hence, the total number of users is
normalized to 1. While platforms know tL and tH as well as the fractions α and (1 − α) of mainstream
and tech-savvy users respectively, they cannot price discriminate according to user type. This implies
that firstly, platforms do not know of which type a given user, they are faced with, is and hence cannot
charge different prices to different users. Secondly, I also assume that platforms cannot offer different
access and price options to users. Thus, platforms can only charge one access or membership fee, which
is the same for every user.
The utility a user derives from participating in a platform depends on the number of content providers,
i.e. the amount of content, on the platform. Users, both high and low transportation cost users, gain
additional utility b from each additional content provider.
As in Choi (2010), I want to analyze a situation in which users are allowed to multi-home. Thus, users
can choose to single-home on A, single-home on B or participate in both platforms.
The model is illustrated in Figure 1.
If a user located at x participates in platform A only, i.e. single-homes on A, her utility is given by:
uA,θ (qA , x, tθ ) = bmA − qA − tθ x
(1)
where θ = {H, L} characterizes whether the consumer is of the high or the low transportation cost
type.
Similarly, a user located at x who single-homes on B obtains utility:
uB,θ (qB , x, tθ ) = bmB − qB − tθ (1 − x)
(2)
Lastly, the utility of a user who is located at x and who multi-homes is given by:
uA,B,θ (qA , qB , x, tθ ) = bm − qA − tθ x − qB − tθ (1 − x)
(3)
where m is the total amount of content available to multi-homing users. The relation between mi and
m, that is the content available on each platform and the total content available to multi-homing users,
47
Figure 1: Two-Sided Market With Multi-Homing on Both Sides
depends on the extent of content duplication. If there is only exclusive content, then m = mA + mB .
If there is some degree of content duplication across platforms δ (with δ ≤ min [mA , mB ]), then
m = mA + mB − δ.
4.1.2
Content Providers
The content provider side is modeled exactly as in Choi (2010). The potential number of content
providers is the same for each platform and normalized to 1 (for each platform). Fixed costs for
content creation are considered to be zero. Content providers derive additional profits π from each
additional user who has access to their content. Profits for a content provider participating in platform
i are hence given by πni − pi .
A content provider is willing to participate in platform i as long as it holds that:57
πni − pi ≥ 0
(4)
Furthermore, in order to create an incentive for users to multi-home, Choi (2010) distinguishes two
types of content: exclusive and non-exclusive content. If every content available on platform A would
also be available on platform B, users would have no incentive to participate in more than one platform.
If platforms however offer access to some amount of exclusive content, which is only available on that
particular platform, users have an incentive to multi-home.
57 Note
that the results would not change if content providers were charged a per user fee rather than a membership fee.
The inequality indicating when a content provider would provide content to a particular user would just be inequality 4
divided by ni . Hence, the optimal price per user charged to a content provider would just be the optimal membership
price divided by the number of users. This is the case because the additional utility a content provider derives from each
additional user present on the platform is constant.
48
λ (� [0, 1]) is defined as the amount of exclusive content available on platform i. Hence both platforms
have the same amount of exclusive content. (1 − λ) is the amount of non-exclusive content that is
potentially available on both platforms. Non-exclusive content providers multi-home if they decide to
make non-exclusive content (1 − λ) available on both platforms.
Choi (2010) assumes that λ is exogenous, hence content providers cannot decide whether they offer
exclusive or non-exclusive content. Choi (2010) argues that this assumption might be justified if one
considers that some content cannot easily be made compatible with another platform for technical
reasons while other types of content might be easier to encode in both formats.
Nevertheless, the assumption that λ is exogenous is one of the main shortcomings of the model. An
extension of the model could be to consider λ endogenous and allow content providers to make content
available on both platforms at some additional cost. If λ was endogenous, it should be in part a
function of the number of users on each platform. I will discuss the implications of λ being endogenous
in more detail in section 4.6.
4.2
Market Equilibrium in Two-Sided Market with Multi-Homing and No
Tying
In this section, I will look for equilibria where both users and content providers multi-home.
I assume that content providers multi-home (and derive conditions for this to hold later). In that
case, each platform has exclusive content λ and non-exclusive content (1 − λ) available. The extent
of content duplication across platforms is hence given by δ = 1 − λ. The amount of content available
on each platform is consequently mA = mB = 1 while the total amount of content available to multihoming users is given by m = 1 + λ.
Substituting the amount of content available to single-homing and multi-homing users in the respective
utility functions, the utility from single-homing on A, single-homing on B or multi-homing can be
obtained for high and low transportation cost users.
The utility from single-homing on A of a type θ user located at x is given by b − qA − tθ x. The utility
from multi-homing of a type θ user located at x is given by (1 + λ) b − qA − tθ x − qB − tθ (1 − x) =
(1 + λ) b − (qA + qB ) − tθ .
By setting the utility from single-homing on A and multi-homing equal, I obtain the user of type θ
indifferent between single-homing on A and multihoming. She is located at:
x=1−
λb − qB
tθ
(5)
Similarly, the utility from single-homing on B of a type θ user located at y is given by b−qB −tθ (1 − y).
Setting equal the utilities obtained from single-homing on B and multi-homing, I find the user of type
θ who is indifferent between single-homing on B and multi-homing to be located at:
y=
λb − qA
tθ
(6)
The number of users who single-home on platform i is the sum of the high and low transportation
cost users who single-home on i. Given the location of the indifferent consumers above, the number of
users single-homing on platform i is given by:
49
Figure 2: User Choices for Type θ
�
�
λb − qj
λb − qj
ni = 1 − α
+ (1 − α)
tH
tL
where i = A, B and j �= i.
(7)
�
�
λb−q
Hence, the number of single-homing high transportation cost users on platform i is given by α 1 − tH j
�
�
λb−q
while the number of low transportation cost users single-homing on platform i is (1 − α) 1 − tL j .
Let nM = 1 − nA − nB be the number of multi-homing users. It is given by:
nM = α
�
�
�
�
2λb − (qA + qB )
2λb − (qA + qB )
+ (1 − α)
−1
tH
tL
(8)
Denote by Ni = ni + nM the total number of users who participate in platform i. Substituting the
respective expressions for ni and nM , Ni is given by:
Ni = α
λb − qi
λb − qi
+ (1 − α)
tH
tL
(9)
These user choices are illustrated in Figure 2.
Next, I look at the incentives of content providers to participate in each platform. Assuming that the
consumer market is covered and that some consumers multi-home (which implies that NA + NB > 1),
exclusive content for platform A will be provided if πNA − pA ≥ 0. On the contrary, the incentives to
provide non-exclusive content on A depend on whether this content is already provided for platform
B. Assuming non-exclusive content is already present on B, non-exclusive content will be provided on
platform A if πnA −pA ≥ 058 since the benefit of providing non-exclusive content on A in addition to B
allows to reach the users single-homing on A in addition to the ones who multi-home and single-home
on B. Given that, under multi-homing of users, NA > nA holds, platforms can either charge pA = πnA
to content providers and hence attract both exclusive and non-exclusive content or they can charge
the higher price pA = πNA and attract only λ exclusive content providers.
Following Choi (2010), I will derive the equilibrium on the user side assuming that content providers
multi-home (hence, the total amount of content on platform i is 1 and the price charged to content
58 Again, this implies that platforms can only charge a fixed membership fee to content providers as opposed to charging
content providers per user their content reaches.
50
providers is pA = πnA ) and derive conditions for this to hold later. Substituting nA from equation 7
in the expression of pA , the optimal price charged to content providers is given by:
�
�
��
λb − qB
λb − qB
p∗A = πnA = π 1 − α
+ (1 − α)
tH
tL
(10)
Note that this optimal price charged to content providers depends only on the price charged to users
on the other platform and not on the price charged to A’s own users qA .
Hence, platform A needs to solve the following maximization problem on the user side only:
�
�
λb − qA
λb − qA
M ax = (qA − d) NA = (qA − d) α
+ (1 − α)
qA
tH
tL
(11)
The first order condition with respect to qA is given by:
α
�
λb
2
−
qA
tH
tH
�
+ (1 − α)
�
λb
2
− qA
tL
tL
�
+α
d
d
+ (1 − α)
=0
tH
tL
(12)
which implies that the optimal price on the user side is given by (See Appendix A.1 for the calculations):
qi∗ =
λb + d
2
(13)
This price is equal to the optimal price on the user side in Choi’s model. Technically, this is due to the
fact that the transportation costs drop out in the calculations and hence the optimal price charged on
the user side does not change with the introduction of the two different user groups. Intuitively, the
reason for why the optimal user price does not change with the introduction of two different user groups
is that platforms cannot price discriminate according to user type. Given that all other assumptions in
my model are the same apart from the introduction of the two user types and given that the total size
of the user market is still equal to 1, the optimal user price does not change compared to Choi (2010).
This already hints at my final conclusion that Choi’s (2010) results are robust to the introduction of
two different user types.
Substituting the optimal price qi∗ charged on the user side in equation 9, the total number of users
present on each platform is given by:
Ni∗ = α
λb − d
λb − d
+ (1 − α)
2tH
2tL
(14)
Similarly, plugging in qi∗ in equation 7, the number of users single-homing on platform i is given by:
n∗i
�
λb − d
λb − d
=1− α
+ (1 − α)
2tH
2tL
�
(15)
Following Choi (2010), I now check under which conditions this equilibrium is consistent with multihoming on both sides.
The first condition makes sure that users multi-home. While Choi (2010) makes sure that NA +NB > 1,
I need to take into account the two different user groups. Since users with high transportation costs
51
incur higher costs of multi-homing than users with low transportation costs while getting the same
additional benefits, the condition needs to make sure that at least some high transportation cost users
multi-home in equilibrium.59 This condition then also ensures that some low transportation cost users
multi-home. This is the case if the following assumption A1 holds (See Appendix A.2 for the derivation
of A1):
λb − d > tH
(A1)
This condition states that for multi-homing to occur on the user side, the amount of exclusive content
λ and the indirect network benefits b should be high compared to the marginal cost of serving an
additional user d and transportation costs tH (and hence also tL ). I assume this assumption to hold
in the rest of the thesis.
Secondly, for the above calculated user and content provider prices qi∗ and p∗i to constitute an equilibrium, neither platform should have an incentive to deviate. A deviation in this case would be to
charge the higher price pi = πNi to content providers and attract only exclusive content λ. Hence,
assumption A2 needs to make sure that it is more profitable for platforms to attract both exclusive
and non-exclusive content providers rather than just attracting exclusive content.
Since in digital media industries marginal costs on both sides are typically small, I assume for the rest
of the thesis and following Choi (2010) that c = d = 0.
Setting marginal costs to zero, the no deviation condition for platforms is given by (See Appendix A.3
for the derivation):
λ [λπ + 2b (1 + λ)]
tH t L
≤
4
α (tL − tH ) + tH
(A2)
For the remainder of the thesis, I assume A1 and A2 to hold. While A1 states that λ should not be
too small (in order to incentivize users to multi-home), A2 makes sure that λ is not too big so that
multi-homing occurs on the content provider side. Hence, for intermediate values of λ, multi-homing
occurs on both sides.
Proposition 1. If both A1 and A2 hold, there is an equilibrium in which both users and content
providers multi-home.
4.3
Market Equilibrium in Two-Sided Market with Multi-Homing and Tying
To analyze tying in this model, I follow Choi (2010) in assuming that platform A is also a monopolist
in good M. In order for my model to reflect the situation of the Microsoft EU case, I assume that the
good M is necessary for users to participate in the two-sided platform. Hence, M can be interpreted
59 Contrary, it would also be possible to assume that without tying all high transportation cost users single-home while
only low transportation cost users multi-home. I argue however that an equilibrium in which absent tying at least some
high transportation cost users multi-home is realistic. As I argued in section 3.2.2, mainstream users keep informed
about the capabilities of different media players by tech-savvy users. In my model, for this equilibrium to hold, it would
be sufficient that under no tying only one high transportation cost user multi-homes, for example because a tech-savvy
low transportation cost users installed a second media player for her. Since there is contact between high transportation
and low transportation cost users, I claim that this assumption is realistic.
52
as the OS while platforms can be interpreted as being competing media players. Marginal cost of
production of M are cM , which I assume to be equal to zero later on in my analysis. This seems
reasonable as in the software industry marginal costs of serving an additional user are typically very
low.
I further assume that all users have valuation v > cM for M and entry is not feasible.60
Note that in this section, I follow Choi (2010) in assuming that the market is fully covered both under
no tying and under tying.61 This implies that v, the intrinsic value of good M, is high enough so that
every user buys and that it is profit-maximizing for platform A to price so that every user buys. In
order to be able to compare the outcomes of my model with the outcomes of Choi (2010), I need to
derive the implicit assumption on v in Choi’s model. I do this in Appendix A.4 and find that the only
assumption on v needed in Choi (2010) is v > cM . Since I assume cM = 0 in my further analysis, it is
possible to compare the outcome of my model to Choi’s (2010) outcomes as long as the intrinsic value
of M is positive.
Following Choi (2010), I assume further that A first decides whether to tie62 or not to tie the two
goods (the OS and the media player) and then, in the second stage, a price game follows in which A’s
decision of the first stage is taken as given.
I first describe the outcome if A decides not to tie in stage 1 and then the outcome if A decides to tie
in stage 1.
