When Do Markets Tip? An Experimental Study
Tanjim Hossain
Hong Kong University of Science & Technology
John Morgan
Haas School of Business and Department of Economics
University of California, Berkeley
March 2007
Abstract
We report the results of laboratory experiments examining platform competition in two-sided markets. Owing to “market size” e¤ects that favor the
platform with the larger customer base, there always exist equilibria in which
all participants “tip” to one platform or the other. When “market impact”
e¤ects are su¢ ciently large, then there also exist interior equilibria where both
platforms enjoy positive market share. We vary the degree of market size and
market impact e¤ects, as well as the e¢ ciency and access price in a market
where there are two competing platforms. Regardless of the underlying parameters, we …nd strong support for tipping in these markets. Moreover, tipping
occurs quite rapidly, often after only a few iterations of the game. The market
impact e¤ect plays no role in leading to a non-tipped market while apparent
non-tipping may arise from market segmentation and slow converegence to a
tipped equilibrium. Finally, we show that participants following the Pareto
criterion or a cognitive hierarchies model of choice explain both tipping as well
the platform that will prevail in this competition.
Preliminary and incomplete. Please do not circulate without the permission of the authors.
1
Introduction
Many markets share the following features— di¤erent types of agents interact with
one another on a platform, which may both serve to match the agents as well as to
facilitate transactions. Fixing the ratio of the number of agents of di¤erent types,
the larger are the number of agents participating on a particular platform, the more
gains from trade are available to those on that platform. While agents of a given type
bene…t when more agents of the opposite type use that platform, they are harmed
when there are more agents of their same type using that platform. Of course, the
…rst feature is merely a generic description of a two-sided market (see Rochet and
Tirole, 2003) and can be thought of as a “scale e¤ect.”The second feature, which may
be thought of as a “market size” e¤ect, is simply a description of a particular kind
of network e¤ect that often occurs in two-sided markets. The third feature, which
may be thought of as a “market impact” e¤ect, is present in markets where agents
of one type compete for the business of agents of the other type. This is one of the
…rst papers to study subjects’choice between two competing platforms in two-sided
markets with these features using laboratory experiments under a broad range of
competitive conditions.
In concrete terms, the online auction market is one example of a market with
these features. There are agents of di¤ering types (buyers and sellers) undertaking
both matching and transactions on a platform (typically eBay in the US). Sellers
bene…t from the presence of more buyers and vice-versa (market size e¤ects) while
sellers are disadvantaged by the competition presented when there are more sellers on
the network (market impact e¤ects). Other examples of markets with these features
include dating services, e-retail competition on price comparison sites, Internet search
engines, credit card markets, stock exchanges and video gaming consoles. As these
platforms facilitate market operations, Evans and Schmalensee (2007) sometimes refer
to them as market makers or economic catalysts.
The presence of market size e¤ects implies the existence of an equilibrium where
all agents choose to be on single platform— a tipping equilibrium— regardless of the
1
quality of that platform relative to those with which it is competing.1 This is straightforward to see in the case of online auctions. Clearly, if all potentials buyers search
for products only on eBay, there is no point in a seller posting an item to Yahoo no
matter how good its auction platform is. Similarly, if all sellers are located on eBay,
there is no point in any buyer browsing Yahoo auctions for non-existent listings.
While tipping is always an equilibrium, Ellison and Fudenberg (2003) showed
that, when market impact e¤ects are su¢ ciently strong, there also exist equilibria
in which competing platforms can coexist even when the platforms are completely
homogeneous.2 Of course, there are other reasons to suspect that tipping is not
inevitable in platform competition. In the online dating space, there is considerable
segmentation and specialization across platforms. For example, Jdate is the dominant
platform for online dating among Jewish people, but is dwarfed in overall market share
by less specialized o¤erings such as Yahoo personals and Match.com. Geographic
segmentation can also make a di¤erence. For example, while eBay is the dominant
online auction site in the US and Europe, Yahoo dominates in Asia.
Segmentation in the form of the specialized niche occupied by Jdate or the geographic segmentation of eBay and Yahoo may still suggest that the “market,” if
de…ned properly, has already tipped to a single platform. Indeed, in a companion paper to this one (Hossain and Morgan, 2007), we o¤er a theoretical model of platform
competition in two-sided markets that shares all of the features we described above.
We depart from standard theoretical models in that we assume that agent decision
making is based on a cognitive hierarchies model a la Camerer, Ho and Chong (2004)
rather than the usual fully rational model. In models of this type, agents best respond
given their hypotheses about the choice behavior of other agents. These hypotheses
are based on the cognitive level of the agent. Level 0 agents are assumed to choose
strategies at random. Level 1 agents hypothesize that all other agents are level 0
1
Technically, the implication is valid only under the restriction that agents are single-homing, i.e.
can choose only a single platform.
2
See also, Ellison, Fudenberg, and Mobius (2004) for an application of this idea to competing
online auction platforms such as eBay and Yahoo. However, Brown and Morgan (2006) investigated
the implications of this model using …eld experiments on eBay and Yahoo and did not …nd support
for the implications of the theory.
2
and optimize accordingly while level k agents believe that all other agents are of
level k 0 2 f0; 1; : : : ; k
1g. Our main …nding is that, when agents behave according
to cognitive hierarchies (hereafter CH), equilibrium coexistence is impossible if the
fraction of level-0 players in the market is close to zero.3 Moreover, the CH models
o¤er precise predictions as to which platform will ultimately prevail. Interestingly,
this equilibrium is also the risk dominant equilibrium. When the platforms have
identical matching capabilities then the CH model predicts that the market achieves
the Pareto dominant equilibrium. However, this may not be the case if platforms
have di¤erent matching capabilities.
