Compatibility, Intellectual Property, Innovation and
Welfare in Durable Goods Markets with Network
E¤ects
Thanos Athanasopoulos1
March 6 20162
Abstract
Competition Authorities consider market leaders’refusals to support compatibility with
competitors as a potential abuse of dominance with detrimental e¤ects on consumer welfare
and competition. A prime example is the 2008 European Commission case against Microsoft
regarding its refusal to support compatibility of its O¢ ce software product with those of
competitors. This paper investigates dominant …rms’approach towards the compatibility of
their durable network goods with that of a future innovative rival in the presence of overlapping generations of forward-looking consumers and the welfare e¤ects from dominant …rms’
refusals to support compatibility. I consider sequential, substitutable product innovations,
where a rival can build on a dominant …rm’s existing knowledge. I …nd that in the limiting case when the market leader’s distribution of future innovation statewise dominates the
rival’s, dominant …rms commit to support future compatibility with the rivals’future innovative products, while when the probability of the dominant …rm is more innovative than
the rival is relatively high, credible dominant …rms currently announce they will support
compatibility with the smaller rival in the future. On the normative side, future incompatible networks increase all groups ex-post surplus when the dominant …rm lacks commitment
power, while if it currently chooses to be incompatible in the future, this may lead to speculations regarding its lack of future innovative ideas but leads to incompatible future networks
1
Department of Economics; University of Warwick.
Email address: A.Athanasopoulos.1@warwick.ac.uk.
2
I would like to express my gratitude to Claudio Mezzetti and Daniel Sgroi, Joseph Harrington, Martin
Peitz, Dan Bernhardt, Guillem Ordonez, participants’comments during presentations in the CRESSE Conference 2014, in the Royal Economics Society PhD Meetings and Job Market (2015), in the EARIE 2015 as
well as in the Department of Economics at the University of Warwick. All the errors in this work are solely
mine.
1
and a higher degree of competition that increases all groups’ expected consumer surplus,
especially when network e¤ects are strong.
1
Introduction
Should dominant …rms with durable network goods like markets for the applications in the
software market industry have the obligation to provide technical compatibility information
to direct competitors? This fundamental question lies at the intersection of competition and
intellectual property law and di¤erent countries give di¤erent answers.
In the European Union, market leaders must provide interoperability3 information to
rivals and failure to do so is a potential violation of Article 102 (ex article 82) of the European competition law.4 In a nutshell, a refusal to license Intellectual Property may, in
itself, constitute a breach of Article 102 if all the following conditions are met: a) access is
indispensable for carrying on a particular business, b) it results in the elimination of competition on a secondary market and c) it may lead to consumer harm.5 A famous example
comes from the 2008 European Commission case against Microsoft, which was related to the
…rm’s refusal to provide competitors technical information about its O¢ ce suite so that they
could craft interoperable software.6 The case followed a complaint7 from …rms-members of
the ECIS [European Committee of Interoperable Systems] and was put on hold in December
2009 after Microsoft’s commitment to comply.8
In contrast, in the United States, a more laissez faire competition law is favoured. For
example, Thomas Barnett of the United States Department of Justice argues that: "U.S.
3
We will use the terms interoperability and compatibility interchangeably throughout the paper.
See http://ec.europa.eu/competition/antitrust/legislation/handbook_vol_1_en.pdf
5
See http://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:52009XC0224(01)&from=EN
6
See http://europa.eu/rapid/press-release_MEMO-08-19_en.htm
4
7
8
See www.techhive.com/article/124813/article.html
See http://europa.eu/rapid/press-release_IP-09-1941_en.htm?locale=en
2
courts recognize the potential bene…ts to consumers when a company, including a dominant
company, makes unilateral business decisions, for example to add features to its popular
products or license its intellectual property to rivals, or to refuse to do so".9 Indeed, the
U.S antitrust authorities conclude that "antitrust liability for mere unilateral, unconditional
refusal to license patents will not play a meaningful part in the interface between patent
rights and antitrust protections".10
In this article I investigate dominant …rms’approaches towards interoperability and the
welfare e¤ects of refusals to supply interoperability that may occur in a laissez faire economy.
More precisely, my work provides answers to the following questions: When do market leaders
block interoperability with a rival future innovator and under what conditions would they
support compatibility? If there is incompatibility, does this de-facto mean that it is socially
undesirable? Could a laissez faire market converge to interoperability when it is socially
e¢ cient? Are consumers better-o¤ in an economy that mandates compatibility?
To answer these questions, I built a sequential game in which an innovative rival initially
decides whether to invest in product quality. The rival’s choice depends on the importance of
her idea and the dominant …rm’s future support or refusal to supply compatibility information due to the leader’s large installed base of consumers. This model …ts a common pattern
in durable, technology goods markets, where a smaller rival may have valuable ideas emerging as follow-on, non-drastic substitutable innovations, after the dominant …rm’s invention
hits the market in a Schumpeterian scenario of creative destruction. In the latter stage, the
dominant …rm chooses its prices for its current product and whether to support compatibility
with its competitor’s future product. It also may wish to invest in further improving product
quality in the future period, where the …rms’R&D processes are realised and competitors
set prices. I …nd that independently of the …rms’ability to exercise price discrimination, the
dominant …rm chooses to support compatibility with the competitor’s potentially innovative
future product if the probability distribution regarding the innovative step of its future prod9
10
See http://uk.reuters.com/article/2007/09/17/microsoft-eu-usa-idUKN1734095320070917
See http://www.justice.gov/atr/public/reports/236681_chapter7.htm
3
uct dominates the rival’s. A relatively less innovative dominant …rm rejects compatibility but
suprisingly, incompatible future networks increase all consumer groups’expected consumer
surplus especially when network e¤ects are strong, as future competition is …ercer when
incompatibility prevails. Our conclusions cast doubts as to whether mandatory interoperability, while trying to support competition, allow technological advancement and protect
consumers from abusive behaviour, may actually distort the market and lead to both socially
undesirable results and customers’harm.
This article is organized as follows: I next discuss related literature. Section 2 presents
the model. In section 3, I characterize equilibrium outcomes when the economy operates
under a laissez faire competition law toward Intellectual Property Rights holders. I then
look at the e¤ects of dominant …rms’refusals to supply compatibility on consumer surplus.
Section 4 discusses applications and concludes.
Related Literature
This work contributes to the literature regarding …rms’incentives toward compatibility with
their competitors when network e¤ects are present. In a seminal article, Katz and Shapiro
(1985) show that …rms with a larger installed base prefer to be incompatible with their rivals. In the same vein, Cremer, Rey and Tirole (2000) analyze competition between Internet
backbone providers and predict that a dominant …rm may want to reduce the degree of
compatibility with smaller market players. Similar results appear in Chen, Doraszelski and
Harrington (2009), who consider a dynamic setting with product compatibility and market
dominance. They …nd that if a …rm gets a larger market share, it may make its product
incompatible. If, instead, …rms have similar installed bases, they make their products interoperable to expand the market. In a static environment, Viecens (2009) distinguishes
between direct and indirect network e¤ects by studying platform competition between two
…rms where users buy a platform and its compatible applications. By allowing for applications to be substitutes, complements or independent, she considers compatibility in two
4
dimensions: 1) compatibility of the complementary good, which she calls compatibility in
applications, 2) inter-network compatibility with direct network externalities. She …nds that
the dominant …rm never promotes compatibility in applications but both …rms …nd internetwork compatibility pro…table. In contrast to this literature, I focus on durable goods with
direct network e¤ects. Both durability and network externalities are important features of
most software products that are at the heart of this compatibility question. Contrary to
the literature, I consider improvements in product quality and …nd that the dominant …rm
may support compatibility when its future ideas dominate the competitors’future innovative step. When the probability that the dominant …rm is less innovative than the rival is
relatively large, market leaders reject compatibility with the smaller rival.