4.3.1
No Tying
Since M is essential for participating in the two-sided market, I follow Choi (2010) in assuming that
users first buy M absent tying. The fact that M is essential for participating in the two-sided market
allows A to extract user surplus from participation in the two-sided market.
The users with the lowest surplus in the market are the high transportation cost users who multi-home
(hence, those located in the middle segment of the Hotelling line). Their equilibrium surplus from
participating in platform A and B is given by:
∗
∗
u∗A,B,H = b (1 + λ) − (qA
+ qB
) − tH
∗
∗
Plugging in the equilibrium user prices qA
and qB
from equation 13, again under the assumption
c = d = 0, u∗A,B,H is equal to:
u∗A,B,H = b + λb −
�
λb λb
+
2
2
�
− tH
60 One possible extension of the model, that is discussed in section 4.6, would be to include a small competitor in the
market for operating systems to account for e.g. Apple.
61 The conditions for the market to be covered in my model under no tying and under tying are derived in Appendix
A.5 and Appendix A.6 respectively.
62 Notice, once again, that the distinction between tying and pure bundling is irrelevant in this model following Tirole
(2005). Even though under tying the media player A would be available separately without the OS M, nobody would
ever want to buy a media player without the OS since it would be useless. Hence, when I analyze the tying situation in
the model, I consider that consumers either buy the bundle of M and platform A, the bundle plus platform B or nothing.
Nevertheless, the fact that tying and pure bundling actually lead to the same outcome in this model is due to A being
a monopolist in the market for good M. Obviously, in reality, there is more than one operating system. However, the
consistently high market shares above 90% of the Windows OS justify modeling the situation as a monopoly.
53
⇐⇒ u∗A,B,H = b − tH
Hence, A will charge a price of
∗
qM
= v + b − tH
(16)
for the monopolistic good M and extract all consumer surplus from the high transportation cost multihoming users. Again, this assumes that the market is fully covered. I show in Appendix A.5 that as
long as assumption A1 is satisfied, the market will be fully covered. This also implies that the only
condition on v needed is v > cM = 0. This is the same condition that needs to hold in Choi (2010) as
I discuss in Appendix A.4.
In the two-sided market the analysis of section 4.2 applies. Hence, A’s profits under no tying are given
by (assuming cM = 0):
Π∗M = v + b − tH + Π∗A
⇐⇒
Π∗M
�
�
λb
λb
= v + b − tH + π 1 − α
+ (1 − α)
2tH
2tL
��
�
2
2
(λb)
(λb)
+ α
+ (1 − α)
4tH
4tL
�
(17)
where the subscript M denotes the monopolist’s profits in order to distinguish A’s total profits from
the profits made in the platform market. Hence v + b − tH are the profits derived from selling M (the
OS) to all users, while the second part of profits represents the profits from selling access to platform
A both to content providers and users. This second part of the profits of platform A is derived in
equation 48 in Appendix A.3.
4.3.2
Tying
Under tying, A bundles/ties the sale of the platform and M and sells them for a bundle price q̃A .
Furthermore, I assume that v (> cM = 0), the intrinsic value of M, is high enough so that A prices the
bundle such that every user buys it (ÑA∗ = 1). The condition on tH for the market to be fully covered
under tying is derived in Appendix A.6. The market outcome is illustrated in Figure 3.
Hence, I need to analyze the incentives of users to multi-home, that is to participate also in platform
B, given that all already have A. On the content provider side, given that all users are on platform A,
non-exclusive content providers have no incentive to multi-home (i.e. to also provide their content on
platform B). I thus follow Choi (2010) in analyzing an equilibrium in which all non-exclusive content
is provided only on platform A, i.e. content providers single-home.
Multi-homing on the user side might take place because there is λ exclusive content provided on
platform B.
The additional benefit from multi-homing for a user located at x and of type θ is λb − tθ (1 − x).
Given the location of the user of type θ indifferent between single-homing on A and multi-homing (see
equation 5) and the resulting number of users single-homing on A, nA (see equation 7), the number of
multi-homing users is given by:
54
Figure 3: Two-Sided Market with Tying by A and Multi-Homing
ñM = ÑB = 1 − ñA
⇐⇒ ñM = ÑB = α
λb − q̃B
λb − q̃B
+ (1 − α)
tH
tL
(18)
where q̃B is the user price charged by platform B. Hence, since under tying users either single-home
on A or multi-home, the total number of users present on platform B, ÑB , is equal to the number of
multi-homing users, ñM . Single-homing on B is no longer possible under tying.
The maximum price platform B can charge to content providers in this situation is p̃B = π ÑB . B’s
profit maximization problem (assuming again c = d = 0) is hence given by:
�
λb − q̃B
λb − q̃B
M axΠ̃B = λπ ÑB + q̃B ÑB = λπ α
+ (1 − α)
q̃B
tH
tL
�
+ q̃B
�
�
λb − q̃B
λb − q̃B
α
+ (1 − α)
tH
tL
(19)
Taking the first order derivative of B’s profits with respect to q̃B and setting it equal to zero leads to
the profit-maximizing user price (see Appendix A.7 for the derivation):
∗
q̃B
=
λ (b − π)
2
(20)
∗
Inserting the expression for q̃B
in equation 18 implies that the number of users who participate in B,
∗
and hence multi-home, ñM = ÑB∗ , is given by:
55
ñ∗M = ÑB∗ = α
λ (b + π)
λ (b + π)
+ (1 − α)
2tH
2tL
(21)
Note that ñ∗M decreases as α increases. This result is intuitive as multi-homing is more costly for high
transportation cost users (so mainstream users) than for low transportation costs users. Thus, as the
fraction of high transportation costs users increases, the number of multi-homing users decreases.
Note also that the total number of users present on platform B, that is users who have access to
exclusive content of platform B, increases under tying since:
ÑB∗ = α
λ (b + π)
λ (b + π)
λb
λb
+ (1 − α)
> NB∗ = α
+ (1 − α)
2tH
2tL
2tH
2tL
∗
∗
This is due to the fact that B decreases its price under tying from qB
= λb
2 to q̃B =
side in order to attract more users when platform A applies a tying strategy.
λ(b−π)
2
on the user
Following Choi (2010), I establish proposition 2.
Proposition 2. Under tying of A and when v is high enough, platform A serves the whole user side market. Content providers single-home on A. Hence, both exclusive and non-exclusive content providers
are present on platform A, platform B on the contrary serves only exclusive content providers.63 The
number of users who multi-home under tying increases as a result of platform B’s lower user price.
4.3.3
Incentives to Tie
∗
In order to analyze the incentives of A to tie, I need to derive the optimal bundle price q̃A
first. A will
set the price of the bundle so that every user buys it, i.e. the market on the user side is fully covered,
again under the assumption that v (> cM = 0) is high enough.
Similarly to the analysis without tying in section 4.3.1, in order to maximize profits while ensuring
that every user buys, A can extract all surplus from those users with the lowest consumer surplus.
Those users are the high transportation cost users who multi-home. Their utility is given by:
∗
∗
∗
ũ∗A,B,H = v + b (1 + λ) − (q̃A
+ q̃B
) − tH = v + b (1 + λ) − q̃A
−
λ (b − π)
− tH
2
Hence, the optimal bundle price which extracts all surplus from those users64 is:
∗
q̃A
= v + b (1 + λ) −
λ (b − π)
− tH
2
(22)
On the content provider side, A can charge π to each content provider, as the content provider reaches
all users when joining platform A.
Hence, A’s profits under tying are given by:
63 This result relies on the fact that λ is exogenous. If λ was endogenous, the question arises whether content providers
would not have an incentive to provide more exclusive content on platform A, where they reach all users, and less on
platform B. Nevertheless, in the media player industry, there still is exclusive content present on different media players
despite Microsoft’s tying strategy.
64 Again, as I show in Appendix A.6, the market will be covered under tying as long as assumption A1 holds. The
only condition on v needed is thus v > cM = 0. Hence, once again, my results are directly comparable to Choi’s (2010)
results, which only rely on v > cM .
56
Π̃∗M = v + b (1 + λ) −
λ (b − π)
− tH + π
2
(23)
In order for the tying to be profitable for A, the profits from tying need to be higher than the profits
under no tying. I show in Appendix A.8, that under assumption A2
Π̃∗M − Π∗M > 0
(24)
holds and hence tying is profitable for A.
Furthermore, I show in Appendix A.9 that the tying adopted by A decreases platform B’s profits.
Proposition 3. While tying is profitable for platform A it decreases platform B’s profits.
4.4
Welfare Analysis
In order to analyze the outcomes of tying in terms of welfare, I compare total welfare under tying and
no tying.
Total welfare absent tying is given by:
W
=
v + (1 + nM λ) b
�ˆ
α−NB,H
−
+
tH xdx +
0
ˆ
(1−α)−NB,L
tL xdx +
0
ˆ
α−NA,H
tH xdx +
0
ˆ
(1−α)−NA,L
tL xdx + nM,H tH + nM,L tL
0
(25)
[λ (NA + NB ) + (1 − λ)] π
where v + (1 + nM λ) b are the total benefits accruing to users both from good M and content on
platforms A and B, the second term in brackets represents total transportation costs incurred by
users and [λ (NA + NB ) + (1 − λ)] π are the total benefits accruing to content providers. Furthermore,
NA = NB = α 2tλbH + (1 − α) 2tλbL and nM = α tλb
+ (1 − α) tλb
− 1.
H
L
Total welfare under tying in contrast is given by:
W̃
=
+
v + (1 + ñM λ) b −
�
�ˆ
α−ñM,H
tH xdx +
0
ˆ
(1−α)−ñM,L
tL xdx + ñM,H tH + ñM,L tL
0
� �
�
�
λ 1 + ÑB + (1 − λ) π
�
(26)
where v + (1 + ñM λ) b are the total benefits accruing to users,�the
once again
� second �term in brackets
�
represents total transportation costs incurred by users and λ 1 + ÑB + (1 − λ) π are the total
λ(b+π)
benefits accruing to content providers. Furthermore, ñM = ÑB = α λ(b+π)
2tH + (1 − α) 2tL .
Hence, the change in total welfare due to tying is given by:
57
�W
=
W̃ − W
=
(ñM − nM ) [λ (b + π)]
�ˆ
ˆ
α−ñM,H
tH xdx +
−
+
0
�ˆ
(1−α)−ñM,L
tL xdx + ñM,H tH + ñM,L tL
0
α−NB,H
tH xdx +
0
ˆ
(1−α)−NB,L
tL xdx +
0
�
α−NA,H
ˆ
tH xdx +
0
(27)
ˆ
(1−α)−NA,L
tL xdx + nM,H tH + nM,L tL
0
Given assumption A2, ñM − nM > 0 (see Appendix A.10 for the derivation of this result), which means
that tying leads to more users multi-homing and ensures that exclusive content is available to more
users. Under tying, all users have access to exclusive content on platform A (since A prices so that
everybody buys) and more consumers have access to exclusive content on platform B since ÑB∗ > NB∗
as shown in section 4.3.2. The first term in the change in total welfare, given by (ñM − nM ) [λ (b + π)],
hence represents the benefits of tying while the second and third term represent the change in transportation costs. It might be the case that overall transportation costs increase due to tying.
Nevertheless, it is possible to manipulate equation 27 so that an unambiguous answer about the change
in total welfare is possible (see Appendix A.11 for the manipulation). Hence, equation 27 changes to:
�W
=
(ñM − nM ) [λ (b + π) − tH ] −
−
�ˆ
−
[(ñM,L − nM,L ) (tL − tH )]
(1−α)−ñM,L
ˆ
tL xdx −
0
�ˆ
α−ñM,H
tH xdx −
0
(1−α)−NB,L
0
tL xdx −
ˆ
ˆ
α−NB,H
tH xdx −
0
(1−α)−NA,L
tL xdx
0
�
ˆ
α−NA,H
tH xdx
0
�
(28)
I show that this change is unambiguously positive in Appendix A.11. Thus, in this model, tying
increases total welfare.
Nevertheless, I can also show that consumer surplus decreases under tying.
Choi (2010) only discusses the surplus of users when talking about consumer surplus and ignores
content provider surplus. In a two-sided market, there are two groups of consumers though and hence
both users and content providers have to be taken into account when discussing the implications of
tying in my model.
I will first discuss user surplus.
As explained in Appendix A.12, user surplus without tying (which I denote by U S) is given by:
US
=
ˆ
α−NB,H
tH xdx +
0
+
ˆ
α−NA,H
tH xdx +
0
ˆ
(1−α)−NB,L
tL xdx +
0
ˆ
(1−α)−NA,L
tL xdx
0
(29)
(1 − α) (tH − tL )
In contrast, user surplus under tying (which I denote by U˜S) is given by:
58
�
U˜S
ˆ
=
α−ñM,H
tH xdx +
0
ˆ
(1−α)−ñM,L
(30)
tL xdx + (1 − α) (tH − tL )
0
Hence, the change in user surplus due to tying is equal to:
�U S
=
=
U˜S − U S
�ˆ
α−ñM,H
0
+
�ˆ
tH xdx −
ˆ
α−NB,H
(1−α)−ñM,L
tL xdx −
0
tH xdx −
0
ˆ
ˆ
α−NA,H
(1−α)−NB,L
tL xdx −
0
tH xdx
0
ˆ
�
(1−α)−NA,L
tL xdx
0
�
(31)
which I show to be negative in Appendix A.12. The explanation for why user surplus decreases given
by Choi (2010) also applies in my model where I introduce different user types. The fact that all
multi-homing high transportation cost users incur total transportation cost of tH , since they travel
the total distance of 1, implies that the surplus of all multi-homing high transportation cost users is
the same and hence does not depend on their location on the Hotelling line. This is turn implies that
platform A, which is a monopolist for the essential good M, can extract all surplus from multi-homing
high transportation cost users and still ensure that every user buys. Since the number of multi-homing
high transportation cost users increases under tying, as I showed in Appendix A.10, platform A can
extract more user surplus under tying.