As many theoretical models lead to multiple equilibria, it is di¢ cult to clearly
predict what the market outcome would prevail in a long-run equilibrium. In this
paper, we investigate if and when markets tip using controlled laboratory experiments.
In our experimental framework, subjects, who are assigned the role of an economic
agent of a particular type, must choose between two competing platforms. Platforms
may di¤er in their cost to access, the magnitude of the market size e¤ect (which
may be thought of as the e¢ ciency of the matching and transaction handling of the
platform) and the degree to which agents of the same type participating on the same
platform a¤ect each other’s payo¤s (i.e., the magnitude of the market impact e¤ect).
By varying the degree of the market impact e¤ect while leaving all else …xed, we are
able to “turn on and o¤” the existence of a non-tipped equilibrium. We also vary
the number of agents of each type participating in the market. Players know the
market size, gross payo¤ from each platform as a function of the number of players of
each type in that platform and the entry fees to the platforms. They simultaneously
choose which platform to enter repeatedly for a number of periods and we test whether
subjects’platform choices converge to any speci…c outcome. Then they participate
in a new market with a new set of gross payo¤ functions for platforms against a new
set of players. Our framework is su¢ ciently ‡exible to allow us to examine cases
where the competing platforms are homogeneous as well as vertically di¤erentiated,
3
Same results hold even when we assume that a level-k player believes that all other players are
of level k 1 as suggested in, for example, Nagel (1995), Stahl and Wilson (1995) and Costa-Gomes
and Crawford (2006).
3
to examine cases where there are a large number of agents in the market as well as a
small number, and to examine how variation in the price of access for agents a¤ects
tipping. This experimental format can represent both markets where an agent may
repeatedly participate in transactions with agents of the opposite type and markets
where she leaves the market as soon as she completes one transaction with success.
Most of the theoretical models in the existing literature deal with platforms that
are identical in terms of matching the agents. In the …rst eight sessions of our experiments, both platforms have identical matching technology and di¤er only in their
entry fees. However, in sessions 9 to 20, the platforms vary in matching e¢ ciency in
addition to varying in the entry fees. In some sense, in these sessions the platforms are
di¤erentiated in two dimensions— both entry fees and matching e¢ ciency. Variations
in quality level of platforms is common in the real life. The search engine Google has
become a leader in bringing Internet users and advertisers to their websites in a relatively short time because of its superior search ability. The dating site eHarmony.com
advertises that it uses its .“Relationship Questionnaire” to create highly compatible
matches based on a rigorous 29-dimension scale, thus di¤erentiating its matching
technology from those of competitors. The “Di¤erentiated Platforms” setting tries
to capture this idea.
In all twenty sessions, we follow the variation of the market impact e¤ect in the
same way. Namely, subjects participate both in markets where the market impact
e¤ect is large enough so that a non-tipped equilibrium exists and in markets where
the market impact e¤ect is small leading to only tipped equilibria. Thus, we can
distinguish between market impact e¤ect and platform di¤erentiation e¤ect in our
results. Speci…cally, if market impact e¤ect is the main driving force behind nontipping, we would see non-tipping in the non-tipped games of all twenty sessions.
Under a broad range of competitive conditions, we …nd strong evidence for the
prevalence of tipping. When platforms were homogeneous, both platforms o¤ered the
same gross payo¤ functions. Then, the markets quickly tipped toward the platform
with the lower access fee— even when market impact e¤ects are strong enough to
sustain equilibrium coexistence. As the platforms varied only in one dimension, it was
4
easier to …gure out for the subjects which platform o¤ered the higher surplus net of the
access fees and the subjects converged to that platform. Convergence required only a
few iterations of the game in most cases. Moreover, once a group of agents converged
to a single platform, it is never the case that they subsequently switched to the rival
platform. These markets always converged to the Pareto dominant equilibrium, which
is also consistent with the CH model’s prediction.
The experimental results were more nuanced when platforms were vertically differentiated. Nevertheless, they are broadly consistent with the predictions of the
CH model. In two of the three settings with di¤erentiated markets, the equilibrium
predicted by the CH model is also Pareto dominant. In these settings the markets appear to favor the Pareto e¢ cient platforms. In some settings, the markets
fail to converge to any particular outcome or some segments of the market tip to
the Pareto dominated tipped equilibrium. Although this gave the overall market an
appearance of reaching a non-tipped outcome, none of the market segments ever converged to the non-tipped equilibrium outcome even when they existed. The markets
never converged to an outcome that is not an equilibrium either. In the third setting with di¤erentiated markets we designed the payo¤ matrices in a way that the
market should tip to the cheaper platform if subjects follow the CH model or choose
the risk-dominant equilibrium. However, the market tipping to the more expensive
platform is the Pareto dominant equilibrium. In this setting, the market fails to converge quite frequently. In the markets where the subjects converged to a particular
outcome, both of the tipped equilibria where more or less equally prevalent. As in
settings Di¤erentiated II and III, sometimes some market segments converged to the
cheaper platform while other segments converged to the more expensive platform.