Absent innovative activity and although the literature has generically supported the
view that incompatibility reduces welfare, as in Economides (2006), recent work in Chen,
Doraszelski and Harrington (2009) has shown that in the long-run, a policy of mandatory
compatibility is not preferable for consumers. Viecens (2009) concludes that compatibility in
the applications may be harmful for users and social welfare, particularly when asymmetries
are strong. Moreover, inter-network compatibility should not be supported by consumers.
When …rms can innovate and durable network goods are considered, I …nd that compulsory
compatibility results in higher future expected prices because of the lower degree of competition compared to the laissez-faire economy and both current and future consumers bene…t
from future incompatible networks, especially when network e¤ects are strong.
In the literature on sequential innovation, Scotchmer (1991, 1996), Scotchmer and Green
(1996) and others study the case of single follow-on innovations. They focus on the breadth
and length of patents needed to secure the initial innovator’s incentives to innovate when
a second innovator threatens to innovate as well. They hold the view that patents for the
…rst innovator should last longer when a sequence of innovative activity is undertaken by
di¤erent …rms than when innovation is concentrated in one …rm. I am mainly interested in
the interplay between Intellectual Property Rights protection and …rms’behaviour towards
5
compatibility. In contrast to these articles, I …nd that the …rst innovator will voluntarily o¤er
compatibility to rivals because strategic pricing enables him to absorb more of the expected
future pro…t when he anticipates that the rival is less likely to come up with an innovative
product as valuable as its own.
2
The Model
My objective is to provide insights into how dominant …rms’ short-run compatibility and
pricing decisions regarding their durable network goods relate both to homogeneous, forwardlooking consumers, and to future products introduced by the rival. The industry I have in
mind is the market for computer software applications highlighted in the introduction.
Supply
In the two-date model, the sequence of events in the supply side is as follows: initially, the
dominant …rm has an installed base
0
of consumers and is marketing its product, which
improves the level of quality from the previously sold version of quality q0 to a higher level
q1 .11 The upgraded version of quality q1 is backward compatible, allowing its purchasers to
interact with the users of the old version of quality q0 . In contrast, forward incompatibility
prevents users of the initial version from editing and saving documents that are created with
the upgrade.12
At the beginning of date t=1, a risk neutral rival can choose to incur a …xed cost F
to create a future substitute product of quality q2 , which is distributed according to the
commonly known continuous cumulative distribution function
R,
which is de…ned in the
semi-closed interval (q1 ; q2 ]. At the end of date t=1, the market leader sets the prices for
his product of quality q1 while he may also potentially innovate in the future period, and
his future product quality q2D is distributed according to the privately known distribution
11
12
I follow Ellison and Fudenberg (2000) who also assume quality as a positive, real number.
See Ellison and Fudenberg (2000) for a paper with backward compatibility but forward incompatibility.
6
function
D;
which is de…ned in the closed interval [q1 ; q2 ]; and its investment cost is F0 . If the
dominant …rm has commitment power, it may also decide whether to support compatibility of
its current and potentially innovative future versions with the rival’s future product, which is
a binary decision. Otherwise, any announcement for its future action is perceived as credible
by consumers: Following Malueg and Schwartz (2006), I assume that compatibility requires
both parties’consent and cannot be achieved unilaterally using converters or adapters. In
addition, in order to avoid potentially collusive behaviour, licensing of Intellectual Property
is free.13
In a laissez faire market, the dominant …rm’s potential refusal to support compatibility
does not, per se, hinder innovation, as there is an alternative route that allows the rival to
innovate without using the dominant …rm’s network of existing customers. This assumption
accords with the Microsoft O¢ ce case highlighted in the introduction: Microsoft’s refusal to
o¤er compatibility did not, per se, prevent rivals from innovating as they could use the Open
Document Format, which could allow product innovation. On the other hand, compatibility
allows the smaller rival to use the dominant …rm’s network of existing consumers.
At date t=2 and if the dominant …rm lacked commitment power, …rms make their compatibility decisions based on the realised states of their R&D processes. The smaller competitor
sets its prices for its product while the dominant …rm is free to choose its pricing strategy if
it fails to innovate; that is, it may either choose to set prices only at t=1 or change its prices
in the future period. Consistent with software applications, I assume that the marginal cost
of production is zero for all versions. Also note that I will consider both the cases when …rms
have the power to price discriminate between the di¤erent consumer classes and when they
cannot.
13
See Malueg and Schwartz (2006).
7
Demand
Consumers are identical and have a per period unitary demand. Initially, there is a mass
0
of customers in the economy who have purchased the dominant …rm’s product of quality q0
at a past date (t=0), and new customers arrive in ‡ows of measure
t
at dates t=1,2. In
order to exclude less interesting cases but also focus on realistic markets, I assume that
0
+
1
>2
2
(*)
that is, I consider a relatively mature industry.
At the end of date t=1, a measure
1
of new customers observes the dominant …rm’s
prices for its products of quality q0 and q1 . Their utility is linear in income and partially
dependent on direct network e¤ects captured by a parameter , while they incur a cost c to
learn how to use a product. Thus, if they purchase the product of quality q1 and because of
its backward compatibility with the old version of quality q0 , they join a network of maximum
size at date t=1 and their total discounted utility is:
q1 + (
where
0
+
1
0
+
1)
c
p11 + EV;
is the market size at t=1, p11 is the dominant …rm’s price, where the …rst
and second subscripts denote the time and the consumers’cohort, respectively and
is the
common discount factor for all the agents in the economy and thus, EV is their net expected
discounted date t=2 utility.14
A measure
0
of old customers owns the product of quality q0 and observes the market
leader’s upgrade price p10 for his product q1 : If a customer buys it, her total discounted
bene…t is
q1 + (
0
+
1)
cu
14
p10 + EV;
Note that the utility function may not be necessarily linear in income (any monotonic transformation
would su¢ ce).
8
where cu is the additional adoption cost she needs to incur (cu < c), while if she sticks to q0 ,
her total discounted utility is
q0 +
0 x0
+
1 x1
0
+ EV :
A date t=1 customer’s overall bene…t depends on her forecast of how other customers make
purchase decisions.