Lastly, I will look at the consequences of tying by A on content provider surplus.
As derived in Appendix A.13, content provider surplus under no tying (which I denote by CP S) is
given by:
CP S
=
�
λb
λb
(1 + λ) π α
+ (1 − α)
−1
tH
tL
�
(32)
Under Assumption A1 this content provider surplus under no tying is positive.
˜ S) is zero.
In contrast, content provider surplus under tying (which I denote by CP
˜S
CP
=
0
(33)
Hence, tying decreases content provider surplus in my model. This is due to the fact that, even though
an increased number of multi-homers increases the benefits accruing to exclusive content providers,
non-exclusive content providers no longer multi-home, which in turn allows platforms to extract all
content provider surplus.65
65 It is not completely clear in Choi (2010) though why non-exclusive content providers would necessarily single-home
on A. In principle, they could also decide to single-home on B. Platform B might then have an incentive to slightly lower
its price charged to content providers in order to attract all non-exclusive content. In that case, content providers would
59
Concluding, even though I introduce two different user groups, one group of mainstream users with
high transportation costs tH and one group of tech-savvy users with low transportation costs tL , I find
the same outcomes as Choi (2010) in his model. In my model with multi-homing by both users and
content providers, I find that tying by platform A increases total surplus as well as profits of platform
A but decreases profits of platform B as well as user and content provider surplus.
4.5
Potential Other Tying Equilibrium: Tying with No Multi-Homing by
Users
In the analysis in section 4.3, I assumed that the market is fully covered not only absent tying but also
under tying. As I show in Appendix A.4, the market will be fully covered under tying in Choi’s (2010)
model as long as the market is fully covered absent tying and multi-homing occurs on both sides.
So far, I explicitly ruled out a situation in which, absent tying, the user market is fully covered and
multi-homing occurs while under tying users do not multi-home and the market is no longer covered.
In this section I hence explore whether these results that hold for Choi (2010) are robust also in my
model with two different user groups.
I thus look at whether an extreme tying situation could occur in which neither high nor low transportation cost users multi-home. Since absent multi-homing, platform B will not have any users under
tying, this tying equilibrium would lead to the exclusion of platform B. As the European Commission
was concerned in the Microsoft EU case that Microsoft’s tie could foreclose competing streaming media
players, it is important to check wether this tying situation could indeed arise in my model.66
In this potential tying situation, A prices the bundle of M and access to platform A so that no user
multi-homes. The market outcome is illustrated in Figure 4.
In order for not only multi-homing high transportation cost users to drop out but also for multi-homing
low transportation cost users to drop out under tying, the bundle price q̃A charged by A needs to be
higher than the surplus from multi-homing low transportation cost users. In that case, platform B
does no longer attract any users and hence also no content providers. Thus, platform B is driven out
of the market.
obtain positive surplus under tying. The solution to this problem might be a timing issue. If non-exclusive content
providers would first have to commit to providing content on platform A, they indeed would no longer have an incentive
to also provide non-exclusive content on platform B under tying.
66 Note that there could potentially also arise an “intermediate” tying equilibrium in which A prices the bundle of
platform access and good M so that high transportation cost users no longer multi-home (and hence not all high
transportation cost users buy) while low transportation cost users continue to multi-home (and hence all purchase the
bundle and some purchase access to platform B in addition). Whether A will find it profitable to price the bundle so that
multi-homing high transportation cost users drop out depends, among others, on the intrinsic value v of good M (the
OS), the difference in transportation costs between multi-homing high and low transportation cost users tH − tL and the
fraction of high transportation cost users α. The higher the intrinsic value v of good M, the less likely it is that A will
find it profitable to price the bundle so that multi-homing high transportation cost users drop out. The reason is that
losing sales of M is very costly compared to the additional profits from a slightly higher bundle price charged to the still
purchasing users. The higher the difference in transportation costs between multi-homing high and low transportation
cost users tH − tL , the more likely A will find it profitable to price the bundle so that multi-homing high transportation
cost users drop out. The reason is that A can increase the bundle price a lot before also multi-homing low transportation
cost users drop out. Lastly, the higher the fraction of high transportation cost users (i.e. mainstream users) α, the less
likely A will find it profitable to price the bundle so that multi-homing high transportation cost users drop out as it will
lose relatively many users and hence sales of the bundle. Since it is realistic to assume that the value of an OS is high
compared to the difference in transportation costs for media players, this potential tying situation will not be analyzed
here.
60
Figure 4: Two-Sided Market with Tying by A and No Multi-Homing
Since platform A offers access to all users who still participate in the two-sided market, both λ exclusive
content providers as well as (1 − λ) non-exclusive content providers will participate in A. A can charge
a price of p̃A = πñA = π ÑA to content providers and hence extract all content provider surplus.
The utility from buying the bundle and single-homing on A of a type θ user located at x is given by
v + b − q̃A − tθ x. This user will purchase the bundle as long as her utility is non negative. This implies
that the user of type θ who is indifferent between purchasing the bundle and not buying is located at:
v + b − q̃A − tθ x
=
x
=
0
v + b − q̃A
tθ
(34)
The total number of users who purchase the bundle is the sum of the high and low transportation
cost users who purchase it. Given the location of the indifferent consumer above, the number of users
purchasing the bundle is given by:
ÑA = ñA = α
v + b − q̃A
v + b − q̃A
+ (1 − α)
tH
tL
This implies that A’s monopolist profits under tying are given by:
61
(35)
Π̃M
=
=
π ÑA + q̃A ÑA
�
�
�
�
v + b − q̃A
v + b − q̃A
v + b − q̃A
v + b − q̃A
π α
+ (1 − α)
+ q̃A α
+ (1 − α)
(36)
tH
tL
tH
tL
The first order condition with respect to q̃A leads to (See Appendix A.14 for the derivation):
∗
q̃A
=
v+b−π
2
(37)
∗
Substituting the optimal bundle price q̃A
on the user side in equation 35, the total number of users
purchasing the bundle and participating in platform A is given by:
ÑA∗ = ñ∗A = α
v+b+π
v+b+π
+ (1 − α)
2tH
2tL
(38)
For this to be an equilibrium, I need to check two conditions. Firstly, there should be no multi-homers,
i.e. no user willing to participate in platform B. Hence, the condition needs to make sure that the
additional utility from multi-homing is negative for a user of type θ. Secondly, I need to check that
not every user buys the bundle, hence ñA < 1 (which implies ñA,H < α and ñA,L < 1 − α).
I first derive the condition that makes sure no user wants to multi-home.
The last user of type θ buying the bundle has a surplus of zero and hence is indifferent between buying
and not buying. The condition needs to make sure that there is no price q̃B that platform B could
charge to that user in order to make her multi-home and purchase also access to B. If platform B could
attract some users to also purchase access to B in addition to the bundle, it would attract λ exclusive
content and could charge p̃B = π ÑB to each of the λ content providers. Hence, total revenues from
content providers would be λπ ÑB . Platform B would thus be willing to give users a subsidy in order
to participate also in platform B, i.e. charge a negative q̃B . The maximal subsidy B could give every
user would hence be λπ (q̃B = −λπ), which would lead to profits equal to zero for platform B. The
condition needs thus to make sure that even given the subsidy, the last user of type θ purchasing the
bundle will not want to participate in B.
This implies that the additional utility from multi-homing is smaller than zero:
λb − (1 − x) tθ − q̃B
<
0
λb − (1 − x) tθ + λπ
<
0
(39)
Plugging in the user indifferent between purchasing the bundle and not buying located at x =
I obtain the following condition on tθ :
�
v+b+π
λb − 1 −
2tθ
�
tθ + λπ
<
0
tθ
>
λb + λπ +
62
v+b+π
2
v+b+π
2tθ ,
(40)
Since the condition on tL is binding, the first necessary condition for this tying situation to hold is
given by:
tL > λb + λπ +
v+b+π
2
(41)
The second condition makes sure that not all users buy the bundle.
Hence, the following conditions need to hold:
ñA,H
v+b+π
α
2tH
<
α
<
α
tH
>
v+b+π
2
(42)
and
ñA,L
v+b+π
(1 − α)
2tL
<
1−α
<
1−α
tL
>
v+b+π
2
(43)
Since the inequalities in 42 and 43 are automatically fulfilled if inequality 41 holds, for this tying
situation analyzed to be an equilibrium, only the following condition needs to hold:
tL > λb + λπ +
v+b+π
2
(44)
Note that this condition on tL is incompatible with assumption A1 derived in section 4.2, which
implies tL < tH < λb. This means that if under no tying a situation arises where users and content
providers multi-home and the market is covered, then a tying situation in which neither high nor low
transportation cost users multi-home and platform B is driven out of the market cannot occur.
4.6
Significance for Microsoft EU Case and Limitations
My model of tying in two-sided markets builds on Choi (2010). Differently from Choi (2010), I assume
that there are two different groups of users, one group, which I call mainstream users, who have high
transportation costs and one group, which I call tech-savvy users, who have low transportation costs.
This assumption accounts for one important aspect in the Microsoft EU case discussed in section 3,
namely that users differ in their costs of multi-homing even if the underlying preferences for media
players are the same. Mainstream users may find it relatively complex to find, download and install a
second media player while the same task is easy for a tech-savvy user.
By introducing this assumption in Choi’s (2010) model, I make the model fit more closely to the
Microsoft EU case.
63
I find in my model that Choi’s conclusions are robust to the introduction of two different user groups.
While platform A’s profits (so Microsoft in the case) as well as total welfare increase under tying,
platform B’s profits (so for example RealPlayer) and consumer surplus (both user and content provider
surplus) decrease under tying.
In addition, I also find that, if absent tying the market is covered and both users and content providers
multi-home, no tying situation will arise in which users no longer multi-home and the competing
platform B is excluded. This conclusion is important in relation to the Microsoft EU case, in which
concerns were raised that competing media players might be excluded due to Microsoft’s tying strategy.
Since the media player industry is characterized by multi-homing of both users and content providers
(see for example Evans, Hagiu, and Schmalensee (2006)), the no tying situation in my model closely
reflects reality. Hence, my model allows to rule out the exclusion of WMP’s competitors due to
Microsoft’s tying strategy.
Nevertheless, the model can only depict certain aspects of reality and the functioning of the media
player industry.
One of the limitations of the model is that it assumes the number of exclusive content providers λ on
each platform as well as the number of non-exclusive content providers (1 − λ) to be exogenous. A
possible extension of the model would allow for λ to be endogenous where content providers could,
for example, encode content for a second format incurring some additional costs. The European
Commission’s concern about foreclosure in the media player industry could be justified if the incentives
for content providers to provide exclusive content change under tying. Intuitively, it could be the case
that under tying, since content providers reach more users (all users in my model since the OS is a
monopolist) on the tied platform A, more exclusive content will be provided on the tied platform A
and less on the competing platform B. If there is less exclusive content on the competing platform B
under tying, the incentives to multi-home on the user side decrease in turn, which further decreases the
incentive to provide exclusive content on platform B and so on. Thus, foreclosure of the rival platform
B under tying becomes more likely.
Whether assuming λ to be endogenous changes the outcome of the model probably depends on the
stage at which content providers decide whether to provide exclusive or non-exclusive content. Note
that also the amount of exclusive content provided on platform A and B respectively does not need to
be the symmetric, as assumed in Choi (2010) and my model. Assuming that absent tying the situation
as analyzed in Choi (2010) and my model arises, where both content providers and users multi-home,
I will try to make an educated guess about what happens to content provision under tying depending
on the stage of the game at which content providers decide about which type of content to provide.
The first possibility is that content providers first decide whether and how much exclusive content and
non-exclusive content to provide. In that case, they need to initially commit to the type of content
they provide before A decides whether to tie or not. Nevertheless, under perfect information, content
providers can solve the game by backward induction and may influence A’s decision by the type of
content they provide. Given that in the model content providers get all surplus extracted under
tying,67 they will want to make tying less profitable for A. I think content providers could achieve this
by committing to provide more non-exclusive content. If they provide more non-exclusive content, then
if A decides to tie, content providers can threaten to provide non-exclusive content only on platform
B. This implies that A, in order to attract content and sell its bundle to users, needs to offer low
67 See
the comment in footnote 65 though.
64
prices to content providers. On the contrary, if A does not tie, content providers will multi-home (i.e.
provide the non-exclusive content both on platforms A and B) as long as the profit from doing so is
non-negative. The higher the fraction of non-exclusive content 1 − λ, the lower the incentives for users
to multi-home. Hence, platform A can extract more content provider surplus under no tying, which
makes tying relatively less attractive.