Nevertheless, none of the markets seemed to converge to the non-tipped equilibrium
when that existed. Overall, given the divergence in equilibrium choice and lack of
convergence, the overall markets get the appearance of a non-tipped one. However,
the overall subjects’ choice of platforms look remarkably similar when we compare
the game with a non-tipped equilibrium versus the game with only tipped equilibria. These results suggest that apparent non-tipping in the real world may result
5
from market segmentation or slow convergence to any particular outcome because of
platform di¤erentiation. The market-impact e¤ect did not seem to ultimately have a
large e¤ect on the platform choice in either homogenous and di¤erentiated platforms
settings. The existence of non-tipped equilibrium was irrelevant in determining the
market outcomes. Overall results also suggest that the market size e¤ect does not
a¤ect tipping vs. non-tipping.
Our results have obvious public policy implications in the regulation of two-sided
markets. Because of the presence of network e¤ects, these markets are easily monopolizable with the usual adverse e¤ects on consumer welfare.4 However, it is rarely
the case that the dominant platform owns a true 100% market share. For instance,
even Microsoft’s Windows operating system, which has been …nd by several courts
to be a de facto monopoly, shares the market with the increasingly resurgent Apple
and Linux operating systems. Furthermore, geographic or taste separation may effectively obscure the true market power of the dominant platform. For instance, no
single player dominates the overall US online dating market; however, there are dominant players, within subsets of the market. The results from di¤erentiated platforms
settings are consistent with these observations.
The remainder of the paper proceeds as follows. The next section relates the
paper to the existing literature on two-sided markets and laboratory experiments on
coordination problems. In Section 3, we summarize the design of the experiments. In
Section 4, we describe the predictions and results of the experiments for sessions in
which the competing platforms are homogeneous. Section 5 describes the predictions
and results of the experiments for sessions in which the competing platforms are
di¤erentiated. In section 6, we summarize the results of all experiments and draw
conclusions.
4
See, for example, Baye and Morgan (2001) for an analysis of the welfare impact of a monopoly
platform in a two-sided market.
6
2
Relation to the Literature
The laboratory experiments in this paper complements the growing theoretical literature on platform choice in two-sided markets.5 In a pioneering paper in this
literature, Caillaud and Jullien (2001, 2003) discuss competition between two matchmakers who may charge two-part tari¤s and di¤erent price schedules to the two types
of agents. They show that only tipping equilibria can be supported by the market when platforms can charge two-part tari¤s and platforms make zero pro…t. In
two other important papers, Rochet and Tirole (2003) and Armstrong (2006) study
platform competition assuming platforms are somewhat di¤erentiated leading to differentiable demand functions for the two platforms. Thus, tipping vs. non-tipping
is not an issue in those two models. The platforms’primary pricing instruments are
transaction fees.
Unlike the above-mentioned papers, the platforms do not compete in prices in the
experiments in this paper, the prices are exogenously given. This can be interpreted as
platforms choosing their marginal cost as their prices. Ellison and Fudenberg (2003)
and Ellison, Fudenberg and Möbius (2004) also study agents’choice among two platforms where platforms do not compete in prices. Although the markets are identical
in terms of matching e¢ ciency, platforms of di¤erent sizes can coexist in equilibrium
because of the market impact e¤ect when there are …nite number of agents. Ambrus and Argenziano (2005) have a similar model, but with continuum of consumers
leading to nonexistence of market impact e¤ect. Price competition among platforms
leads to tipping when agents are homogenous. Nevertheless, non-tipped equilibrium
with platforms of di¤erent sizes exist when agents of both types have heterogenous
preferences. In Damiano and Li (2005), consumers are heterogeneous and platforms
use entry fees to separate di¤erent types of consumers. They show that multiple platforms can coexist in equilibrium in a sequential game when player type distributions
are su¢ ciently di¤used. However, unlike most models, consumers do not enjoy any
network externality from the platforms in their model. In our experiments, agents
are homogenous and the two sides of the market are symmetric. Most theoretical
5
See Armstrong (2006) for a more extensive review of the theory literature on two-sided markets.
7
models assume that platforms are symmetric in terms of matching e¢ ciency while
we consider both homogenous and di¤erentiated platforms. As the access prices to
platforms di¤er, agents choose between platforms that may be di¤erent in two dimensions in our experiments. Ambrus and Argenziano (2005) consider coalitionally
rationalizable equilibria in their paper. In our experiments, agents cannot cooperate
and form a coalition to make platform choice decision. As this may be possible in
small markets where agents know each other (such as markets for rare or specialized
products), that can be considered in future experiments.
To the best of our knowledge, we are the …rst to study competing two-sided
markets using laboratory experiments under such a general framework. Clemons
and Weber (1996) ran experiments with both students and ‡oor traders from NYSE
where in each period sellers and buyers decided on how to divide 10 shares to buy
or sell (depending on their roles in the experiment) between two stock exchanges X
and Y . The subjects did not pay any price for using the platforms. However, the
di¤erence in e¢ ciency levels between these two platforms changed direction during
the experiment. Initially, when platform Y was not fully developed, the subjects
used both stock exchanges and the market reached interior outcomes. However, once
platform Y completely developed and became more e¢ cient than platform X, traders
of both types converged to trading only on platform Y .
This paper is also related to the literature on coordination game experiments.
In Van Huyck, Battalio and Beil (1990), subjects played a minimum action game
repeatedly where each player chooses an action ei 2 f1; 2; : : : ; eg. A subject’s payo¤
depends positively on the minimum of all players’actions and may negatively depend
on her action if it is above the minimum action. Any strategy pro…le where all players
choose the same action is a pure strategy equilibrium. However, these equilibria can
be Pareto ranked where all players choosing e Pareto dominates all other equilibria.