At date t=2, a measure
0
+
1
of old consumers observes the competitors’ prices. If
a customer that belongs to this group keeps the product of quality q1 and because of its
forward incompatibility with any new product of quality q2 ; her utility is
V = q1 +
2 x2
+ (
0
+
0
1 )x1 ;
0
where x2 and x1 are the new and old date t=2 customers’fractions that also own q1 at date
t=2, respectively. If she purchases a product of higher quality q2i from the dominant or the
rival …rm in the presence of compatibility, her net utility is
V = q2i +
cu
p21 ; i = D; R
due to backward compatibility of the product of quality q2 , after normalizing the date t=2
market size to unity where D,R stand for the dominant and the rival …rm, respectively. If
compatibility is not supported, her utility by purchasing q2i is
q2i +
where 1
x2 and 1
2 (1
x2 ) + (
0
+
1 )(1
0
x1 )
cu
0
p21 ; i = D; R;
0
x1 are the new and old date t=2 customers’fractions that also purchase
q2i at date t=2, respectively. Although old consumers’ coordination problem has multiple
equilibria, I assume that they coordinate on the Pareto optimum.
9
A measure
2
of new consumers also observes the competitors’prices. If they purchase
the dominant …rm’s product of quality q1 , their utility is
q1 +
2 x2
+ (
0
where x2 and x1 are the new ( 2 ) and old (
0
0
+
1 )x1
1)
0+
c
p12 ;
date 2 customers’fractions that also own
q1 , respectively. When the dominant …rm does not support compatibility with the rival’s
new product of quality q2 , their bene…t from getting the product of quality q2i is
q2i +
2 (1
x2 ) + (
0
+
1 )(1
0
x1 )
c
0
p22 ; i = D; R;
as they form a network only with those consumers who also own it. If they buy the product
of quality q2i and compatibility is present, their utility is
q2i +
c
p22
due to the product compatibility with any other product in the market. New customers’
purchasing decision resembles a coordination game and following the literature, I assume
that they behave as a single player.15 All consumers make their purchasing decisions simultaneously and prefer a new product rather than an older version when they gain the same
net utility from each of these two choices.
3
Market outcome
Laissez faire Market
Independently of the competitors’ability to exercise price discrimination between the di¤erent consumer groups:
15
See Ellison and Fudenberg (2000).
10
Proposition 1 (a) The dominant …rm currently announces that it will support compatibility
if the probability of being more innovative than the rival is relatively large and commits
to supporting compatibility in the limiting scenario that it knows with certainty it is more
innovative than the rival. (b) When the probability that the dominant …rm is more innovative
than the rival is relatively small, the dominant …rm rejects compatibility.
Proof. See the Appendix
Think …rst of the states when the dominant …rm’s new product is more innovative than
the rival’s with certainty. The dominant …rm currently supports compatibility when …rms
lack the power to price discriminate and the installed base of consumers
0
is large enough
to allow the dominant …rm to currently serve all date t=1 consumers. This happens as the
lesser degree of future competition between the competitors’ products when compatibility
is present allows the dominant …rm to bene…t from higher future prices, while its current
revenue is identical in the presence of compatible or incompatible future networks. The
dominant …rm faces a trade-o¤ when its optimal choice is to currently serve only the new
date t=1 consumers: although the lower degree of future competition increases its future
revenue under compatible networks, its current price to the measure
1
of new date t=1
consumers is higher if it refuses to be compatible with the smaller rival. Thus, it still
supports compatibility when the former e¤ect of higher expected pro…t ouweighs the latter
of the decreased current bene…t.16
When the smaller competitor is more innovative than the market leader with certainty,
the dominant …rm is always better-o¤ by currently refusing to be compatible. In the limiting
case when the dominant …rm lacks any innovative ideas, it can bene…t both from higher prices
at t=1 and potentially enjoy a positive expected payo¤ at date t=2. More precisely, if both
…rms lack the power to price discriminate between the consumer groups, the dominant …rm
may currently decide to serve either all or only the new date t=1 consumers, who can pay
more than the upgrade price that old date t=1 consumers are ready to pay. For a relatively
16
A similar condition applies when …rms have the power to price discriminate.
11
small number of the installed base of consumers
0;
it can currently charge the measure
1
of
new date t=1 consumers more under incompatible networks because of the higher expected
surplus that results from …ercer competition for any future product quality q2 . For a larger
installed base, the market leader can charge all date t=1 consumers more at date t=1 when
it refuses to be compatible, as it can currently charge a premium for less innovative future
states than in the economy mandating compatibility.
17 18
More precisely, if the dominant
…rm changes its prices at date t=2, an old date t=1 consumer’s net surplus in less innovative
future states is zero when compatible networks arise, as her optimal future choice either
after purchasing the product of quality q1 or after sticking to q0 is to purchase the product of
quality q2 and pay the date t=2 equilibrium price. Under incompatible networks, although
her optimal future choice after purchasing the product of quality q1 is to stick to it for
relatively less innovative future states, her alternative future payo¤ if she currently sticks to
the product of quality q0 is lower, as she purchases the product of quality q1 by paying the
equilibrium date t=2 price. Her net surplus in these states of the world is positive and leads
the dominant …rm to set a higher current price under incompatible networks.19 Note that if
the dominant …rm rejects to be compatible and decides to set prices both at t=1 and t=2,
it enjoys positive, rather than zero expected revenue under compatible networks, from the
measure
2
of new date t=2 consumers for less innovative states.
Overall, the dominant …rm commits to support compatibility when the random variable
q2D dominates the variable q2R with certainty. Otherwise, its alternatives are either to announce its future support to compatibility or currently follow the path of incompatibility,
as it knows that consumers will perceive lack of any announcement as lack of the dominant
…rm’s any future innovative ideas. Thus, it currently announces its support to future compatibility when its expected bene…t under compatible future networks for the states it is
17
Obviously, the dominant …rm can bene…t from both the old and new date t=1 consumers if it can price
discriminate betwen the di¤erent consumer groups.
18
A similar argument holds if the dominant …rm is less innovative and sells at t=2 a product of lower
physical quality q2 than the rival.
19
A similar argument holds when the dominant …rm chooses not to change its prices at date t=2.
12
more innovative than the rival outweighs its current loss from currently rejecting incompatibility due to the foregone current income. In particular, in a laissez faire market where …rms
cannot price discriminate between the di¤erent consumer groups, the dominant …rm decides
to announce future compatibility for values of the probability that it is more innovative than
the rival above a threshold that satisfy the following inequality:
Pr ob(q2D
+(
0
+
(
where q = q1 + (
1 )[Pr ob(q2D
0
+
0+
q2R )[ (
< q2R < q )(q1
1 ) Pr ob(q2R
1 ) + cu
< q )](q1
20
2.
0
+
1)
2 ]+
q2R + (
0
q2R + (
0
+
+
1)
1)
+ cu ))
2
+ cu )] > 0
Note that if the dominant …rm currently announces
it will support compatibility, date t=1 consumers in a laissez faire economy observe the price
currently set by the dominant …rm and can estimate the probability : For example, if the
dominant …rm chooses to serve all date t=1 consumers, the measure
0
+
1
of old date t=1
consumers can compare the current price
p10 =
+ (1
where
q+
1
cu +
Pr ob(q2R < q )[q1
) Pr ob[q2D < q2R < q )(q1
q2R + (
q2R + (
0
+
0
+
1)
1)
2
+ cu ]
+ cu ];
is the probability of the dominant …rm failing to innovate and
q = q1
q0 with
the price the dominant …rm would have chosen absent any announcement:
p10 =
q+
1
cu + Pr ob(q2R < q )[q1
20
q2R + (
0
+
1)
+ cu ]
There are similar conditions when …rms have the power to price discriminate between the di¤erent
consumer groups.