The second possibility is that content providers observe whether A ties or not and then decide what
type of content to provide before A and B set prices. I think that in this case, if A decides to tie,
content providers have an incentive to only provide non-exclusive content. By only providing nonexclusive content, they can threaten A to provide content only on platform B. In the next stage of
the game, A and B set prices to content providers and users simultaneously. If content providers only
provide non-exclusive content, A has to price very aggressively in order to attract that content. This
is the case because under tying, for every user who decides not to buy the bundle, A also loses the
highly profitable sale of good M (the OS). This implies that A will have to offer very low prices to
content providers (if not zero) in order to attract all (non-exclusive) content. Since (non-exclusive)
content providers have no incentive to provide their non-exclusive content also on B once they provide
it on A under tying, I think the outcome of the game would be that all content providers only provide
non-exclusive content on A under tying. Content providers would gain maximal surplus and platform
B would be foreclosed since there would be no content provided on it. However, in this situation, tying
would also become less profitable for platform A. Thus, the question arises whether platform A would
want to tie in this situation.
The third possibility is that first platform A decides whether to tie or not, then A and B set prices and
only afterwards content providers decide whether and which type of content to provide. I think that
if content providers decide about content provision at this stage, their incentives change. If A decides
to tie at the first stage and both platforms set their respective prices to users and content providers
at the second stage, there will be no incentive to provide non-exclusive content under tying at the
third stage. This is because in order to participate in any platform, users need M. Hence, either they
purchase the bundle, which means that they automatically participate in A or they cannot participate
in any platform. Given that all users participating in the platform market automatically have access
to platform A, non-exclusive content providers cannot reach any additional users by providing nonexclusive content on B in addition to A. Thus, either a content provider provides exclusive content on
A and reaches all users or he provides exclusive content on B and reaches only multi-homing users.
As the decision of whether to provide exclusive content on a given platform will be a function of the
number of users and the membership fee charged to the content provider by the given platform, my
guess is that there might still be some exclusive content provided on platform B, if B can offer low
prices to content providers. Compared to the tying situation in Choi (2010) and my model though,
I think that there will be more exclusive content provided on platform A and less exclusive content
provided on platform B. This implies that users have less incentives to multi-home all else equal, which
in turn implies that less exclusive content will be provided on platform B and so on.
Concluding, making the amount of exclusive content λ endogenous might change the outcome of the
model depending on the stage at which content providers decide which type of content to provide.
Given that tying ensures that content providers can reach all users on platform A, the incentives to
provide content on platform B decrease. Hence, the European Commission’s concern that Microsoft’s
tie would foreclose rival platforms becomes more realistic as λ is made endogenous.
Secondly, in Choi (2010) as well as in my model, firm A is a monopolist in the OS market. While it is
65
true that Microsoft has very large market shares in the OS market, it is not a monopolist and there
exist alternative OSs such as Linux or Mac OS. Thus, it would be interesting to investigate whether
the conclusions of the model are robust to the introduction of a small competitor in the OS market.
This would at least imply that under tying, users do no longer need to purchase the bundle in order
to also use platform B but could instead avoid buying the bundle and purchase the competing OS in
order to participate in platform B. As soon as there is a competing OS available in the market, also the
distinction between tying and pure bundling becomes relevant again. This implies that under tying by
firm A, platform A (hence the media player) would still be available separately, while the OS can only
be purchased together with the media player. Hence, even under tying by firm A, users could purchase
the competing operating system and access to platform A (the media player) separately. This makes
it likely that in this scenario tying would be less profitable for firm A than in the model analyzed here.
In addition, neither the model developed by Choi (2010) nor my extension allow to depict the different
business strategies pursued by different media players. Evans, Hagiu, and Schmalensee (2006) state
that two-sided platforms within one industry typically pursue similar business strategies for example
concerning on which side of the platform they make money. This is different in the media player
industry. Evans, Hagiu, and Schmalensee (2006) explain, for instance, in detail how Apple’s and RealNetwork’s business strategies evolved over time. The main media players make money very differently.
In general though, companies in the media player industry do not seem to see media players as a main
source of revenues but rather make money from the sale of complementary goods and services. Hence,
in general, the basic version of media players is downloadable for free and mostly also basic encoding
software is given for free to content providers. Thus, the question arises where media player firms get
revenues from.
Microsoft, as a pure software company, does not intend to make money with WMP but makes profits
mainly from sales of its OS. Applications and programs add value to an OS and as such WMP makes
the Windows OS more valuable.
Apple, which sells both hardware and software, has a unique strategy of “give away the blades and sell
the razor” (Evans, Hagiu, and Schmalensee, 2006, p.229). Thus, both itunes and the itunes store are
not primarily designed to make money. Rather, they help to enhance the sales of ipods and to some
extent also Macs. Hence, Apple makes most of its revenues from hardware sales.
Lastly, while RealNetworks initially also made money from licensing software to content providers
(necessary to make content available to users of RealPlayer), as of 2005, it earned most of its revenues from the sale of content. Namely, it operated the Real Music Store, its SuperPass program (a
subscription service for both audio and video content) and diversified into gaming (Evans, Hagiu, and
Schmalensee, 2006).
Furthermore, firms in the media player industry also differ in terms of integration into, for example,
content provision and content owning as well as their degree of interoperability with other platforms.
Thus, different firms active in the media player industry pursue very different business strategies.
These aspects are not accounted for in my model.
Lastly, my model does not account for dynamic efficiency and how tying influences the incentives to
innovate. Some of the European Commission’s concerns in this respect have been discussed in section
3.2.4.
66
5
Conclusion
In one-sided markets, tying and bundling have traditionally been considered as anti-competitive by
competition authorities. These strategies were seen as being adopted either for price discrimination or
foreclosure reasons.
The goal of this thesis was to investigate whether these results of standard economic theory also hold in
a two-sided market context. In this thesis I hence addressed the question of whether the particularities
of two-sided markets could lead to tying and bundling being profit-maximizing strategies rather than
instruments to foreclose competitors and potential entrants. In addition, I investigated the likely
welfare consequences of tying and bundling in two-sided markets with the example of the Microsoft
EU case.
The review of the literature showed that in two-sided markets tying and bundling can be profitmaximizing strategies rather than means to price discriminate or foreclose competitors. This result is
due to the indirect network externalities and there are circumstances, under which tying and bundling
not only increase profits but also consumer surplus. These results in turn have important policy
implications and rather than per se prohibiting tying practices, competition authorities should adopt
a rule of reason standard.
Reviewing the literature, I concluded that there are three main factors determining whether tying or
bundling in two-sided markets is welfare enhancing. Firstly, the higher the magnitude of the indirect
network externalities, the more likely tying or bundling increases total welfare as well as consumer
surplus. Secondly, the symmetry between network externalities matters. The more asymmetric the
indirect network externalities across sides, the more likely it is that tying or bundling on the low
externality side is welfare and consumer surplus enhancing. In these cases bundling or tying can be a
means to subsidize participation on the low externality side, which in turn benefits the high externality
side. Lastly, tying or bundling is less likely to be welfare detrimental if consumers do not face too high
costs of multi-homing.
Hence, competition authorities should assess these factors when analyzing cases of tying or bundling in
two-sided markets. Depending on whether competition authorities adopt a total welfare or a consumer
surplus standard, the optimal treatment of tying and bundling in a two-sided market context differs
in cases where total welfare increases but consumer surplus decreases.
Furthermore, I discussed the Microsoft EU case. This case is relevant for several reasons. Firstly, it is
one of the most important abuse of dominance cases decided by the European Commission. Secondly,
it concerns tying in the two-sided market of streaming media players. Thirdly, some of the important
aspects of tying in two-sided markets have not been sufficiently discussed in the decision. This case
is thus also important in light of future abuse of dominance investigations in the software industry,
especially given the recent focus of the European Commission on the high-tech sector. This hightech sector is characterized by many two-sided markets, in which software products are often sold in
bundles.
I found that especially the two-sided nature of the streaming media player market mattered for the
economic assessment of Microsoft’s tying practice. The European Commission was concerned that
exactly this two-sided nature of the media player industry would make the market tip in favor of
WMP under tying. While it is true that indirect network effects as well as economies of scale promote
few large platforms and hence favor tipping of the market, I found that platform differentiation and
67
multi-homing prevented tipping of the media player market in favor of WMP. Secondly, I argued that
Microsoft’s tying could actually be profit-maximizing for Microsoft rather than a strategy to foreclose
competing media players. As tying is also a means to overcome the coordination problem of getting
both sides of the market “on board” in the two-sided media player industry, it could furthermore
increase total welfare.
Lastly, I supported these results from the case discussion with a game-theoretic model on tying in
a two-sided market where both groups of consumers multi-home and users differ in their assessment
of the costs of multi-homing. This model is based on Choi (2010). Differently from Choi (2010), I
assumed two types of users: one group of users with high transportation costs (mainstream users) and
one group of users with low transportation costs (tech-savvy users). By assuming two different types
of users, I tried to adapt the model better to the Microsoft EU case.
In my model, I found that Choi’s conclusions were robust to the introduction of these two different
user groups. While platform A’s profits (so Microsoft in the case) as well as total welfare increased
under tying, platform B’s profits (so for example RealPlayer) and consumer surplus (both user and
content provider surplus) decreased under tying.
In addition, I also found that, if the market is covered and both users and content providers multihome absent tying, no tying situation will arise in which users no longer multi-home and the competing
platform B is excluded. This conclusion is important in relation to the Microsoft EU case, in which
concerns were raised about competing media players being excluded due to Microsoft’s tying strategy.
Since the media player industry is characterized by multi-homing of both users and content providers,
the no tying situation in my model closely reflects reality. Hence, my model allows to rule out the
exclusion of WMP’s competitors due to Microsoft’s tying strategy.
Nevertheless, the model also shows that while total welfare increases, consumer surplus decreases.
Thus, if the European Commission adopted a consumer surplus standard in its decision against Microsoft, it might have taken the right decision. However, the model does not capture dynamics and
innovation in the software industry. One aspect tending to increase consumer surplus is that the tie
ensures the ubiquity of WMP on almost all PCs worldwide. This ubiquity of WMP in turn allows
software developers to build applications that rely on WMP’s APIs. Since building applications on
WMP’s APIs implies that software developers do not need to take care of interoperability of their
applications with the different underlying operating systems, they can concentrate on developing more
innovative applications, which ultimately benefit users.
Another aspect in the fast moving software industry is also that products, demands and expectations
change over time. Hence, it could be the case that, over time, streaming media players become
an integral part of an operating system as users demand integrated media functionalities, just like
spell-checkers, which were once a separate product category, are now an integrated feature of word
processors. Thus, in evaluating the outcomes of tying and bundling practices in software markets, not
only the two-sided aspects of the industry have to be taken into account but also the dynamics and
rapid changes in this particular industry.
68
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71
A
A.1
Appendix
Profit Maximization on User Side with Multi-Homing and No Tying
Platform A’s profit maximization problem is given by the following expression:
�
�
λb − qA
λb − qA
M ax = (qA − d) NA = (qA − d) α
+ (1 − α)
qA
tH
tL
The first order condition with respect to qA is given by:
α
�
λb
2
−
qA
tH
tH
⇐⇒
�
α
�
+ (1 − α)
�
2
2
+ (1 − α)
tH
tL
λb
2
− qA
tL
tL
�
qA = α
�
+α
d
d
+ (1 − α)
=0
tH
tL
λb + d
λb + d
+ (1 − α)
tH
tL
�
�
�
�
2 (α (tL − tH ) + tH )
α (tL − tH ) + tH
⇐⇒
qA =
(λb + d)
tH tL
tH tL
⇐⇒ qA =
λb + d
2
The second order derivative of A’s profits on the user side with respect to qA is negative, hence at
qA = λb+d
there is a maximum:
2
∂ 2 ΠA
2
2
− (1 − α)
<0
2 = −α t
∂qA
t
H
L
A.2
Derivation of Assumption A1
Assumption A1 needs to make sure that at least some high transportation cost users multi-home. For
∗
∗
this, NA,H
+ NB,H
> α needs to hold, where I define Ni,H as the total number of high transportation
cost users present on platform i.
This implies that the following assumption A1 needs to hold:
∗
∗
NA,H
+ NB,H
>α
⇐⇒ α
⇐⇒
λb − d
λb − d
+α
>α
2tH
2tH
λb − d λb − d
+
>1
2tH
2tH
⇐⇒
2λb − 2d
>1
2tH
72
⇐⇒ λb − d > tH
If assumption A1 is satisfied, at least some high transportation cost users multi-home, which implies
that also some low transportation cost users multi-home.
A.3
Derivation of Assumption A2
In an equilibrium with multi-homing on both sides, no platform should have an incentive to deviate
by charging a higher price pi = πNi to content providers and attracting only exclusive content.
Hence, assumption A2 needs to make sure that the profits from attracting only exclusive content are
lower than the profits from attracting both exclusive and non-exclusive content.
Deviation profits Π̂A are given by:
Π̂A = λ (πNA − c) + (q̂A − d) NA
where λ (πNA − c) are the profits derived from λ exclusive content providers on platform A and
(q̂A − d) NA are the profits derived from users on platform A.