When an action above the minimum of all players’actions strictly reduced a subject’s
payo¤, at least one player chose the lowest possible action latest by period 4 in all
sessions with 14-16 subjects in a group. After that, it stayed as the minimum action
chosen in all future periods. However, when subjects played in 2-player groups or
8
a player’s own action did not reduce her payo¤s, quite frequently all subjects chose
the highest possible action. Thus, subjects chose the worst-possible equilibrium in a
strict minimum action game when the group size was large enough, but the selected
equilibrium was a¤ected by the group size. In Van Huyck, Battalio and Beil (1991),
subjects played a median action game which is similar to a minimum action game
with the di¤erence that a subject’s payo¤ positively depends on the median, instead
of the minimum, of the action taken by all players. They …nd more cooperation
than in minimum action games. Following Schelling (1980), they suggest that which
equilibrium subjects would coordinate to depends on saliency of attributes such as
payo¤-dominance or security; in the games where payo¤-dominance is more salient
then subjects choose the highest possible action while they choose a medium range
action when security is a more salient feature. Signi…cant attention also has been
given to how subjects learn to play coordination games. Battalio, Samuelson and
Van Huyck (2001) investigate coordination failure in stag hunt games. Crawford
(1995) theoretically study adaptive dynamics of subjects’ learning in coordination
games and then apply the model on the data from Van Huyck, Battalio and Beil
(1990, 1991) experiments. Costa-Gomes and Crawford (2006) runs experiments with
2-person guessing games and …nd that subjects’initial responses can be well explained
by a cognitive hierarchical model of thinking. Platform choice in a two-sided market
can be viewed as a coordination problem between the two types of agents. Similar to
the coordination games literature, there exist multiple equilibria that can be Pareto
ranked in our setting. This is one of …rst experiments where two di¤erent types of
agents coordinate on location choice. Thus, the above-mentioned coordination games
to not have a platform competition interpretation. Nevertheless, the focus of this
paper is less on how learning by players propagate in coordination games and more
on ultimately what kind of outcomes players coordinate to in a two-sided market
model with a broad applicability in industrial organization.
9
3
Experimental Design
In this section, we outline the procedures used in all experimental sessions as well as
summarizing various descriptive statistics pooled over all experimental sessions. In
later sections, we describe the individual payo¤ functions used in each session and
analyze the results under each treatment.
We designed a laboratory experiment that investigates subjects’choices of platforms in a two-sided market with two competing platforms. Platforms may di¤er
from one another in their matching and transactions technology, which we represent abstractly as di¤erences in the gross payo¤ functions of a player under a given
market share con…guration. The gross payo¤s for each platform are given in matrix
forms for each possible con…guration of platform choices by the players of two types.
The platforms in the experiment thus represent generic platforms for most two-sided
markets. Platforms also di¤er in the prices that they charge each of the agents for
access. Our main interest is whether and how fast competition leads to “tipping”—
situations where all agents choose the same platform. While the theory models of
competition in two-sided markets are mainly static, of interest to policy makers is
dynamic behavior— how does market share between competing platforms evolve as
agents participate on the platforms over time. Thus, we thought it was important to
explore the dynamics of market share among competing platforms. To operationalize
this, we organized subjects into groups of agents. All subjects who were members of a
given group interacted repeatedly in a two-sided market over several iterations of the
stage game. After these iterations were complete, subjects were then randomly and
anonymously re-matched into new groups and play proceeded. In all treatments, the
payo¤ functions were such that a subject would get a positive payo¤ in each period
under all possible con…gurations of choices by her and other subjects
Our other main interest was whether the possibility of a non-tipped equilibrium
would lead to coexistence. To implement this, we used a within-subjects design where
we varied the market impact e¤ects across iterations of a given session. In half of
the iterations, an interior equilibrium existed while in the other half, tipping was
the only equilibrium possibility. We also varied the presentation order of the payo¤
10
matrices so that sometimes interior equilibria came …rst and sometimes later. Since
the presence of interior equilibrium with possibly highly unequal market shares has
been used by Microsoft and others as the basis for arguing the absence of monopoly
power, we thought it was highly important to examine this aspect of extant theory.
We now o¤er an overview of our sessions. Between May 2006 and March 2007, we
ran 20 sessions with ten di¤erent treatments. In total, 352 undergraduate students of
Hong Kong University of Science and Technology participated in these sessions. All
subjects were recruited electronically by using a software developed by the university
and each subject participated in only one session. The subjects spent slightly less
than 90 minutes in the laboratory including reading the instructions and receiving
payments. The average payment to subjects was almost HKD 170, considerably
above the outside work options available to most subjects.6 The experiment was
programmed and conducted with the software z-Tree developed by Fishbacher (1999).
Sessions 1 to 6 consisted of 40 periods and sessions 7 to 20 consisted of 60 periods of
the platform competition game (depending on our priors about the speed at which a
given payo¤ matrix would lead to convergence). Subjects earned points for all periods
and the total points earned were translated into HKD according to an exchange rate
speci…ed at the beginning of the experiment. The session length, payo¤ functions and
exchange rate were designed in a way that if all players choose the Pareto dominant
equilibrium in every period then a player would earn HKD 180 from the session. With
the exception of the two large market sessions (where 32 subjects participated), 16
subjects participated in each session.