13
and this comparison allows them to understand the value of the probability : In the limit,
when the dominant …rm’s future product quality statewise dominates the rival’s with probability 1, its optimal date t=1 choice is to commit to supporting compatibility at t=2.
Otherwise, the dominant …rm’s optimal choice is to announce its support to future compatibility and passes the probability of being more innovative into the date t=1 price charged
to consumers, who understand the relative distribution functions of the future competitors.
When the dominant …rm is less likely to be more innovative than the rival, the dominant
…rm refuses to be compatible.
Unlike the undisputable decision to currently refuse compatibility when it is less likely to
be innovative than the rival, the dominant …rm faces a trade-o¤ when it decides whether to
change its prices at t=2. While it bene…ts from setting prices twice because of the current
higher revenue from the measure
revenue from the measure
2
1
of new date t=1 consumers as well as the future expected
of new date t=2 consumers, setting prices only at t=1 allows
this …rm to charge the old date t=1 consumers more. In particular, by setting prices both
at dates t=1 and t=2, it can exploit the higher degree of future competition in relatively
less innovative future states and charge the measure
1
of new date t=1 consumers more in
the present market. It also enjoys positive expected revenue from the measure
2
of new
date t=2 consumers for less innovative future states. On the other hand, the dominant …rm
bene…ts from setting a higher current price to the measure
0
of old date t=1 consumers
when it only sets prices at t=1, as a consumer’s alternative expected payo¤ from sticking
to the product of quality q0 is lower for less innovative states compared to the case it sets
prices twice and thus, the dominant …rm can charge her more today to purchase its version
of quality q1 .
From the discussion above, it is reasonable to infer that the dominant …rm’s current
choice of incompatibility may lead to speculations about its lack of any innovative ideas.
But even so, do incompatible networks both when the dominant …rm can commit and when
it lacks this power necessarily harm current and future consumers?
14
4
Welfare
The following proposition summarises the welfare e¤ects from dominant …rms’ refusals to
support compatibility and is independent of the competitors’ability to price discriminate:
Proposition 2 (a) When the dominant …rm lacks commitment power, all consumer groups
are better-o¤ when the dominant …rm fails to innovate and incompatible networks arise
at t=2, (b) When the dominant …rm currently chooses to be incompatible and for strong
network e¤ects, (1) incompatible networks increase both the new ( 2 ) and old ( 0 ) date t=2
consumers’ expected surplus when the probability that the rival’s future product quality is
above a threshold is relatively high and the dominant …rm decides to set prices both at t=1
and t=2. (2) old date t=1 consumers’ expected surplus may be higher when incompatible
networks arise and the dominant …rm decides to set prices only at t=1.
Proof. See the Appendix
When the dominant …rm currently announces its support to future compatibility, incompatible future networks increase all consumer groups ex-post surplus when the dominant …rm
fails to innovate at t=2. The rationale is that independently of the competitor’s product
quality, old date t=2 consumers are better-o¤ at t=2 under incompatible networks, as …ercer
competition increases their surplus. In particular, old date t=1 consumers are better-o¤ when
incompatible networks arise when their date t=2 bene…t from incompatibility surpasses their
loss due to the higher price already paid at t=1 compared to the economy mandating compatibility.21 New date t=2 consumers are always better-o¤ under incompatible networks
unless when the rival’s product is more innovative and …rms can price discriminate, in which
case they are indi¤erent between compatible and incompatible networks.
When network e¤ects are strong and the dominant …rm chooses the path of incompatibility at t=1, all consumers’expected surplus may be greater when incompatible networks
arise. In particular, if the dominant …rm’s optimal choice is to change its prices at t=2
21
A similar argument holds for the new date t=1 consumers.
15
and …rms lack the power to price discriminate between the di¤erent consumer classes, both
the measures
0
and
2
of old and new future expected consumers’surplus is higher under
incompatible networks when there is a relatively high probability of reaching more innovative future states, which allow these customers to enjoy higher surplus when compatibility is
rejected because of the …ercer future competition, while compatible networks increase their
surplus for less innovative states. When …rms can exercise price discrimination, incompatible
networks still increase
0
customers’surplus in more innovative future states and new date
t=2 consumers are always better-o¤ provided that less innovative states are reached with a
non-zero probability. If the dominant …rm announces its support to future compatibility but
incompatible networks arise, all consumer groups are ex-post better-o¤. Thus, both old and
new date t=2 consumers may be better-o¤ when incompatible networks arise.
These results are very important, as they indicate that a policy of mandatory compatibility results in consumer harm for all consumer classes when network e¤ects are strong and the
probability of reaching more innovative future products is relatively large. So, when network
e¤ects are not negligible like in software markets, a laissez faire economy is likely to bene…t
all consumer groups. In fact, when the probability distributions of future innovations place a
relatively high weight on rather "important innovation", future and current consumers both
bene…t from incompatible networks.
When network e¤ects are weak, I obtain similar results although it is no longer straightforward that future consumers are always better-o¤ when incompatible networks arise. In
particular, all consumer groups’surplus is higher in more innovative future states, as competitive forces decrease equilibrium future prices but for a smaller inventive step, compatibility
leads to higher surplus.
16
5
Applications/ Discussion/ Future Research
This article analyses dominant …rms’behaviour towards the compatibility of their durable
network goods and the welfare e¤ects from their refusals to support compatibility. By using
a sequential game, we give a smaller rival the ability to build on innovations previously
introduced by the market leader.
The …rst new result is that …rms with innovative ideas with more important relative magnitude compared to their competitors, currently embrace compatibility when their bene…t
from the lower degree of future competition that allows them to charge more in the future
outweighs the potential current loss from the lower price set to existing consumers. Dominant …rms with less innovative future ideas choose the path of incompatibility. In the limit,
dominant …rms who lack any future ideas, may decide to change their prices in the future.
Our normative analysis yields new results in industries where network e¤ects play an
important role: I showed that when there is an alternative process that allows product
innovation, incompatibility bene…ts both current and future consumers when network e¤ects
are strong. The rationale behind this result is that future consumers bene…t from the …ercer
degree of future competition that arises under incompatible network. But this is not the
whole story. Current consumers also bene…t from incompatibille future networks when the
smaller competitor’s future product quality is likely to be above a threshold. In such a
case, current consumers’future expected surplus is higher under incompatibility when their
bene…t for more innovative future states outweighs their loss in less innovative future states.
The model applies in the scenario highlighted in the introduction: Microsoft sold Microsoft O¢ ce in 2007 and denied to support compatibility with its competitor’s products.
Corel’s substitute product followed as well as the European Commission’s mandate to the
technology giant for compatibility. I showed that when network e¤ects are strong, as it is
considered in software markets, this and similar mandates may harm current and future
consumers.
The policy implication of these …ndings is that Competition Authorities should investigate
17
whether mandating compatibility may not necessarily bene…t consumers or even harm them.
Instead, markets that allow unilateral refusals to supply interoperability information improve
consumers’ welfare in industries that involve network externalities. More precisely, in an
economy where network e¤ects are strong, all consumers are more likely to bene…t from
incompatible networks, as the higher degree of future competition increases their surplus in
more innovative states.