Plugging in the expression for NA given in equation 9, I obtain:
� �
�
�
�
�
λb − q̂A
λb − q̂A
λb − q̂A
λb − q̂A
Π̂A = λ π α
+ (1 − α)
− c + (q̂A − d) α
+ (1 − α)
tH
tL
tH
tL
Taking the first order condition on Π̂A with respect to q̂A , I find:
−α
λπ
λπ
λb
q̂A
λb
q̂A
d
d
− (1 − α)
+α
− 2α
+ (1 − α)
− 2 (1 − α)
+α
+ (1 − α)
=0
tH
tL
tH
tH
tL
tL
tH
tL
⇐⇒ 2
�
α
(1 − α)
+
tH
tL
⇐⇒
�
�
q̂A = α
�
λ (b − π) + d
tH
�
+ (1 − α)
�
λ (b − π) + d
tL
�
�
�
��
�
α (tL − tH ) + tH
λ (b − π) + d α (tL − tH ) + tH
q̂A =
tH tL
2
tH tL
Hence:
∗
q̂A
=
λ (b − π) + d
2
(45)
The second order derivative of A’s deviation profits on the user side with respect to q̂A is negative,
∗
hence at q̂A
= λ(b−π)+d
there is a maximum:
2
∂ 2 Π̂A
2
2
− (1 − α)
<0
2 = −α t
∂ q̂A
t
H
L
∗
Plugging in the expression for q̂A
in equation 9, N̂A∗ is given by:
73
N̂A∗
�
�
�
�
λ (b + π) − d
λ (b + π) − d
=α
+ (1 − α)
2tH
2tL
(46)
Assuming c = d = 0, the deviation profits Π̂A are given by:
Π̂A = λπ N̂A∗ + q̂A N̂A∗
⇐⇒ Π̂A =
�
�
λ (b + π)
λ (b + π)
λ (b + π)
α
+ (1 − α)
2
2tH
2tL
(47)
In contrast, the equilibrium profits of the equilibrium with multi-homing on both sides, derived in
section 4.2, are given by (again setting c = d = 0):
∗
Π∗A = πn∗A + qA
NA∗
∗
where πn∗A are the profits derived from content providers and qA
NA∗ are the profits derived from users.
∗
Plugging in the expressions for n∗A , qA
and NA∗ from equations 15,13 and 14 respectively, equilibrium
profits are given by:
Π∗A
�
�
λb
λb
=π 1− α
+ (1 − α)
2tH
2tL
��
�
2
2
(λb)
(λb)
+ α
+ (1 − α)
4tH
4tL
�
(48)
The no deviation condition is given by:
Π∗A ≥ Π̂A
Plugging in the expressions for Π∗A and Π̂A and simplifying, assumption A2 is given by:
λ [λπ + 2b (1 + λ)]
tH t L
≤
4
α (tL − tH ) + tH
A.4
Assumption on v in Choi (2010)
In order to derive the implicit assumption on v, the intrinsic valuation of the good M in Choi (2010),
I not only need to make sure that the surplus from the lowest surplus users is bigger or equal to zero
but also that it is profit-maximizing for platform A to price so that every user buys.
Hence, I first look at the three possible no tying situations in the model set-up of Choi (2010) in order
to derive the condition on v that makes sure that platform A finds it profit maximising to price so that
every user purchases M. Secondly, I also look at whether there could be an alternative tying outcome
in which the market is no longer covered, nobody multi-homes, and platform B is driven out of the
market.
74
A.4.1
No Tying with Covered Market and Multi-Homing
This situation is the one analyzed in Choi (2010). In this equilibrium, the market is fully covered.
Every user buys M and every user participates in at least one of the two platforms. Some users
multi-home.
The assumptions needed for this equilibrium to hold are derived in Choi (2010) and are the following:
t < λb
t>
λ [λπ + 2b (1 + λ)]
4
v > cM
(49)
(50)
(51)
Additionally, in order for every user to buy, it needs to hold that the gross surplus from those users
that have the lowest surplus is bigger or equal to zero. Hence, it needs to holds that v ≥ t − b which
is always true when equations 49 and 51 hold.
A.4.2
No Tying with Not Fully Covered Market and No Multi-Homing
In this section I look at what happens if A prices so that not all users buy. In that case, those users
with the lowest surplus, that is the multi-homing users in the middle segment of the Hotelling line will
drop out. There are two cases which need to be distinguished. In the first one, the multi-homing users
drop out and buy neither platform access nor good M. In the second case, the previously multi-homing
users do no longer participate in the platform market but still buy M.
I analyze each of these situations in turn.
Users Dropping out Buy neither M nor Platform Access Assume A prices so that there are
no longer any multi-homing users. Hence, some users in the middle segment of the Hotelling line drop
out and platform A and B do no longer compete directly. Under this scenario, those users who drop
out also do not purchase good M any longer.
The utility of a consumer located at x, purchasing M and participating in platform A is given by:
uA (qA , qM , x) = v + b − qA − qM − tx
(52)
where qA is the price charged for access to platform A and qM is the price charged for good M. Note
that the fact that users do not multi-home in this scenario makes sure that non-exclusive content will
be provided on both platforms and that platforms can charge a price of pi = πNi = πni 68 to content
providers and extract all content provider surplus. Hence, the total content available on each platform
is equal to 1 and user benefits of participating in a particular platform consequently equal to b.
68 Note that the number of single-homing users on platform i, n , is equal to the total number of users present on
i
platform i, Ni , since there are no multi-homing users.
75
A user will buy M and participate in platform A as long as her utility is bigger or equal to zero. Hence,
demand for A is given by:
v + b − qA − qM − tx
≥
0
tx
≤
x
≤
v + b − qA − qM
v + b − qA − qM
t
(53)
This implies that the number of users on platform A is given by:
nA =
v + b − qA − qM
t
(54)
Similarly, the number of users participating in platform B is given by:
nB =
v + b − qB − qM
t
(55)
Hence, platform A’s (who also sells good M) profits are given by:
ΠA
=
=
πnA + qA nA + qM (nA + nB )
�
�
�
�
�
�
v + b − qA − qM
v + b − qA − qM
2v + 2b − qA − qB − 2qM
π
+ qA
+ qM
(56)
t
t
t
The first order condition with respect to qA is given by:
v+b−π 2
2
− qA − qM = 0
t
t
t
(57)
This implies that:
qA =
v+b−π
− qM
2
(58)
Note that the second derivative of platform A’s profits with respect to qA is negative, hence at qA =
v+b−π
− qM , there is a maximum.
2
The first order condition with respect to qM is given by:
2v + 2b − π 2
1
4
− qA − qB − qM = 0
t
t
t
t
(59)
which implies:
qM =
2v + 2b − π − 2qA − qB
4
(60)
Note that the second derivative of platform A’s profits with respect to qM is negative, thus at qM =
2v+2b−π−2qA −qB
, there is a maximum.
4
76
Platform B’s profits are given by:
ΠB
=
=
πnB + qB nB
�
�
�
�
v + b − qB − qM
v + b − qB − qM
π
+ qB
t
t
(61)
The first order condition with respect to qB is given by:
v+b−π 2
1
− qB − qM = 0
t
t
t
(62)
This implies:
qB =
v + b − π − qM
2
Note that the second derivative of B’s profits with respect to qB is negative, hence at qB =
there is a maximum.
(63)
v+b−π−qM
2
,
Substituting these expressions into each other, I find:
v + b − 5π
6
(64)
v+b+π
3
(65)
v + b − 2π
3
(66)
n∗A =
v+b+π
2t
(67)
n∗B =
v+b+π
3t
(68)
∗
qA
=
∗
qM
=
∗
qB
=
This in turn implies:
For this to be an equilibrium, I need to check two conditions. Firstly, there should be no multi-homers,
hence, the condition needs to make sure that uA,B ≤ 0. Secondly, I need to check that the consumer
who is indifferent between single-homing on A and not buying is to the left of the consumer who is
indifferent between single-homing on B and not buying. This makes sure that indeed A and B do no
longer compete directly since some users in the middle segment of the Hotelling line drop out.
Hence, I first derive a condition that makes sure uA,B ≤ 0.
The utility from multi-homing is given by:
∗
∗
∗
u∗A,B (qA
, qB
, qM
, x) =
1
1
7
v + b + π + λb − t
6
6
6
77
(69)
This utility needs to be smaller than or equal to zero, which implies:
t≥
1
1
7
v + b + π + λb
6
6
6
(70)
The second condition makes sure that indeed platforms do not compete directly.
Hence, the following condition needs to hold:
v+b+π
2t
<
t
>
v+b+π
3t
5 (v + b + π)
6
1−
(71)
Consequently, for the situation analyzed to be an equilibrium, the following condition needs to hold:
t > max
�
1
1
7
5 (v + b + π)
v + b + π + λb,
6
6
6
6
�
(72)
Note that this condition on t is incompatible with assumption A1 in Choi (2010), which implies t < λb.
This means that in the no tying situation, platform A does not have the choice between charging prices
so that everybody buys and charging prices so that some users in the middle segment drop out but
that the type of no tying equilibrium is determined by transportation costs.
Lastly, I also need to make sure that in this equilibrium indeed those people who drop out of the
platform market also do not want to purchase good M. For this to be the case, I need to derive
a condition that makes sure that the surplus from only purchasing M without participating in the
two-sided market is negative.
Hence, the following needs to hold:
∗
v − qM
v+b+π
v−
3
≤
0
≤
0
(73)
which implies:
v≤
π+b
2
(74)
Thus, there exists a no tying equilibrium where the market is no longer covered, users single-home
and those dropping out do not purchase M individually as long as the conditions on t and v given in
equations 72 and 74 respectively hold. This equilibrium also implies that the utility from purchasing
M separately is negative and that the benefits derived from content hence need to be large in order to
compensate the negative utility from purchasing M. Thus, for this no tying situation to arise, v needs
to be small compared to b and π, that is benefits from content accruing to users and benefits from user
participation accruing to content providers.
78
Users only Drop out of Platform Market The second no tying case in which not all users buy
is the case in which all users purchase M but not all users participate in the platform market. Hence,
just as in the previous case, there are some users in the middle segment of the Hotelling line who do
not buy platform access and platforms A and B do not compete directly anymore. Since there are no
multi-homing users, just as in the previous situation, non-exclusive content 1 − λ will be provided on
both platforms and platforms can extract all content provider surplus.
Since all users buy good M, the best price A can charge is qM = v. Thus, users get all surplus from
buying M extracted. Hence, they will participate in a platform only if their utility from content is
bigger than zero.
This implies that user demand for platform A is:
uA
≥
0
b − qA − tx
≥
0
tx
≤
x
≤
b − qA
b − qA
t
(75)
Hence, the number of users participating in platform A is given by:
nA =
b − qA
t
(76)
Similarly, user demand for platform B is given by:
uB
≥
0
b − qB − t (1 − x)
≥
0
tx
≥
x
≥ 1−
qB + t − b
b − qB
t
(77)
This in turn implies that the number of users on platform B is equal to:
nB =
b − qB
t
(78)
Platform A’s profits derived from selling platform access to both users and content providers are:
ΠA
=
=
πnA + qA nA
�
�
�
�
b − qA
b − qA
π
+ qA
t
t
Profits from selling good M are equal to v since A sells M to all users.
79
(79)
The first order condition with respect to qA is given by:
b−π 2
− qA
t
t
=
(80)
0
which implies:
∗
qA
=
b−π
2
∗
Note that the second derivative of A’s profits with respect to qA is negative. Thus, at qA
=
is a maximum.
(81)
b−π
2 ,
there
Equivalently, platform B’s profits are given by:
ΠB
=
=
πnB + qB nB
�
�
�
�
b − qB
b − qB
π
+ qB
t
t
(82)
which implies that the optimal user price platform B will charge is given by:
∗
qB
=
b−π
2
(83)
For this to be an equilibrium, I need to check two conditions. Firstly, there should be no multi-homers,
hence, the condition needs to make sure that uA,B ≤ 0. Secondly, I need to check that the consumer
who is indifferent between single-homing on A and not buying is to the left of the consumer who is
indifferent between single-homing on B and not buying. This makes sure that indeed A and B do no
longer compete directly since some users in the middle segment of the Hotelling line drop out.
Hence, I first derive a condition that makes sure uA,B ≤ 0.
The utility from multi-homing is given by (I ignore the market for good M here since users get extracted
all surplus):
∗
∗
u∗A,B (qA
, qB
, x)
=
(1 + λ) b + π − t
=
λb + π − t
(84)
This utility needs to be smaller than or equal to zero, which implies:
t ≥ λb + π
The second condition makes sure that indeed platforms do not compete directly.
80
(85)
Hence, the following condition needs to hold:
nA
b+π
2t
t
1 − nB
b+π
1−
2t
b+π
<
<
>
(86)
Since the condition on t in inequality 85 is always satisfied if inequality 86 holds, for this no tying
situation to be an equilibrium, the following condition needs to hold:
t
>
b+π
(87)
Note that this condition on t is incompatible with assumption A1 in Choi (2010), which implies t < λb.
This means that in the no tying situation, platform A does not have the choice between charging prices
so that everybody buys and charging prices so that some users in the middle segment drop out but
that the type of no tying equilibrium is determined by transportation costs.
Concluding on the three different no tying situations, I can say that in the model setup of Choi (2010)
the two situations in which some users in the middle segment of the Hotelling line drop out and no
users multi-home are not compatible with the covered market multi-homing equilibrium. This implies
that when assumptions A1 and A2 of Choi (2010) hold, then the no tying situation will be the one
analyzed in the paper. The only assumption needed on v is v > cM .