To get a feel for the ‡ow of the experiment, we describe in detail the procedures for
the “baseline” sessions (sessions 1-6), all other sessions proceeded similarly save for
the scaling in terms of the number of periods or numbers of subjects. At the start of
a baseline session, subjects were formed randomly and anonymously into four equalsized groups or markets of four players each. Two of the subjects in a given group
were assigned the identity “triangle” while the other two were assigned the identity
“square.” The members of a group and their identities remained …xed for the …rst
6
On average, 1 USD = 7.79 HKD.
11
10 rounds of the game. During each period, subjects chose which of two platforms
(labeled “…rm %” and “…rm #”) to access. In making this decision, subjects were
informed of the costs to access and their payo¤s from accessing a given platform as a
function of the choices made by the other players. The gross payo¤s from accessing
any given platform was given by a payo¤ matrix. Particular payo¤ matrices used in
di¤erent sessions are provided in sections 4 and 5. For homogenous platforms, the
gross payo¤ function for the two platforms were identical and were given by the same
payo¤ matrix in the instructions. In the di¤erentiated platforms settings, the gross
payo¤s for the two platforms were given by two di¤erent matrices. The platforms
can thus very easily be vertically di¤erentiated. The access or entry fees of the two
platforms were announced at the beginning of a session and were kept unchanged
through out the session. A sample instruction sheet supplied to the subjects during
the baseline sessions is provided in the appendix.
After the end of each period, each subject was told how many players of each
type in her 4-player market joined which platform and her net payo¤ equalling the
gross payo¤ minus the access fee. Subjects played the same game for 10 periods.
At the conclusion of period 10, subjects were randomly re-matched into new groups,
randomly re-assigned a type (square or triangle) and the payo¤ matrices for accessing
each of the platforms changed. Following round 20, we reverted back to the original
payo¤ matrices while following round 30, we reverted back to the matrices used at the
start of round 11. The access fees were held constant throughout the entire session.
Thus, our setup may be thought of as a fairly typical abab experimental design.
Following round 40, subjects were paid in cash on the basis of the number of points
earned in the game according to an exchange rate announced at the beginning of the
session. To control for presentation e¤ects, each session had a pair that di¤ered from
it only in the presentation order of the payo¤ matrices (i.e. a baba design). As we
shall see, the presentation order of the payo¤ matrices appears to have little e¤ect on
subject choice. Payo¤ matrices were changed so that the market impact e¤ect di¤ers
between the a speci…cation and the b speci…cation. When there is a strong market
impact e¤ect, there exists an equilibrium where the platforms can coexist, which we
12
shall refer to as a type N treatment (the N is a mnemonic for non-tipping). Where
the market impact e¤ect is weak, then only tipping equilibria exist and we shall refer
to these are T treatments (where T is a mnemonic for tipping).
Both the labels used for a subject’s identity as well as those used for the names of
the two competing platforms were designed to present as neutral a frame as possible.
Even though we called the two markets % and # in all 20 sessions, we rotated which
platform had the lower access fee and also the sequence of the two platforms in
the choice screen. For purposes of exposition, we will refer to the two platforms as
platforms A and B following the norm that platform A is the one with the higher
access fee. Likewise, we will refer to square type as “male”type and triangle type as
“female” type of player to give the ‡avor of a (heterosexual) online dating market.
In all settings, the gross payo¤s are the same for male and female players. As the
same subject participated as both types during a session, we did not expect behavior
of the two types of players to vary systematically and we do not see any evidence to
the contrary in our experimental results.
Treatments
Our treatments may be usefully divided into those where the competing platforms
are homogeneous and those where the platforms are di¤erentiated. Within each of
these divisions, we varied the market impact e¤ects to create N and T treatments.
Half of the sessions were run with N T N T treatments and half were run with T N T N
treatments. We ran six “baseline” sessions with homogeneous platforms. We also
ran two “jumbo”sessions with homogeneous platforms. Jumbo sessions di¤ered from
baseline in that the number of agents of each type in the market was doubled.
Next, we ran 12 sessions where platforms were di¤erentiated; that is, one platform
was more e¢ cient in matching agents than the other. More speci…cally, the more
e¢ cient platform also charged a higher entry fee. These sessions may usefully be
divided in three di¤erent settings where we ran four sessions of each setting. In
Setting I, the cheaper platform also o¤ers the greater overall surplus in the event
that all agents visit it. In Setting II, the more expensive platform o¤ers the higher
overall surplus in the event that the market tips to it. Finally, in Setting III, the
13
more expensive platform o¤ers greater overall surplus; however the payo¤ functions
are designed in such a way that CH players will opt for the cheaper platform.
4
Homogeneous Platforms
As a …rst step for answering the broad questions raised in this paper, we ran experiments where both platforms were equally e¢ cient in matching agents for transactions,
a common assumption in the theory literature. In the experiments we can achieve
that by providing the same gross payo¤ matrix for the two platforms. The platforms just di¤er in the entry fees they charge. We call these setting the homogenous
platforms settings. We ran two kinds of sessions— “Baseline Sessions” and “Jumbo
Sessions”under the homogenous platform settings. They di¤ered basically in the size
of the entire market and were otherwise similar.