Nevertheless, there are a number of issues that are important and are not addressed in
this article. Perhaps the most intriguing would be to see how the results are generalised
in a scenario when …rms’annoucements are perceived by consumers as credible with some
probability and test empirically the predictions of the model. It may also be interesting
to study the competitors’interoperability/investment decisions in the presence of stochastic
demand and innovation.
18
6
Appendix
6.1
Proof of Proposition 1
(a) Strong network e¤ects/ The dominant …rm’s future product is more innovative than the
rival’s.
Compatibility/Price Discrimination
Incompatibility
No price discrimination
Compatibility
At t=2, the dominant …rm sells a product q2D , which is superior than the rival’s q2R :
New date t=2 consumers purchase the product q2D and they are ready to pay a price such
that:
q2D +
c
p22D
q2R +
c
p22R
where p22D ; p22R are the dominant and the rival’s date t=2 prices, respectively.
An old date t=2 consumer purchases the product q2D when
q2D +
cu
p22D
maxfq2R +
cu
p22R ; q1 + (
0
+
1 )g:
When …rms lack the power to price discriminate, the dominant …rm’s date t=2 price is
p22D =
00
q = q2D
q2R (p2R = 0) and all consumers purchase it.
Going back to period t=1, an old date t=1 consumer decides to purchase the dominant
…rm’s product of quality q1 instead of sticking to q0 when:
q1 + (
0
+
1)
cu + q 2 +
cu
p22D
19
p10
q0 +
0
+ q2 +
cu
p22D ;
00
where p22D =
q : A new date t=1 customer purchases the product of quality q1 , given the
price p10 set by the dominant …rm when:
q1 + (
+
0
1)
c + q2D +
cu
p22D
p10
0:
Thus, the dominant …rm may choose to serve all date t=1 consumers by setting a price
p10 =
q+
1
cu (where
a price p10 = q1 + (
0
+
q = q1
1)
q0 ) or only the date t=1 new customers by setting
cu : A su¢ cient condition for the dominant
c + q2R +
…rm setting a price such that all date t=1 consumers purchase the product of quality q1 is:
(
0
+
1 )(
0
q +
1
cu )
1 [q1
which is satis…ed when the installed base
+ (
0
+
1)
c + q2R +
cu ];
(1)
is very large.
0
Incompatibility
At t=2, the dominant …rm sells a product q2D , which is superior than the rival’s q2R :
New date t=2 consumers purchase the product q2D and they are ready to pay a price such
that:
q2D + (
0
+
1 )(2x1
1)
c
p22D
q2R
c
p22R
where p22D ; p22R are the dominant and the rival’s date t=2 prices, respectively.
An old date t=2 consumer purchases the product q2D even when all other old date t=2
consumers purchase q2R or stick to q1 if:
q2D +
q2D +
2
cu
p22D
q2R + (
cu
p22D
q1 + (
0
0
0
+
+
1)
20
p22R ;
1 ):
Thus, the dominant …rm’s optimal price at t=2 is p22D =
and all date t=2 consumers purchase q2D :
cu
00
q +
2
( 0 + 1 ) (p22R = 0)
Going back to period t=1, an old date t=1 consumer decides to purchase the dominant
…rm’s product of quality q1 instead of sticking to q0 when:
q1 + (
0
+
1)
cu + q2 +
00
where p22D =
q +
(
2
cu
0
+
1 ):
p22D
p10
q0 +
0
+ q2 +
cu
p22D ;
A new date t=1 customer purchases the product of
quality q1 , given the price p10 set by the dominant …rm when:
q1 + (
0
+
1)
c + q2D +
cu
p22D
p10
0:
Thus, the dominant …rm may choose to serve all date t=1 consumers by setting a price
p10 =
q+
cu (where
1
a price p10 = q1 + (
0
+
q0 ) or only the date t=1 new customers by setting
q = q1
1)
c + q2R + 2
(
0
+
1)
cu : A su¢ cient condition for
the dominant …rm setting a price such that all date t=1 consumers purchase the product of
quality q1 is:
(
0
+
1 )(
0
q +
1
cu )
1 q1
+ (
which is satis…ed when the installed base
0
0
+
1)
c + q2R + 2
(
0
+
1)
cu :
(1)
is very large.
(b) The dominant …rm lacks innovative ideas
(a)Strong network e¤ects (
2
cu )
Price discrimination
At t=2, the rival sets the same price to any user, who holds the dominant …rm’s either
q0 or q1 :
Compatibility
Think about a consumer that belongs to the measure
0
of old date t=1 consumers when
the dominant …rm can change its price at date t=2. This consumer decides independently
21
of other customers any time that she potentially makes purchasing decisions. Thus, she
purchases the product of quality q1 when her total expected discounted payo¤ if she purchases
q1 , given the price p10 ; exceeds her total expected payo¤ from sticking to q0 :
q1 + (
where
0
+
1)
0
cu + q 2 +
q1 and p21 =
q = q2
cu
0
q +
p21
p10
q0 +
0
+ q2 +
cu
p21 ;
cu; is the date t=2 price they will face to purchase
2
q2 . Thus, the date t=1 price set to these consumers is:
p10 =
Think now of the measure
1
q+
1
cu :
of new date t=1 consumers. The dominant …rm’s optimal
price for its product of quality q1 is such that their total discounted expected payo¤ by
purchasing it is at least equal to their outside opportunity:
q1 + (
where p21 =
0
q +
2
0
+
1)
c + q2 +
cu
p21
p11
0;
cu and thus, the dominant …rm’s optimal price choice is:
p11 = q1 + (
0
+
1)
c + q1 +
(
0
+
1 ):
Note that the dominant …rm receives no revenue from the measure
2
of new date t=2
consumers.
Also note that the prices above also hold for the case when the dominant …rm only charges
prices at t=1.
Incompatibility
Let’s …rst think of the case where the dominant …rm sets prices both at t=1 and t=2. A
consumer that belongs to the measure
0
of old date t=1 consumers purchases the product
22
of quality q1 at date t=1 even if all others stick to q0 when, given the dominant …rm’s price
0
p10 , her total expected discounted payo¤ is at least equal to her total expected discounted
payo¤ from sticking to q0 :
q1 + (
1)
cu +
0
+
(q )(q1 +
where q = q1 + (
0
0
+
q0 +
+
states [q2 < q = q1 + (
1)
(q )(q1 + ) + [1
cu
+ cu
0+
2:
1 ) + cu
(q )][q2 +
p12 ) + [1
0
cu
(q )](q2 +
0
p21 ]
p10
0
cu
p21 );
Note that if she sticks to q0 and for less innovative
2 ],
she knows that everyone else keeps or purchases
the product of quality q1 and thus, she purchases it at t=2, by paying the equilibrium price
set to the measure
2
of new date t=2 consumers p12 = q1
q2 + (
0
+
1 ).
Thus, the
dominant …rm’s optimal price choice at date t=1, p10 ; is
p10 =
q+
cu +
1
(q )[(q1
q2 + (
0
+
1)
+ cu ]:
Note that a su¢ cient and necessary condition for this price to be higher than the price under
mandatory compatibility is that the probability of reaching the relatively less innovative
future states is non-zero.