Next, I turn to the different possible tying situations in Choi’s (2010) model.
A.4.3
Tying with Covered Market and Multi-Homing
The tying situation with covered market and multi-homing is the one analyzed in Choi (2010). In this
equilibrium, the market is fully covered. Every user buys the bundle of M and access to platform A
and some users also participate in platform B, hence multi-home.
This tying situation is consistent with the assumptions given in section A.4.1.
Additionally, in order for every user to buy, it needs to hold that the gross surplus from those users
who have the lowest surplus, i.e. the multi-homing users, is bigger or equal to zero. Hence, it needs to
holds that v ≥ t − b − λ(b−π)
which is always true when equations 49 and 51 hold.
2
A.4.4
Tying with No Multi-Homing
The second possible tying situation is one in which A prices the bundle so that nobody multi-homes
and some users drop out. Those users with the lowest surplus are those the furthest away from A,
hence, people at the right end of the Hotelling line will drop out. This implies that nobody will multihome anymore. Hence, there will no longer be any demand for platform B, which will be driven out
of the market.
Platform A offers access to all users participating in the platform market. Hence both λ exclusive
content providers and (1 − λ) non-exclusive content providers will participate in A and get all surplus
extracted.
81
Users will purchase the bundle as long as their utility derived from doing so is positive. Hence, demand
for the bundle of M and A is given by (where q̃A is the bundle price):
uA (q̃A , x)
≥
0
v + b − q̃A − tx
≥
0
tx
≤
x
≤
v + b − q̃A
v + b − q̃A
t
(88)
This implies that the number of users present on platform A is given by:
nA =
v + b − q̃A
t
(89)
Platform A’s profits derived from selling the bundle to users and platform access to content providers
are:
Π̃A
=
=
πnA + q̃A nA
�
�
�
�
v + b − q̃A
v + b − q̃A
π
+ q̃A
t
t
(90)
The first order condition with respect to q̃A is given by:
v+b−π 2
− q̃A
t
t
=
0
(91)
which implies:
∗
q̃A
=
v+b−π
2
(92)
Note that the second derivative of A’s profits with respect to q̃A is negative, which implies that there
∗
is a maximum at q̃A
= v+b−π
.
2
This in turn leads to:
n∗A =
v+b+π
2t
(93)
For this to be an equilibrium, I need to check two conditions. Firstly, there should be no multi-homers,
i.e. no users willing to participate in platform B. Hence, the condition needs to make sure that the
additional utility from multi-homing is negative. Secondly, I need to check that not every user buys
the bundle, hence nA < 1.
I first derive a condition that makes sure no user wants to multi-home.
82
The last user buying the bundle has a surplus of zero and hence is indifferent between buying and not
buying. The condition needs to make sure that there is no price q̃B that platform B could charge to
that user in order to make her multi-home and purchase also access to B. If platform B could attract
some users to also purchase access to B in addition to the bundle, it would attract λ exclusive content
and could charge pB = πNB to each of the λ content providers. Hence, total revenues from content
providers would be λπNB . Platform B would hence be willing to give users a subsidy in order to
participate also in platform B, i.e. charge a negative q̃B . The maximal subsidy B could give every
user would hence be λπ (q̃B = −λπ), which would lead to profits equal to zero for platform B. The
condition needs thus to make sure, that even given the subsidy, the last user purchasing the bundle
will not want to participate in B.
This implies that the additional utility from multi-homing is smaller than zero:
λb − (1 − x) t − q̃B
<
0
λb − (1 − x) t + λπ
<
0
(94)
Plugging in the user indifferent between purchasing the bundle and not buying located at x =
I obtain the following condition on t:
�
�
v+b+π
λb − 1 −
t + λπ
2t
<
0
t
>
λb + λπ +
v+b+π
2
v+b+π
2t ,
(95)
The second condition makes sure that not all users buy the bundle.
Hence, the following condition needs to hold:
nA
v+b+π
2t
<
1
<
1
t
>
v+b+π
2
(96)
Since the inequality in 96 is automatically fulfilled if inequality 95 holds, for this tying situation
analyzed to be an equilibrium, only the following condition needs to hold:
t > λb + λπ +
v+b+π
2
(97)
Note that this condition on t is incompatible with assumption A1 in Choi (2010), which implies t < λb.
This means that if under no tying the assumptions in Choi (2010) hold, the no tying equilibrium is an
equilibrium with a covered market and multi-homing by both users and content providers. Secondly, if
absent tying this equilibrium holds, then the tying situation can only be the one in which the market
is covered and some users multi-home. Contrary, the tying equilibrium in which no users multi-home
83
and B is driven out of the market is incompatible with the no tying situation with a covered market
and multi-homing on both sides.
Concluding, I have shown in this Appendix that in the model setup of Choi (2010) the two no tying
situations in which some users in the middle segment of the Hotelling line drop out and no users multihome are not compatible with the covered market multi-homing no tying equilibrium. This implies
that when assumptions A1 and A2 of Choi (2010) hold, then the no tying situation will be the one
analyzed in the paper. The only assumption needed on v is v > cM . Furthermore, I have shown that
this no tying situation is incompatible with a tying situation in which the market is no longer covered,
some users drop out, no user multi-homes and platform B is driven out of the market.
A.5
Derivation of Covered Market Condition under No Tying
The condition that ensures the market will be fully covered under no tying needs to be a condition on
tH . This condition makes sure that tH is not too high so that it is profitable for A to price such that
every user buys platform access and good M absent tying.
In order to derive this condition on tH , I hence need to analyze potential no tying situations in which
the market is not covered and make sure these will not occur.
There a four possible no tying situations in which the market is not fully covered.
The first possibility for the market not to be covered is that those users with the lowest surplus in my
model drop out of the two-sided market. These are the multi-homing high transportation cost users
who have zero surplus under no tying in my model. If there are no longer any high transportation cost
users who multi-home, there is a hole in the middle line segment of the high transportation cost users’
Hotelling line. Two cases can arise. In the first case those high transportation cost users dropping out
of the platform market no longer buy the operating system M either. The other case is that those high
transportation cost users who no longer participate in the platform market still purchase the operating
system M.
The second possibility for the market not to be covered is that prices are so high that also the multihoming low transportation cost users drop out of the platform market. In that case, there no longer is
any multi-homing and platforms A and B do not compete directly anymore. Also here, two cases can
arise. Either those users who drop out of the platform market do not purchase the operating system
M either or they continue to buy M even though they do not participate in the two-sided market
anymore.
The relevant price which determines whether users multi-home or not is the sum of all three prices
charged to users: the price for M, qM , the price for access to platform A, qA , and the price for access
to platform B, qB . The sum of these prices is compared to the benefits from multi-homing, which are
given by v + (1 + λ) b − tθ .
The sum of the three prices in the covered market no tying situation analyzed in sections 4.2 and 4.3
is given by:
∗
∗
∗
qM
+ qA
+ qB
=
84
v + (1 + λ) b − tH
(98)
The condition that makes sure the market is covered absent tying, needs to ensure that the highest
sum of the prices of the four no tying situations, in which the market is not covered, is smaller than
or equal to the sum of the prices given in equation 98. If the highest sum of the prices is smaller than
the sum of the prices given in equation 98, the other sums will be smaller as well and these situations
will not arise.
The highest sum of the prices under no tying and no fully covered market will arise in one of the
two situations in which also the low transportation cost users no longer multi-home. This is the case
because multi-homing low transportation cost users have a higher surplus than multi-homing high
transportation cost users. The difference in surplus is given by tH − tL . Hence, if also the multihoming low transportation cost users drop out, the sum of the prices needs to be higher than in case
only high transportation cost multi-homers drop out of the platform market.
This implies that I need to analyze the two possible no tying situations in which users, both high and
low transportation cost users, no longer multi-home, find the higher sum of the prices and make sure
it is smaller or equal to the sum of the prices given in equation 98.
I will first look at the situation in which the users dropping out of the two-sided market no longer
purchase good M either and then at the case in which they continue to buy good M even though they
no longer participate in the platform market.
Users Dropping out Buy neither M nor Platform Access Assume A prices so that there are
no longer any multi-homing users (neither high nor low transportation cost users multi-home). Hence,
some users in the middle segment of both Hotelling lines drop out and platform A and B do no longer
compete directly. Under this scenario, those users who drop out also do not purchase good M any
longer.
The utility of a consumer of type θ located at x, purchasing M and participating in platform A is given
by:
uA,θ (qA , qM , x, tθ ) = v + b − qA − qM − tθ x
(99)
where qA is the price charged for access to platform A and qM is the price charged for good M. Note
that the fact that users do not multi-home in this scenario makes sure that non-exclusive content will
be provided on both platforms and that platforms can charge a price of pi = πNi = πni 69 to content
providers and extract all content provider surplus. Hence, the total content available on each platform
is equal to 1 and user benefits of participating in a particular platform consequently equal to b.
A user of type θ will buy M and participate in platform A as long as her utility is bigger or equal to
zero. Hence, demand for A by type θ users is given by:
v + b − q A − q M − tθ x
≥
0
tθ x
≤
x
≤
v + b − qA − qM
v + b − qA − qM
tθ
(100)
69 Note that the number of single-homing users on platform i, n , is equal to the total number of users present on
i
platform i, Ni , since there are no multi-homing users.
85
This implies that the total number of users on platform A is given by:
N A = nA = α
v + b − qA − qM
v + b − qA − qM
+ (1 − α)
tH
tL
(101)
Similarly, the total number of users participating in platform B is given by:
N B = nB = α
v + b − qB − qM
v + b − qB − qM
+ (1 − α)
tH
tL
(102)
Hence, platform A’s (who also sells good M) profits are given by:
ΠA
=
=
+
πnA + qA nA + qM (nA + nB )
�
�
v + b − qA − qM
v + b − qA − qM
(π + qA ) α
+ (1 − α)
tH
tL
�
�
2v + 2b − qA − qB − 2qM
2v + 2b − qA − qB − 2qM
qM α
+ (1 − α)
tH
tL
(103)
The first order condition with respect to qA is given by:
α
v+b−π
v+b−π
2
2
2
2
+ (1 − α)
− α qA − (1 − α) qA − α qM − (1 − α) qM = 0
tH
tL
tH
tL
tH
tL
(104)
This implies that:
qA =
v+b−π
− qM
2
(105)
Note that the second derivative of platform A’s profits with respect to qA is negative, hence at qA =
v+b−π
− qM , there is a maximum.
2
The first order condition with respect to qM is given by:
α
2v + 2b − π
2v + 2b − π
2
2
1
1
4
4
+(1 − α)
−α qA −(1 − α) qA −α qB −(1 − α) qB −α qM −(1 − α) qM = 0
tH
tL
tH
tL
tH
tL
tH
tL
(106)
which implies:
qM =
2v + 2b − π − 2qA − qB
4
(107)
Note that the second derivative of platform A’s profits with respect to qM is negative, thus at qM =
2v+2b−π−2qA −qB
, there is a maximum.
4
Platform B’s profits are given by:
86
ΠB
=
=
πnB + qB nB
�
�
v + b − qB − qM
v + b − qB − qM
(π + qB ) α
+ (1 − α)
tH
tL
(108)
The first order condition with respect to qB is given by:
α
v+b−π
v+b−π
2
2
1
1
+ (1 − α)
− α qB − (1 − α) qB − α qM − (1 − α) qM = 0
tH
tL
tH
tL
tH
tL
(109)
This implies:
qB =
v + b − π − qM
2
Note that the second derivative of B’s profits with respect to qB is negative, hence at qB =
there is a maximum.
(110)
v+b−π−qM
2
,
Substituting these expressions into each other, I find:
∗
qA
=
∗
qM
=
∗
qB
=
v + b − 5π
6
(111)
v+b+π
3
(112)
v + b − 2π
3
(113)
Users only Drop out of Platform Market The second no tying case in which no users multi-home
is the case in which all users purchase M but neither high nor low transportation cost users multi-home.
Hence, just as in the previous case, there are some users in the middle segment of the two Hotelling
lines who do not buy platform access and platforms A and B do not compete directly anymore. Since
there are no multi-homing users, just as in the previous situation, non-exclusive content 1 − λ will be
provided on both platforms and platforms can extract all content provider surplus.
Since all users buy good M, the best price A can charge is qM = v. Thus, users get all surplus from
buying M extracted. Hence, they will participate in a platform only if their utility from content is
bigger than zero.
This implies that a user of type θ buys access to platform A if:
uA,θ
≥
0
b − q A − tθ x
≥
0
tθ x
≤
x
≤
b − qA
b − qA
tθ
87
(114)
Hence, the number of users participating in platform A is given by:
N A = nA = α
b − qA
b − qA
+ (1 − α)
tH
tL
(115)
Similarly, a user of type θ participates in platform B if:
uB,θ
≥
0
b − qB − tθ (1 − x)
≥
0
tθ x
≥
q B + tθ − b
b − qB
tθ
≥ 1−
x
(116)
This in turn implies that the number of users on platform B is equal to:
N B = nB = α
b − qB
b − qB
+ (1 − α)
tH
tL
(117)
Platform A’s profits derived from selling platform access to both users and content providers are:
ΠA
=
=
πnA + qA nA
�
�
b − qA
b − qA
(π + qA ) α
+ (1 − α)
tH
tL
(118)
Profits from selling good M are equal to v since A sells M to all users.