Cognitive Hierarchies
Using the results of Hossain and Morgan (2007), it is straightforward to show that
for both the N and T matrices, the unique equilibrium under the CH model is for
all players (with cognitive sophistication level of 1 or above) to go to the cheaper
platform. Intuitively, a level 1 player believes that all other players are level 0 and
hence, the size of the two platforms is, in expectation, equal. Therefore, it pays
for such a player to simply choose the platform with the cheaper access fee. For
level 2 and higher players, the cost-bene…t calculation is similar though tilted more
in favor of the cheaper platform B owing to the fact that all of the level 1 and
higher sophistication players will have selected this platform. Thus, platform B will,
in the eyes of these players, both have a size and cost advantage which leads to the
market tipping to platform B. This equilibrium is also the risk-dominant and Paretodominant equilibrium. These results are independent of the number of participants in
the market, the market size e¤ect and the market impact e¤ect. That is, the cognitive
hierarchy model suggests that the unique equilibrium is the Pareto-dominant and the
risk-dominant equilibrium where the market tips to the cheaper platform no matter
whether or not a non-tipped equilibrium exists with completely rational players in
both baseline and jumbo sessions.
14
4.1
4.1.1
Baseline Sessions
Description
As the experimental design is already described in section 3, we begin by describing
the payo¤s in the baseline sessions. Since platforms only di¤er in terms of their access
fees, these sessions represent the purest possible test for the attractiveness (or lack
thereof) of an equilibrium in which the platforms coexist. For each of these sessions,
the access costs are pA = 4 and pB = 2. Recall that a player’s net payo¤ from using
a particular platform equals her gross payo¤ minus that platform’s access fee.
For the N (non-tipping) treatment of the baseline sessions, subjects were presented
with the following gross payo¤ matrix.
Table 1: Baseline: N Payo¤ Matrix
Number of players of the
player's own type (including
herself) in the platform she
joined
Number of
players of the
opposite type
in the platform
she joined
1
2
0
5
5
1
9
6
2
12
11
Here the gross payo¤ entry in row t and column s represents the gross expected
payo¤ from entering a platform with s players of the player’s own type and t
1
players of the opposite type. Notice that, with rational players, there exist three
equilibria of the above game. All players going to platform A or all going to platform
B are equilibria. Moreover, one male player and one female player going to platform
A and the remaining two players going to platform B is also an equilibrium. Owing
to the severe market impact e¤ects, none of the players can bene…t from a unilateral
move to another platform.
15
For the T (tipping) treatment of the baseline sessions, subjects were presented
with the gross payo¤ matrix given in Table 2. Notice that the T matrix di¤ers from
the N matrix in the impact of a second player of the same type joining a given
platform. In the case of the T matrix, the payo¤ consequences of having to share the
platform with more players of the same type are less severe than they are under the
N matrix.
Table 2: Baseline T Payo¤ Matrix
Number of players of the
player's own type (including
herself) in the platform she
joined
Number of
players of the
opposite type
in the platform
she joined
1
2
0
5
5
1
9
8
2
12
11
Given that pA = 4 and pB = 2, when players are rational, there exist two pure
strategy Nash equilibria of the above game— all players going to platform A or all
going to platform B. There is no equilibrium where some players go to platform B
and some go to platform A. A subject earned a net payo¤ of the gross payo¤ received
according to the population composition of the platform of her choice minus the entry
fee of her chosen platform. The payo¤s and entry fees were calculated in points and
subjects earned points for all 40 periods. At the end of the session, they received
payment in cash receiving 1 HKD for each 2 points earned.
4.1.2
Results
Recall that in each period, subjects made binary choices between the platform with
the higher access fee (platform A) or the cheaper platform (platform B): Moreover,
for each set of ten periods, the same set of subjects interacted with one another.
16
We examine the percentage of subjects choosing the cheaper platform for a given
“period,” which we de…ne as the iteration over which a given group of subjects has
interacted together. Thus, “period” x corresponds to rounds x, 10 + x, 20 + x, and
30 + x in each session. A key di¤erence across observations in the same period is
in the payo¤ matrix (N or T ) subjects faced, thus we aggregate the choices across
payo¤ matrices separately.
Figure 1 presents the percentages of subjects that chose the cheaper platform in
periods 1 to 10 for the twelve sets of non-tipped (N ) and tipped (T ) games. The
results from our experiment, in percentage terms, for these two games are presented
as “Actual Numbers in the Non-Tipped Game”and “Actual Numbers in the Tipped
Game”respectively. Each line thus represents 192 decisions as there were in together
twelve 10-period games with 16 subjects each in these six sessions. The …gure displays
two benchmark lines as well. One of these, labeled “CH Prediction,”corresponds to
the tipping prediction of the CH model when the proportion of level-0 types goes to
zero. The other, labeled “Non-tipped Equilibrium Prediction,” corresponds to the
equilibrium in which both platforms coexist that is present in the N treatments.
Two features of the …gure are noteworthy. First, the presence of an equilibrium
in which the two platforms can, theoretically, coexist appears to have little attractive
power to subject choices. Regardless of treatment, a very high percentage of subjects
choose the cheaper platform even in period 1. By period 5, nearly every subject
is selecting the cheaper platform. Furthermore, there is little di¤erence in either
the speed or amount of convergence to the cheaper platform between the T and N
treatments.
Second, theory o¤ers the possibility that some groups of subjects will converge to
the “wrong”platform. That is, it is quite possible for a given group of subjects to end
up coordinating on the more expensive platform A and the market would then tip
to this platform. However, we never …nd a market that tipped to the platform that
provided lower surplus to the consumers in our experiment. There were 96 iterations
(6 sessions
4 groups per session
4 iterations of 10 periods per group) where
groups participated in 10 periods of the game with the same payo¤ matrix. In none
17
of these 96 iterations did a group coordinate on the more expensive platform.