Think of the measure
1
of new date t=1 consumers. The dominant …rm’s optimal price
p11 is such that their total discounted expected payo¤ by purchasing q1 at t=1 is at least
equal to their outside opportunity:
q1 + (
where p21 =
0
+
1)
0
q +
c+
(q )(q1 + ) + [1
(
2
0
+
1)
(q )](q2 +
cu
p21 )
p11
0;
cu ; and thus, the maximum price the dominant …rm
can charge them is:
p11 = q1 + (
0
+
1)
c+
(q )(q1 + ) + [1
23
(q )][q1 + 2 (
0
+
1 )]
=
q1 + (
+
0
1)
c + q1 +
(
0
+
1)
+
(q )
2
+ [1
(q )] (
0
+
1 )):
Note that this price is always greater than the optimal price the dominant …rm can charge
under an economy mandating compatibility (p11 = q1 + (
0
+
1)
c + q1 +
Let’s think now of the dominant …rm’s optimal price to the measure
0
(
0
+
1 )).
of old date t=1
consumers when it only sets prices at t=1.
A consumer that belongs to this group purchases the product of quality q1 even if all the
other members of her group stick to q0 if:
q1 + (
q0 +
0
0
+
1)
+
0
where p21 =
cu +
(q )[q1 + (
(q ) maxfq0 ; q1 + (
0
q+
2
(
0 + 1)
0
0
+
+
1 )]
1)
+ [1
cu
(q )][q2 +
0
p10 g + [1
0
cu
p21 ]
(q )][q2 +
cu
0
p10
0
p21 ]
cu . Note that the di¤erence compared to the case where
the dominant …rm sets prices both at t=1 and t=2 is that the measure
2
of new date t=2
consumers always purchase the product of quality q2 (their net surplus by getting q1 with
the date t=1 price p11 is negative). Thus, and although the measure
the measure
0
+
1
2
always purchases q2 ;
of old date t=2 consumers may or may not purchase q2 :Thus, the date
t=1 optimal price set by the dominant …rm is:
p10 =
q+
1
cu +
(q )[ q + (
0
+
1 )];
It is straightforward to see that a necessary and su¢ cient condition for this price to be higher
than the equilibrium price under compatibility is that the relatively less innovative states
0
are reached with non-zero probability [ (q ) > 0]:
Think of the measure
1
of new date t=1 consumers. The dominant …rm’s optimal price
p11 is such that their total discounted expected payo¤ by purchasing q1 at t=1 is at least
24
equal to their outside opportunity:
q1 + (
0
+
0
where p21 =
1)
c+
0
q +
[q )[q1 + (
2
(
1)
c+
0
+
+
0
1 )]
+ [1
(q )](q2 +
cu
0
p21 )
p11
0;
cu ; and thus, the maximum price the dominant …rm
1)
can charge them is:
p11 = q1 + (
0
+
q1 + (
0
+
1)
(q )[q1 + (
c + q1 +
(
0
0
+
+
1 )]
1)
+ [1
+ [1
(q )(q1 + 2 (
(q )] (
0
+
0
+
1 ))
=
1 )):
Note that a necessary and su¢ cient condition for the price to be higher than the optimal
price under compatibility is that more innovative states are reached with non-zero probability.
Also note that the optimal price set to the measure
1
of the new date t=1 consumers when
the dominant …rm only sets prices at t=1 is smaller than the scenario when the dominant …rm
charges prices twice when the less innovative states are reached with non-zero probability.
When the dominant …rm sets prices both at t=1 and t=2, its expected second period
revenue from the measure
2
of new date t=2 consumers is positive, as it receives posi-
tive revenue for less innovative future states, and thus, when these states are reached with
non-zero probability, the dominant …rm is better-o¤ by not supporting compatibility. The
dominant …rm is also better-o¤ by setting prices both at t=1 and t=2 instead of only at
t=1 to these consumers, as when it only sets price at t=1, it receives no revenue from these
consumers.
Thus, the dominant …rm is better-o¤ by setting price both at t=1 and t=2 when the
following condition is satis…ed:
2
(q )[q1
q2 + (
0
+
1 )]
+
1
(q )
2
+
0
(q )[q0
q2 + cu ] > 0;
or equivalently, it chooses to do so when its expected bene…t from the measures
25
2
and
1
outweighs the loss from the lower price to the measure
0:
No price discrimination Under an economy mandating compatibility, the rival …rm’s
0
only choice when network e¤ects are strong is to set a price p2 =
q +
2
cu and both
the new and old date t=2 consumers purchase it. Thus, the date t=1 optimal choices for the
dominant …rm are identical to its choices when the rival has the ability to price discriminate.
Thus, its optimal choices are:
p10 =
q+
1
cu
and
p11 = q1 + (
for the measures
0
and
1
0
+
1)
c + q1 +
(
0
+
1 );
of old and new date t=1 consumers, respectively.
When incompatible networks arise, there is also one price choice for the rival …rm, as its
optimal price choice is:
p2 =
0
q +
(
2
0
+
1)
cu
for the more innovative future states, and thus, it gains positive expected payo¤ by serving
all date t=2 consumers. Thus, the date t=1 optimal prices set by the dominant …rm are
identical to its price choices when the rival has the power to price disciminate between the
di¤erent consumer groups.
If the dominant …rm sets prices only at date t=1, the optimal prices set at date t=1 to
the measures
0
and
1
of olds and new date t=1 consumers are already calculated.