The first order condition with respect to qA is given by:
α
b−π
b−π
2
2
+ (1 − α)
− α qA − (1 − α) qA
tH
tL
tH
tL
=
(119)
0
which implies:
∗
qA
=
b−π
2
∗
Note that the second derivative of A’s profits with respect to qA is negative. Thus, at qA
=
is a maximum.
(120)
b−π
2 ,
there
Equivalently, platform B’s profits are given by:
ΠB
=
=
πnB + qB nB
�
�
b − qB
b − qB
(π + qB ) α
+ (1 − α)
tH
tL
88
(121)
which implies that the optimal user price platform B will charge is given by:
∗
qB
b−π
2
=
(122)
Comparison of Sum of Prices Lastly, to derive the condition, which makes sure the market is
fully covered absent tying, I need to compare the sum of the user prices in the two different no tying
situations without multi-homing.
In case users drop out not only of the platform market but also no longer purchase M, the sum of the
user prices is given by:
qM + qA + qB
=
=
v + b + π v + b − 5π v + b − 2π
+
+
3
6
3
5v + 5b − 7π
6
(123)
In case users only drop out of the platform market but still purchase good M, the sum of the user
prices is given by:
qM + qA + qB
=
=
b−π b−π
+
2
2
v+b−π
v+
(124)
Note that the sum of the user prices in the second situation is higher than in the first:
v+b−π
>
5
5
7
v+ b− π
6
6
6
Hence, the condition that ensures the market is covered needs to make sure that the sum of the user
prices given in equation 124 is smaller or equal to the sum of the user prices in case the market is
covered, given in equation 98. This implies:
v+b−π
≤
v + (1 + λ) b − tH
tH
≤
λb + π
(125)
Note that inequality 125 is always satisfied if assumption A1, which implies tH < λb, is fulfilled. Hence,
as long as assumption A1 holds, the market will be covered absent tying. This also implies that the
only condition on v needed, which makes sure that A wants to sell to every user in my model, is
v > cM = 0.
89
A.6
Derivation of Covered Market Condition under Tying
The condition that ensures the market will be fully covered also under tying needs to be a condition
on tH as well. This condition makes sure that tH is not too high so that it is profitable for A to price
such that every user buys the bundle of access to platform A and good M under tying.
In order to derive this condition on tH , I hence need to analyze potential tying situations in which the
market is not fully covered and make sure these will not occur.
There a two possible tying situations in which the market is not fully covered, as I discuss in section
4.5.
The first possible tying situation, in which the market is not fully covered, is an extreme case, in which
neither high nor low transportation cost users multi-home. Since absent multi-homing, platform B
will not have any users under tying, this tying equilibrium would lead to the exclusion of platform B.
I analyze this tying equilibrium in section 4.5.
The second possible tying situation, in which the market is not fully covered, is an “intermediate” tying
equilibrium in which A prices the bundle of platform access and good M so that high transportation
cost users no longer multi-home while low transportation cost users continue to multi-home. Thus,
no high transportation cost user participates in platform B and not all buy the bundle while all low
transportation cost users purchase the bundle and some buy access to platform B in addition.
Again, just as in the no tying case analyzed in Appendix A.5, the relevant price, which determines
whether users multi-home or not, is the sum of the bundle price, q̃A , and the price for access to
platform B, q̃B , charged to users under tying. The sum of these prices is compared to the benefits
from multi-homing, which are given by v + (1 + λ) b − tθ .
The sum of the bundle price and the price for access to platform B in the covered market tying situation
analyzed in section 4.3 is given by:
∗
∗
q̃A
+ q̃B
=
v + (1 + λ) b − tH
(126)
The condition that makes sure the market is covered under tying, needs to ensure that the higher sum
of the prices of the two different tying situations, in which the market is not covered, is smaller than
or equal to the sum of the prices given in equation 126. If the higher sum of the prices is smaller than
the sum of the prices given in equation 126, the other sum will be smaller as well.
The higher sum of the prices under tying and no fully covered market will arise in the situation in which
also the low transportation cost users no longer multi-home. This is the case because multi-homing
low transportation cost users have a higher surplus than multi-homing high transportation cost users.
The difference in surplus is given by tH − tL . Hence, if also the multi-homing low transportation cost
users drop out, the sum of the prices needs to be higher than in case only high transportation cost
multi-homers drop out of the platform market.
This implies that I only need to analyze the extreme tying situation in which platform B is foreclosed.
I do so in section 4.5. The optimal bundle price in this tying situation, given in equation 37, is
∗
q̃A
= v+b−π
.
2
90
Hence, the condition that ensures the market is covered needs to make sure that the optimal bundle
price v+b−π
in this tying situation is smaller or equal to the sum of the user prices in case the market
2
is covered, given in equation 126. This implies:
v+b−π
2
≤
v + (1 + λ) b − tH
tH
≤
λb +
v+b+π
2
(127)
Note that inequality 127 is always satisfied if assumption A1, which implies tH < λb, is fulfilled. Hence,
as long as assumption A1 holds, the market will be covered under tying. This also implies that the only
condition on v needed, which makes sure that A wants to sell to every user under tying, is v > cM = 0.
A.7
Profit Maximization of Platform B under Tying
Platform B’s maximization problem is given by:
�
λb − q̃B
λb − q̃B
M axΠ̃B = λπ ÑB + q̃B ÑB = λπ α
+ (1 − α)
q̃B
tH
tL
�
+ q̃B
�
λb − q̃B
λb − q̃B
α
+ (1 − α)
tH
tL
�
The first order condition yields:
−α
⇐⇒
�
λπ
λπ
λb
λb
q̃B
q̃B
− (1 − α)
+α
+ (1 − α)
− 2α
− 2 (1 − α)
=0
tH
tL
tH
tL
tH
tL
1
1
α
+ (1 − α)
tH
tL
�
q̃B =
αλ (b − π) tL + λ (b − π) tH − αλ (b − π) tH
2tH tL
�
�
�
�
α (tL − tH ) + tH
λ (b − π) α (tL − tH ) + tH
⇐⇒
q̃B =
tH tL
2
tH tL
∗
q̃B
=
λ (b − π)
2
(128)
The second order derivative of B’s profits under tying by A on the user side with respect to q̃B is
∗
negative, hence at q̃B
= λ(b−π)
there is a maximum:
2
∂ 2 Π̃B
2
2
= −α
− (1 − α)
<0
2
∂ q̃B
tH
tL
91
A.8
Profit Comparison of Platform A under Tying and No Tying
Platform A will adopt tying if it is more profitable to tie than to sell good M and access to the platform
A to users separately. Hence, I need to show that:
Π̃∗M − Π∗M > 0
�
�
�
�� �
2
2
λ (b − π)
λb
λb
(λb)
(λb)
⇐⇒ v+b (1 + λ)−
−tH +π > v+b−tH +π 1 − α
+ (1 − α)
+ α
+ (1 − α)
2
2tH
2tL
4tH
4tL
2
⇐⇒
⇐⇒
2
λb λπ
λbπ
λbπ
(λb)
(λb)
+
+α
+ (1 − α)
>α
+ (1 − α)
2
2
2tH
2tL
4tH
4tL
λb λπ λbπ (α (tL − tH ) + tH )
λ2 b2 (α (tL − tH ) + tH )
+
+
>
2
2
2tH tL
4tH tL
⇐⇒
(2λb + 2λπ) tH tL
+ 2λbπ > λ2 b2
α (tL − tH ) + tH
⇐⇒
(2b + 2π) tH tL
> λb2 − 2bπ
α (tL − tH ) + tH
⇐⇒
tH tL
λb2 − 2bπ
>
α (tL − tH ) + tH
2b + 2π
(129)
From assumption A2, I know that:
tH tL
λ [λπ + 2b (1 + λ)]
≥
α (tL − tH ) + tH
4
Hence, if I insert the smallest possible value for the left-hand side expression of the profit comparison
in equation 129 and the inequality holds, it will also hold for larger values.
Inserting
λ[λπ+2b(1+λ)]
4
for
tH t L
α(tL −tH )+tH
in equation 129, I obtain:
λ [λπ + 2b (1 + λ)]
λb2 − 2bπ
>
4
2b + 2π
�
�
λ2 π + 2λb + 2λ2 b (2b + 2π)
4λb2 − 8bπ
⇐⇒
>
4 (2b + 2π)
4 (2b + 2π)
⇐⇒
6bλ2 π + 4λ2 b2 + 4λbπ + 2λ2 π 2 + 8bπ
>0
4 (2b + 2π)
(130)
Hence, since the inequality in equation 130 holds under assumption A2, I have shown that it is profitable
for A to tie.
92
A.9
Profit Comparison of Platform B under Tying and No Tying
Platform B’s profits in the no tying situation analyzed in section 4.2, in which both exclusive and
non-exclusive content providers are present on platform B, are given by:
Π∗B
=
πn∗B
+
∗
qB
NB∗
�
�
λb
λb
=π 1− α
+ (1 − α)
2tH
2tL
��
2
+α
2
(λb)
(λb)
+ (1 − α)
4tH
4tL
(131)
On the contrary, B’s profits when A ties are given by:
Π̃∗B
=
λπ ÑB∗
+
∗
q̃B
ÑB∗
�
�
�
�
�
λ 2 b2 − π 2
λ 2 b2 − π 2
λ (b + π)
λ (b + π)
= λπ α
+ (1 − α)
+α
+ (1 − α)
2tH
2tL
4tH
4tL
(132)
�
Now, I have to show that:
Π̃∗B < Π∗B
Choi (2010) argues in this respect that B’s profits under no tying need to be higher than under A’s
tying strategy since assumption A2 makes sure that platforms prefer to attract both exclusive and
non-exclusive content while under A’s tying B only has exclusive content. However, Choi (2010) does
not prove that B’s profits actually decrease under tying.
In order to show that B’s profits actually decrease under tying, I will take the difference Π̃∗B − Π∗B and
show that it is negative under assumption A2.
Plugging in the expressions for Π̃∗B and Π∗B , I obtain:
Π̃∗B
−
Π∗B
=
−
⇐⇒
�
�
�
�
�
λ 2 b2 − π 2
λ 2 b2 − π 2
λ (b + π)
λ (b + π)
λπ α
+ (1 − α)
+α
+ (1 − α)
2tH
2tL
4tH
4tL
� �
�
�
��
2
2
λb
λb
(λb)
(λb)
π 1− α
+ (1 − α)
+α
+ (1 − α)
2tH
2tL
4tH
4tL
�
Π̃∗B − Π∗B =
⇐⇒ Π̃∗B − Π∗B
=
α
λ2 bπ
λ2 π 2
λbπ
λ2 bπ
λ2 π 2
λbπ
+α
+α
+ (1 − α)
+ (1 − α)
+ (1 − α)
−π
2tH
4tH
2tH
2tL
4tL
2tL
2λ2 bπ [α (tL − tH ) + tH ] + λ2 π 2 [α (tL − tH ) + tH ] + 2λbπ [α (tL − tH ) + tH ] − 4πtH tL
4tH tL
⇐⇒
Π̃∗B − Π∗B =
⇐⇒ Π̃∗B − Π∗B
=
�
[α (tL − tH ) + tH ] � 2
2λ bπ + λ2 π 2 + 2λbπ − π
4tH tL
2λ2 bπ + λ2 π 2 + 2λbπ − π
93
4tH tL
[α (tL − tH ) + tH ]
Hence, I need to show that:
2λ2 bπ + λ2 π 2 + 2λbπ − π
4tH tL
≤0
[α (tL − tH ) + tH ]
(133)
From assumption A2, I know that:
4tH tL
≥ λ2 π + 2λb + 2λ2 b
α (tL − tH ) + tH
Thus, if the expression in equation 133 is negative for the smallest value of
also be negative for bigger values of that expression.
Plugging λ2 π + 2λb + 2λ2 b in for
4tH tL
α(tL −tH )+tH ,
4tH tL
α(tL −tH )+tH ,
then it will
I obtain:
�
�
2λ2 bπ + λ2 π 2 + 2λbπ − π λ2 π + 2λb + 2λ2 b
⇐⇒ 2λ2 bπ + λ2 π 2 + 2λbπ − λ2 π 2 − 2λbπ − 2λ2 bπ = 0
H tL
I obtain that under the smallest possible value of α(tL4t
−tH )+tH , B’s profits are the same under no
2
2
H tL
tying and tying by platform A. For any value of α(tL4t
−tH )+tH > λ π + 2λb + 2λ b, platform B’s profits
decrease under A’s tying strategy.
A.10
Change in Number of Multi-Homing Users due to Tying
In order to derive the welfare implications of tying, I need to know whether the change in the number
of multi-homing users induced by the tying is positive or negative.