In Figure 2, we also present a time series of the percentages of players going to
the cheaper platform in sessions 1, 3 and 5 together and in 2, 4 and 6 together in
all 40 periods to see how platform choice dynamics works throughout the game and
also to see whether presenting the game with only tipped equilibria …rst or second
makes any di¤erence in outcomes. Each of the lines in Figure 2 represents decisions
by 48 subjects in each period. This …gure shows that once a market converges to the
cheaper platform, the market stays tipped there throughout the session. Moreover,
there is little evidence of a presentation e¤ect. Hence, we feel justi…ed in pooling the
sessions as in Figure 1. Another point to note is that if all subjects chose the cheaper
platform B, in all periods each would earn HKD 180 and the average payment to
subjects in these sessions was above HKD 172.
4.2
Jumbo Sessions
4.2.1
Description
In the baseline sessions, there were four players in a market. These players quickly
coordinated to reach the most e¢ cient equilibrium (for the players) regardless of
the treatment or the presentation order. One limitation of these results is that the
coordination problem may be too simple since there are only a small number of
agents operating in each two-sided market. Perhaps in markets with more agents,
tipping to the less ine¢ cient platform and equilibrium coexistence are more plausible
as coordination becomes more di¢ cult.
To investigate this possibility, we doubled the number of agents participating in
markets with homogeneous platforms. Speci…cally, for sessions 7 and 8 we designed
a market with four male and four female players. We also increase the number of
rounds from 40 to 60 to allow us to observe shifting market dynamics in this more
complicated setting. Thus, each of N or T treatment was played continually for 15
rounds.
Payo¤s
The access fees for the two platforms were pA = 6 and pB = 2. Table 3 presents
18
the gross payo¤ matrix for the N treatment where equilibrium coexistence is possible.
The usual equilibria in which all players coordinate on either platform A or platform
B are present. Of more interest is the equilibrium where the platforms coexist— here
this occurs when 2 female and 2 male players go to one platform while the remaining
players go to the platform.
Table 3: Jumbo: N Payo¤ Matrix
Number of players of the player's own type
(including herself) in the platform she joined
Number of
players of
the opposite
type in the
platform
she joined
1
2
3
4
0
7
7
7
7
1
11
10
7
7
2
13
12
7
7
3
15
14
13
10
4
17
16
15
14
Table 4 presents the gross payo¤ matrix for the T treatment. As in the Baseline
sessions, the matrix di¤ers from the N treatment payo¤ matrix in that the market
impact e¤ects are less severe thus allowing the market size e¤ects to dominate and
tipping to result.
19
Table 4: Jumbo: T Payo¤ Matrix
Number of players of the player's own type
(including herself) in the platform she joined
Number of
players of
the opposite
type in the
platform
she joined
1
2
3
4
0
7
7
7
7
1
11
10
9
8
2
13
12
11
10
3
15
14
13
12
4
17
16
15
14
For reasons identical to those in the Baseline sessions, the model with CH agents
predicts that all agents of level 1 and higher will coordinate on the cheaper platform.
Sessions 7 and 8 were mirror images of each other. In session 7, the gross payo¤
matrix were given by table 4 in periods 1 to 15 and 31 to 45 and were given by table
5 in periods 16 to 30 and 46 to 60. In session 8, the gross payo¤ matrix were given by
table 5 in periods 1 to 15 and 31 to 45 and were given by table 4 in periods 16 to 30
and 46 to 60. The exchange rate in these sessions was HKD 1 for 4 points implying
that if all subjects choose the cheaper market in all sessions then they would earn
HKD 180 each from the sessions.
4.2.2
Results
Figure 3 reproduces the analysis of Figure 1 for the Jumbo sessions. Notice that,
despite the apparent increase in the di¢ culty of coordination associated with doubling
the size of the market, subjects quickly learn to coordinate on using the cheaper
platform and remain there once this coordination is achieved. As with the Baseline
sessions, the presence or absence of a non-tipped equilibrium appears to have little
in‡uence on subject choices. Also, much as in the Baseline sessions, any Pareto
20
dominated equilibrium never arose.
Figure 4 presents a time series of the percentages of subjects going to the cheaper
platform in all sixty periods of the two Jumbo sessions. The …gure shows that in both
treatments, the market converges to the cheaper platform very quickly. The results
are very similar to those in the benchmark setting. In fact, doubling the number of
players do not seem to a¤ect the coordination problem at all. The market converges
as fast as it did in the benchmark setting, if not faster.
4.3
Discussion
In the homogenous platform settings, the presence of a non-tipped equilibrium does
not a¤ect subjects’ platform choices. Using Wilcoxon signed-rank test, we fail to
reject the null hypothesis that subjects played the games N and T for both baseline
and Jumbo sessions.7 Theory models also o¤er the possibility that some groups of
subjects will converge to the “wrong”platform in a two-sided market and then getting
stuck with this outcome. Indeed, there are many widely discussed examples in the real
world of this type of convergence including the Dvorak versus QWERTY keyboard,
Betamax versus VHS, and Mac OS versus Windows. We do not see any examples
of QWERTY-like convergence at all in either of the homogenous platform settings.
Although QWERTY keyboards were introduced long before Dvorak keyboards and
thus that may be the reason behind the ine¢ cient tipping, VHS and Betamax video
systems were launched more or less at the same time and still the market tipped to
the, arguably, inferior system VHS.