(b) When network e¤ects are weak (
to the measure
0
< cu ), think …rst of a consumer who belongs
2
of old date t=1 consumers when compatibility is present. Given the
dominant …rm’s current price, p10 , this consumer purchases the product of quality q1 instead
of sticking to the product of quality q0 if:
q1 + (
0
+
1)
cu
p10 +
0
(q )[q1 + (
0
26
+
1 )]
+ [1
0
(q )][q2 +
cu
p21 ]
q0 +
0
+
0
(q )[q2 +
0
where q = q1 + cu
0
p22 =
q ; p21 =
cu
0
p22 ] + [1
(q )][q2 +
cu
p21 ]
or equivalently, after substituting the equilibrium date t=2 prices,
2;
0
q +
cu ; the dominant …rm’s optimal price at date t=1 is
2
p10 =
Now think of the measure
q+
0
cu +
1
(q )(cu
2 ):
of new date t=1 consumers. Given the dominant …rm’s date
1
t=1 price, p11 ; they decide to purchase the product of quality q1 if:q
q1 + (
0
+
1)
c
p11 +
0
(q )[q1 + (
0
+
and after substituting the date t=2 price, p21 =
1 )]
0
+ [1
0
q +
(q )][q2 +
cu
p21 ]
0
cu ; the dominant …rm’s optimal
2
date t=1 price choice p11 is:
p11 = q1 + (
6.1.1
0
+
1)
c + q1 +
(
0
+
1 ):
Incompatibility
Think of a consumer that belongs to the measure
0
of old date t=1 consumers. Given
0
the dominant …rm’s price p10 ; she currently purchases the product of quality q1 instead of
sticking to the product of quality q0 if:
q 1 + ( 0 + 1 ) cu +
q0 +
0+
where q
(q )[q1 + ]+ [ (q )
(q )[q1 +
= q1 + (
0
cu p12 ]+ [ (q )
0 + 1 );
q = q1 + (
(q )][q1 + ( 0 + 1 )]+ [1
(q )][q1 + ( 0 + 1 )]+ [1
0 + 1 )+cu
2
(q )][q2 +
and p12 = q1 q2 + (
dominant …rm’s date t=2 equilibrium prices to the measure
27
0
(q )][q2 +
2
0
0
cu p21 ] p10
0
cu p21 ]
0 + 1)
is the
of new date t=2 consumers
0
and p21 =
measure (
q +
0 + 1)
(
2
0
+
cu is the smaller competitor’s date t=2 price to the
1)
of old date t=2 consumers. After substituting these prices in the inequality
above, the equilibrium date t=1 price p10 is:
0
p10 =
q+
cu +
1
q+
(q )[q1
cu +
1
(q )(cu
q+
as q = q1 + (
0
+
1)
q2 + (
+ cu
2
Think now of the measure
1
+
2)
1)
+ cu ] + [ (q )
+ [ (q )
0
cu +
1
0
(q )(cu
0
> q = q 1 + cu
(q )](cu
(q )](cu
2)
2)
2)
>
>
= p10 ;
2:
of new date t=1 consumers. Given the dominant …rm’s date
t=1 price, p11 ; they purchase the product of quality q1 and the highest price the dominant
…rm can currently charge them is such that:
q1 + ( 0 + 1 ) c+
(q )[q1 + ]+ [ (q )
(q )][q1 + ( 0 + 1 )]+ [1
(q )][q2 +
0
0
cu p21 ] p11
0;
or equivalently, after substituting the date t=2 prices,
0
p11 = q1 + ( 0 + 1 ) c+ q1 +
6.1.2
(b)
1
( 0 + 1 )+
(q )
2+
[1
(q )] ( 0 + 1 ) > p11 = q1 + ( 0 + 1 ) c+ q1 +
can postpone their purchase
Think of the measure
1
of new date t=1 consumers when network e¤ects are strong and the
dominant …rm sets prices both at t=1 and t=2. When compatibility is present, the highest
price that the dominant …rm can charge them to purchase the product q1 instead of waiting
until the future period to make their purchasing decision satis…es the equation:
q1 + (
0
+
1)
c + q2 +
cu
28
p21
p11 = (q2 +
c
p22 );
0
where, given the price p11 ; p21 =
q +
date t=2 consumers and p22 =
q + (
measure
2
cu is the equilibrium date t=2 price to the old
2
0
0
+
1)
is the equilibrium date t=2 price to the
of new date t=2 consumers. Thus, after substituting these prices in the above
equation, one gets that the optimal price choice at date t=1. p11 , is given by the expression:
p11 = q1 + (
0
+
q1 + (
0
1)
+
c + [q1 + (
1)
c+
(
0
0
+
+
1]
(q1 +
1)
2
2
c) =
+ c:
Note that if the dominant …rm sets prices only at t=1, these customers’expected payo¤ from
postponing their purchasing decision is zero, as there is no price competition at t=2 and their
surplus by purchasing the product of quality q2 tomorrow is zero. Thus, the dominant …rm
can set them a higher price if it only sets a price at t=1. This price is:
p11 = q1 + (
6.1.3
0
+
1)
c + [q1 + (
0
+
1 ]:
Incompatibility
Think of the measure
1
of new date t=1 consumers when network e¤ects are strong and
the dominant …rm sets prices both at t=1 and t=2. When compatibility is not present, the
highest price that the dominant …rm can charge them to purchase the product q1 instead of
waiting until the future period to make their purchasing decision satis…es the equation:
q1 + ( 0 + 1 ) c+
(q )(q1 + )+ [1
(q )(q1 +
0
where p11 = q1
q2 + (
0+
c
1 );
(q )]fq2 +
p12 ) + [1
p22 =
0
q + (
0
cu [ q +
2
(q )]fq2 +
0+
1 );
p21 =
c
0
q +
0
( 0 + 1 ) cu ]g p11 =
p22 g;
2
(
0+
1)
cu are
the equilibrium date t=2 prices set to old and new date t=2 consumers. After substituting
these prices in the equality above yields that the optimal date t=1 price that the dominant
29
…rm can set to
1
consumers is:
0
p11 = q1 + ( 0 + 1 ) c+
q1 + (
0 + 1)
c+
(
(q )(q1 + )+ [1
0 + 1)
2+
(q )][q1 +2 ( 0 + 1 )]
c+ f (q )(q1 q2 +
[ (q )(q2 +
2 +c)+[1
2
(q )] (
c)+[1
0 + 1 )g
Note that these consumers’alternative payo¤ by waiting is higher when incompatible networks arise and may outweigh their higher actual payo¤ by purchasing the product q1 at date
t=1. So, the price under compatibility may be higher when the probability of the relatively
less innovative states is relatively large.
If the dominant …rm sets prices only at t=1, the measure
1
customers’expected payo¤
from defering their purchasing choice to t=2 is zero, as there is no price competition at t=2
between the competitors’ products. Thus, the dominant …rm can charge these consumers
more if it sets prices only at t = 1: This price is:
p11 = q1 + (
6.2
0
+
1)
c+
(q )(q1 + ) + [1
(q )][q1 + 2 (
0
+
1 )]:
Proof of Proposition 2
(a) If …rms can price discriminate, the dominant …rm announces compatibility and incompatible networks prevail unambiguously at t=2 (when the dominant …rm fails to innovate and
q2R < q ), the next expressions give the di¤erence between consumer suplus for the di¤erent
customers’groups when incompatible networks arise and when compatibility is mandated:
CS(
0 inc )
CS(
p10
0 c)
= q1 + (
0+
p21 ] = fq1 + (
1)
0
+
cu + q 1 +
1)
0
p10
cu + q 1 +
Pr ob(the d.f fails) Pr ob(q2R < q )(q1
30
[q1 + (
( q+
q2 + (
0
+
0+
1)
cu + q 2 +
1
cu g
1)
+ cu )g
cu
(q )](q1 +
2
fq1 + (
[q0 +
0
Pr ob((q2D < q2R < q )(q1
q2 + (
+
( q+
1)
cu + q 2 +
cu
+
1
1)
2
+ cu )g
cu )
[ q+
cu ]g =
2
Pr ob(the d.f fails) Pr ob(q2R < q )(q1 q2 + ( 0 + 1 ))] [q0 +
0 +q1 +
Pr ob((q2D < q2R < q )(q1
=
0
q2 + (
0
+
1)
Pr ob(the d.f fails) Pr ob(q2R < q )(q1
2
Pr ob((q2D < q2R < q )(q1
q2 + (
0
1)
( 0 + 1 )]
+ cu )g =
2
q2R + (
+
0 +q1 +
0
2
+
1)
+ cu )
+ cu )g:
Note that when the date t=2 bene…t from the larger network under incompatible networks
outweighs the higher price incurred yesterday, old consumers are better-o¤ when incompatible networks arise.22
New consumers are always better-o¤ at t=2 under incompatibility, as the di¤erence in
their surplus is:
CS(
q1 +
c
2 inc )
[q1
CS(
2 c)
= q1 +
q2R + (
0
q2R +
2
+
c
1 )]
c
0
p12
[q2R +
(q1 +
2
[q2R +
c
c
0
( q + (
p22 ] =
0
+
1 )]
=
c) > 0:
Similarly, date t=1 consumers are better-o¤ when incompatible networks arise in the
scenario when the dominant …rm refuses to be compatible after failing in its R&D e¤ort and
the competitor sells a product q2D > q : Old date t=2 consumers are better-o¤ because of
the …ercer competition and new date t=2 customers are indi¤erent.