The change in the number of multi-homing users is given by:
ñM − nM
=
=
=
�
�
λ (b + π)
λ (b + π)
λb
λb
α
+ (1 − α)
− α
+ (1 − α)
−1
2tH
2tL
tH
tL
λ (π − b)
λ (π − b)
α
+ (1 − α)
+1
2tH
2tL
λ (π − b) [α (tL − tH ) + tH ]
+1
2tH tL
(134)
In order to show that ñM − nM > 0, I need to prove that:
λ (π − b) > −2
tH tL
α (tL − tH ) + tH
From assumption A2, I know that:
tH tL
λ [λπ + 2b (1 + λ)]
≥
α (tL − tH ) + tH
4
94
(135)
tH tL
Hence, inserting the smallest possible value for α(tL −t
makes sure that the right-hand side of
H )+tH
inequality 135 is the least negative, hence the biggest. If λ (π − b) is bigger than this expression, it
tH t L
t H tL
will also be bigger for any higher values of α(tL −t
. I thus insert λ[λπ+2b(1+λ)]
for α(tL −t
4
H )+tH
H )+tH
in inequality 135 and obtain:
λπ − λb + 2
�
�
λ2 π + 2λb + 2λ2 b
4
λ2 π
λπ +
+ λ2 b
2
>
0
>
0
(136)
Since the expression in equation 136 is always positive, I have shown that the number of multi-homers
increases under tying, i.e. ñM − nM > 0.
A.11
Change in Total Welfare due to Tying
The change in total welfare derived in equation 27 is given by:
�W
=
W̃ − W
=
(ñM − nM ) [λ (b + π)]
�ˆ
ˆ
α−ñM,H
tH xdx +
−
+
0
�ˆ
(1−α)−ñM,L
tL xdx + ñM,H tH + ñM,L tL
0
α−NB,H
tH xdx +
0
ˆ
(1−α)−NB,L
tL xdx +
0
ˆ
�
α−NA,H
tH xdx +
0
ˆ
(1−α)−NA,L
tL xdx + nM,H tH + nM,L tL
0
This formula can be manipulated to:
�W
=
−
(ñM − nM ) [λ (b + π)]
�ˆ
ˆ
α−ñM,H
tH xdx −
0
α−NB,H
tH xdx −
0
α−NA,H
ˆ
tH xdx
0
−
�ˆ
−
[((ñM − ñM,L ) − (nM − nM,L )) tH + (ñM,L − nM,L ) tL ]
(1−α)−ñM,L
tL xdx −
0
ˆ
(1−α)−NB,L
tL xdx −
0
ˆ
�
(1−α)−NA,L
tL xdx
0
�
This expression is equivalent to:
�W
=
(ñM − nM ) [λ (b + π) − tH ] −
−
�ˆ
−
[(ñM,L − nM,L ) (tL − tH )]
0
(1−α)−ñM,L
tL xdx −
ˆ
0
�ˆ
α−ñM,H
tH xdx −
0
(1−α)−NB,L
tL xdx −
95
ˆ
0
ˆ
α−NB,H
0
tH xdx −
(1−α)−NA,L
tL xdx
�
ˆ
0
α−NA,H
tH xdx
�
�
Now I need to show that this change in total welfare due to tying is positive. I will analyze the different
terms in turn.
• Firstly, it holds that (ñM − nM ) [λ (b + π) − tH ] > 0. As has been shown in Appendix A.10,
ñM − nM > 0. Furthermore, since assumption A1 ensures that tH < λb, [λ (b + π) − tH ] > 0.
�´
�
´ α−NB,H
´ α−NA,H
α−ñ
• Secondly, 0 M,H tH xdx − 0
tH xdx − 0
tH xdx < 0 since ñM,H = α λ(b+π)
>
2tH
NB,H = NA,H = α 2tλbH .
�´
�
´ (1−α)−NB,L
´ (1−α)−NA,L
(1−α)−ñM,L
• Thirdly, 0
tL xdx − 0
tL xdx − 0
tL xdx < 0 since ñM,L = (1 − α) λ(b+π)
>
2tL
NB,L = NA,L = (1 − α) 2tλbL .
• Fourthly, [(ñM,L − nM,L ) (tL − tH )] < 0. This is true because tH − tL < 0 by definition of low
and high transportation costs. Furthermore, it holds that ñM,L − nM,L > 0 since
ñM,L = ÑB,L
λ (b + π)
λb
> NB,L = (1 − α)
≥ nM,L = (1 − α)
= (1 − α)
2tL
2tL
�
�
λb
−1 .
tL
Thus, the change in total welfare due to tying is positive in my model.
A.12
Change in User Surplus due to Tying
In order to calculate the change in user surplus due to tying, I first need to derive user surplus absent
tying as well as user surplus under tying.
In the no tying situation analyzed in section 4.3.1, A prices good M so that all surplus from multihoming high transportation cost users is extracted.
Hence, of the high transportation cost users, only those single-homing on A or single-homing on B get
any surplus. The only difference between a high transportation cost user who is indifferent between
single-homing on A and multi-homing (and who hence gets a surplus of 0) and a high transportation
cost user single-homing on A is the difference in transportation costs. Similarly, the only difference
between a high transportation cost user who is indifferent between single-homing on B and multihoming (and who hence gets a surplus of 0) and a high transportation cost user single-homing on B is
the difference in transportation costs. This implies that the total user surplus of high transportation
cost users absent tying, which I denote by U SH , is given by:
U SH
=
ˆ
α−NB,H
tH xdx +
0
ˆ
α−NA,H
tH xdx.
0
Low transportation cost users all get positive surplus. The difference between a multi-homing high
transportation cost user (who gets a surplus of 0) and a multi-homing low transportation cost user
is the difference in transportation costs. Hence, every multi-homing low transportation cost user gets
a surplus of tH − tL . In addition, the only difference between a low transportation cost user who is
indifferent between single-homing on A and multi-homing (and who hence gets a surplus of tH −tL ) and
a low transportation cost user single-homing on A is the difference in transportation costs. Similarly,
the only difference between a low transportation cost user who is indifferent between single-homing
96
on B and multi-homing (and who hence gets a surplus of tH − tL ) and a low transportation cost
user single-homing on B is the difference in transportation costs. This implies that all (1 − α) low
transportation cost users get a surplus of tH − tL . Low transportation cost users single-homing on
platform i get additional surplus equal to the difference in transportation costs incurred by them and
low transportation cost users indifferent between single-homing on platform i and multi-homing. This
implies that total user surplus of low transportation cost users absent tying, which I denote by U SL ,
is given by:
U SL
=
ˆ
(1−α)−NB,L
tL xdx +
0
(1−α)−NA,L
ˆ
tL xdx + (1 − α) (tH − tL )
0
Hence, total user surplus under no tying, U S, is equal to:
US
US
=
ˆ
α−NB,H
tH xdx +
0
+
ˆ
=
U SH + U SL
α−NA,H
tH xdx +
0
ˆ
(1−α)−NB,L
tL xdx +
0
ˆ
(1−α)−NA,L
tL xdx
0
(1 − α) (tH − tL )
Now I need to derive user surplus in the tying situation analyzed in section 4.3.2.
In the tying situation, A prices the bundle of good M and access to platform A so that all users buy
and hence all surplus from multi-homing high transportation cost users is extracted.
Thus, of the high transportation cost users, only those single-homing on A get any surplus. The
only difference between a high transportation cost user who is indifferent between single-homing on
A and multi-homing (and who hence gets a surplus of 0) and a high transportation cost user singlehoming on A is the difference in transportation costs. This implies that the total user surplus of high
transportation cost users under tying is given by:
U˜S H
=
ˆ
α−ñM,H
tH xdx
0
Just as under no tying, low transportation cost users also all get positive surplus under tying. The
difference between a multi-homing high transportation cost user (who gets a surplus of 0) and a
multi-homing low transportation cost user is the difference in transportation costs. Hence, every
multi-homing low transportation cost user gets a surplus of tH − tL . In addition, the only difference
between a low transportation cost user who is indifferent between single-homing on A and multihoming (and who hence gets a surplus of tH − tL ) and a low transportation cost user single-homing on
A is the difference in transportation costs. This implies that all (1 − α) low transportation cost users
get a surplus of tH − tL . Low transportation cost users single-homing on platform A get additional
surplus equal to the difference in transportation costs incurred by them and low transportation cost
97
users indifferent between single-homing on platform A and multi-homing. This implies that total user
surplus of low transportation cost users under tying is given by:
U˜S L
(1−α)−ñM,L
ˆ
=
tL xdx + (1 − α) (tH − tL )
0
Hence, total user surplus under tying is equal to:
U˜S
ˆ
=
U˜S
=
tH xdx +
ˆ
α−ñM,H
0
U˜S H + U˜S L
(1−α)−ñM,L
tL xdx + (1 − α) (tH − tL )
0
Lastly, I need to compare user surplus under tying with user surplus under no tying.
The change in user surplus due to tying is given by:
�U S
=
=
U˜S − U S
�ˆ
α−ñM,H
0
+
�ˆ
tH xdx −
ˆ
α−NB,H
(1−α)−ñM,L
tL xdx −
0
tH xdx −
0
ˆ
ˆ
α−NA,H
(1−α)−NB,L
tL xdx −
0
tH xdx
0
ˆ
�
(1−α)−NA,L
tL xdx
0
�
Now I need to show that this change in user surplus due to tying is negative. I will analyze the different
terms in turn.
• Firstly,
NB,H =
�´
α−ñM,H
tH xdx
0
NA,H = α 2tλbH .
´ α−NB,H
tH xdx −
´ α−NA,H
´ (1−α)−NB,L
tL xdx −
0
(1−α)−ñM,L
tL xdx
0
λ(b+π)
> NB,L = NA,L
2tL
• Secondly,
(1 − α)
�´
−
−
0
= (1 − α)
λb
2tL .
0
�
tH xdx < 0 since ñM,H = α λ(b+π)
>
2tH
´ (1−α)−NA,L
0
tL xdx
�
< 0 since ñM,L =
Thus, the change in user surplus due to tying is negative in my model. This is the same outcome as
in Choi’s (2010) model.
A.13
Change in Content Provider Surplus due to Tying
In order to calculate the change in content provider surplus due to tying, I first need to derive content
provider surplus under no tying as well as content provider surplus under tying.
98
Under no tying, recall that equation 10 gives the optimal prices charged by platforms A and B to
content providers absent tying. These are given by:
��
�
�
λb
λb
p∗i = πn∗i = π 1 − α
+ (1 − α)
2tH
2tL
There are λ exclusive content providers on A and B respectively. Hence, there is a total of 2λ exclusive
content providers whose total surplus CP SE is given by:
CP SE
=
=
2λπ (NA − nA )
�
�
λb
λb
2λπ α
+ (1 − α)
−1
tH
tL
There are 1−λ non-exclusive content providers who, in the equilibrium absent tying analyzed in section
4.2, multi-home and hence reach all users.
Their total surplus CP SN E is hence given by:
CP SN E
=
=
=
=
(1 − λ) [π − (πn∗A + πn∗B )]
(1 − λ) [π (1 − n∗A − n∗B )]
(1 − λ) πn∗M
�
�
λb
λb
+ (1 − α)
−1
(1 − λ) π α
tH
tL
Total content provider surplus absent tying is consequently equal to:
CP S
⇐⇒ CP S
=
=
CP SE + CP SN E
�
�
λb
λb
(1 + λ) π α
+ (1 − α)
−1
tH
tL
From Assumption A1, I know that tL < tH < λb. This implies that CP S > 0.
Under tying, as analyzed in section 4.3.2, platform A charges a price p̃∗A = π to content providers
while platform B charges a price of p̃∗B = π ÑB∗ to content providers. Non-exclusive content (1 − λ) is
only present on platform A. The fact that under tying there is no content duplication across platforms
allows platforms to extract all surplus from content providers.
The surplus of λ exclusive content providers and (1 − λ) non-exclusive content providers on platform
A is given by:
99
˜ SA
CP
=
[λ + (1 − λ)] (π − π)
=
0
The surplus of λ exclusive content providers on platform B is given by:
˜ SB
CP
=
=
�
�
λ π ÑB∗ − π ÑB∗
0
Hence, tying decreases content provider surplus in my model. This is due to the fact that, even though
an increased number of multi-homers increases the benefits accruing to exclusive content providers,
non-exclusive content providers no longer multi-home, which in turn enables platforms to extract all
content provider surplus.
A.14
Profit Maximization of Platform A under Tying with No MultiHoming
Platform A’s profits in this tying scenario are given by:
Π̃M
=
=
π ÑA + q̃A ÑA
�
�
�
�
v + b − q̃A
v + b − q̃A
v + b − q̃A
v + b − q̃A
π α
+ (1 − α)
+ q̃A α
+ (1 − α)
(137)
tH
tL
tH
tL
The first order condition with respect to q̃A yields:
−α
π
π
v
v
b
b
q̃A
q̃A
− (1 − α)
+α
+ (1 − α)
+α
+ (1 − α)
− 2α
− 2 (1 − α)
=0
tH
tL
tH
tL
tH
tL
tH
tL
⇐⇒
�
1
1
α
+ (1 − α)
tH
tL
⇐⇒ q̃A =
�
q̃A = α
�
v+b−π
2tH
�
+ (1 − α)
�
v+b−π
2tL
�
� �
�
�
��
tH tL
v+b−π
v+b−π
α
+ (1 − α)
α (tL − tH ) + tH
2tH
2tL
∗
q̃A
=
v+b−π
2
(138)
The second order derivative of A’s profits under tying on the user side with respect to q̃A is negative,
∗
hence at q̃A
= v+b−π
there is a maximum:
2
∂ 2 Π̃A
2
2
− (1 − α)
<0
2 = −α t
∂ q̃A
t
H
L
100