If …rms cannot price discriminate, all date t=2 consumers are still better-o¤ when incompatible networks arise.
(b) When the dominant …rm chooses the path of incompatibility at t=1, think of the
22
Similarly, new date t=1 consumers’surplus is higher when incompatible networks arise at t=2.
31
measure
of new date t=2 consumers. When …rms can price discriminate and under an
2
economy mandating compatibility, these consumers’total expected surplus is: (q2 +
p22 )= [q2 +
c
q
0
(
+
0
1 )]
= (q1 +
c); where p22 =
2
0
q + (
0
+
c
1)
is
the date t=2 price to purchase q2 :
Under incompatible networks and when the dominant …rm’s optimal choice is to set prices
twice, these consumers’expected surplus is:
p22 ) =
(q )fq1 +
=
c [q1
(q )(q2 +
q2 + (
c)+ [1
2
0+
(q )(q1 +
1 )]g+
(q )](q1 +
[1
2
c p12 )+ [1
(q )][q2 +
c
(q )](q2 +
q
0
(
0+
c
1 )]
=
c):
It is straightforward to see that a su¢ cient condition for incompatible networks to bene…t this class of consumers is that the less innovative states are reached with a non-zero
probability.
Think now of the measure
of old date t=1 consumers. Under an economy mandating
0
compatibility, their expected total surplus is: q1 + (
p21 = q1 + (
q0 +
0
0
+ q1 +
+
(
1)
0
cu
+
( q+
0
+
1)
cu
cu ) + q2 +
1
p10 + q2 +
0
cu
( q +
cu
cu ) =
2
1 ):
Under incompatible networks, these consumers’expected total surplus when the dominant …rm’s optimal choice is to set prices twice is: q1 + (
) + [1
(q )][q2 +
q1 + (
[1
q0 +
(
0
+
0+
1)
cu
(q )]fq2 +
0
1)
+
+ [1
(q )[ q 0 +
p21 ] =
f q+
1
(q )(q2 +
2
(
0
cu +
0
[ q +
0
+
2
(q )[q1
(
cu ) + [1
2
(q )] (
+
0
(q )(q1 +
1 ) + cu ]g +
(q )(q1 + )+
1)
cu
p10 +
0
cu
cu
0
+
1)
0
+
q2 + (
1)
0+
cu ]g =
(q )][q1 + 2 (
0
+
1 )]
= q0 +
0
+ q1 +
1 )+
cu ]:
It is also straightforward to see that old date t=1 consumers bene…t from incompatible
networks for relatively more innovative states and they are overall better-o¤ when incompatible networks arise when their expected bene…t in the future relatively more innovative
states o¤sets their loss in the less innovative future states.
32
The measure
1
of new date t=1 consumers are indi¤erent between compatible and
incompatible networks, as their surplus is zero in both cases.
If the dominant …rm’s optimal choice is to set prices only at t=1, the measures
2
1
and
are indi¤erent between compatible and incompatible networks.
Think of the measure
of the old date t=1 consumers when incompatible networks arise
0
and the dominant …rm decides to set prices only at t=1.
These consumers’expected total surplus is:
q1 + (
0
+
where p10 =
1)
q+
cu
1
0
p10 +
cu +
(q )[q1 + (
0
+
1 )]
(q )[ q + (
0
+
1 )];
+ [1
(q )][q2 +
0
0
p21 =
q +
cu
(
2
0
p021 ];
+
1)
cu
and thus, these consumers’expected surplus is:
q0 +
0
+
(q )q0 + [1
(q )][q1 + 2 (
0
+
1 )]:
(a2)When …rms lack the power to price discriminate, future consumers’expected surplus
under compatibility is: [q2 +
1)
c
p22 ) = [q2 +
0
c
( q +
cu )] = [q1 + (
2
0
+
c + cu ]:
When there is incompatibility, future consumers’expected surplus is
f (q )(q1 +
f (q )[q1 +
c
p12 ) + (1
(q )(q2 +
c (q1 q2 + ( 0 + 1 ))]+(1
(q )(q2 +
f (q )[q2 +
(q )(q1 + 2 (
2
c] + (1
cu
0
c ( q+
0
+
1)
p021 )g =
2
( 0 + 1 ) cu ))g =
c + cu g:
Note that for more innovative states, these consumers are better-o¤ when incompatible
networks arise, while compatibility bene…ts them for less innovative future products.
Think about the measure
0
of old date t=2 consumers. For installed base of consumers
33
0
above the threshold de…ned in (1), the dominant …rm’s optimal t=1 price choices are
p10 =
q+
1
0
cu ; p10 =
q+
cu +
1
(q )[q1
q2 + (
+
0
1)
+ cu ]; under
compatible and incompatible networks, respectively. Then, their expected surplus under the
two regimes is identical with a1 above.23
(b) When compatibility is present, the measure
(q2 +
0
c)
(q ) q
(q1 +
0
expected surplus is:
0
[1
c)
2 ’s
0
(q )][ q + (
0
[1
(q )] (
0
+
0
+
1 )]
=
1 ):
These consumers’expected surplus under incompatible networks is:
(q )fq1 +
c [q1 q2 + ( 0 + 1 )]g+ [ (q )
(q1 +
c) +
(q )[ q
0
(
0
(q )]fq2 +
+
1 )]
[1
2
c [ q
(q )] (
0
0
( 0 + 1 )]g+ [1
+
1 ):
0
As q > q ; consumers bene…t from incompatible networks for more innovative states but for
less innovative states (reached with
under incompatible networks), they are better-o¤
(q
when compatibility is madnated.
Similarly, old date t=1 consumers’ expected consumer surplus when compatibility is
mandated is:
q1 + (
0
+
1)
cu
q0 +
p10 +
0
0
(q )[q1 + (
+ q1 +
(
0
0
+
23
+
1)
1 )]
+ [1
0
(q )(cu
0
(q )][q2 +
cu
p21 ] =
2 );
Similarly, these consumers’expected payo¤ in more innovative states is larger when incompatible networks arise and the installed base of consumers is relatively smaller.
34
(q )]fq2 +
while their expected surplus when incompatible networks arise is:
q 1 + ( 0 + 1 ) cu +
q0 +
0+
q1 +
(q )[q1 + ]+ [ (q )
( 0 + 1 )+
0
(q )[ q +
(q )](q1 + ( 0 + 1 ))+ [1
( 0 + 1 ) cu ]
2
[ (q )
(q )][q2 +
(q )](cu
0
2 )+
[1
Note that for more innovative future states, these consumers are better-o¤ when incompatible
networks arise, while compatibility is bene…cial for relatively less innovative future states.
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