In our experiments, in both baseline and jumbo sessions markets converged equally
quickly to the more e¢ cient platform as evidenced in …gures 1 to 4 and Table 17.
The market size did not a¤ect the …nal outcome or even the speed of convergence. In
the minimum action games in Van Huyck, Battalio and Beil (1990), the size of the
market a¤ected whether subjects could coordinate to the most e¢ cient equilibrium.
Subjects converged to taking the lowest possible action as the minimum action in all
sessions with 14-16 subjects in a group. However, when subjects played in 2-player
7
We ignore the …rst few periods of a session in these tests.
21
groups, quite frequently all subjects chose the highest possible action. The games our
subjects play are not minimum action games and this game seems to be una¤ected by
the market size. Interestingly, the CH model suggests that the equilibrium predictions
are independent of the market size in our model but are dependent on the market
size in a minimum action game a la Van Huyck, Battalio and Beil (1990).
5
Vertically Di¤erentiated Platforms
The results from sessions 1 to 8 suggest that when platforms are homogeneous, subjects quickly learn to coordinate on the cheaper platform regardless of the size of
the market or the presentation order of the payo¤ matrices. Perhaps surprisingly,
this result also holds regardless of the severity of the market impact e¤ect. In other
words, even when equilibrium coexistence is a possibility, it seems to play no role in
subject choices. On the other hand, the results coincide with the predictions of the
CH model.
Of course, there are a number of other heuristics and equilibrium re…nements that
yield the same prediction as the CH model. For instance, if subjects follow the simple
heuristic strategy of choosing the cheaper of the two platforms, one obtains the same
prediction. Perhaps a more sophisticated path to the same prediction is to use the
Pareto criterion to re…ne the set of Nash equilibrium. Since the cheaper platform is
also the more e¢ cient platform under homogeneous platforms, this leads to the same
conclusion. However, the overall results of Van Huyck, Battalio and Beil (1990, 1991)
should give one pause in using the Pareto criterion as an obvious basis for predicting
subject behavior in coordination games.8
To disentangle these competing predictions requires that we enrich the modeling
framework by allowing the platforms to di¤er in ways other than the access fees
they charge. Moreover, such di¤erences across platforms are obviously present (and
important) in the real world and hence of considerable interest in their own right. In
the next set of experiments, we look at a market where the two competing platforms
8
Predicition from the CH model coincide with the risk-dominant equilibrium in all the settings
in this paper.
22
have di¤erent e¢ ciency levels as well as di¤erent access fees. Thus, the di¤erence
between the platforms are two-dimensional instead of one-dimensional. The two
platforms have di¤erent e¢ ciency levels in matching the players who join that market
and they may be di¤erentiated in other quality aspects too. As a result, the gross
payo¤ matrices for the two platforms will typically di¤er.
In our experimental design, it is very simple to create platforms that di¤er in the
level of e¢ ciency in matching the agents of two types. As the gross payo¤ matrix
denotes matching e¢ ciency, we just provide the subjects with di¤erent gross payo¤
matrices for the two platforms in these settings. The platforms also vary in the entry
fee and we look at cases where the more expensive …rm is generally more e¢ cient in
matching agents. That is it o¤ers higher gross payo¤s for most outcomes.
With vertically di¤erentiated platforms, the market tipping to the cheaper platform is not always the CH model’s prediction and also is not always the Paretodominant equilibrium. In sessions 9 to 20, we run four sessions each under three
di¤erent settings with di¤erentiated platforms. In the …rst case, both the CH model
and Pareto criterion suggest tipping to the cheaper platform. Next we look at the case
where both models predict that the market will tip to the more expensive platforms.
In the last setting, the CH model predicts that the market tips to the cheaper platform while the market tipping to the more expensive platform is the Pareto dominant
equilibrium.
5.1
5.1.1
Di¤erentiated I Sessions
Description
In these sessions, platform A is more e¢ cient in matching males and females than is
platform B; however, the access fee for platform A is set su¢ ciently high so that, net
of access fees, surplus is still higher in the cheaper platform. Speci…cally, in sessions 9
to 12, we gave the subjects two di¤erent gross payo¤ matrices for the two platforms.
For the N treatment, the gross payo¤ matrices for platforms A and B are presented
in Tables 5 and 6 respectively. The access fees are pA = 5 and pB = 2.
With these payo¤s there are the usual tipping equilibria as well as an equilibrium
23
in which both platforms can coexist where one pair of male and female players goes
to platform B and the other pair goes to platform A.
Table 5: Di¤erentiated I: N Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
6
6
1
10
7
2
13
12
Table 6: Di¤erentiated I: N Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
1
2
0
3
3
1
9
6
2
12
11
However, in the CH model, there is a unique equilibrium where all players of level
1 and higher go to platform B: A rough intuition is as follows: a level 1 player expects
an average of one player of the other type an each platform. The other player of her
own type goes to either of the platform with equal probability leading to expected
payo¤ of 10 and 7 with equal probability. In contrast, accessing platform B yields a
lottery of 9 and 6. However, accessing A costs an additional 3 points compared to B;
hence, it is optimal for these types to choose platform B: For higher level players, the
prospect of level 1 types, all of whom choose platform B; strengthens the bene…ts of
24
choosing B versus A owing to the size e¤ect. The market tipping to platform B is
also the Pareto dominant equilibrium.
T Treatments
Next, we turn to the T treatment where there is no non-tipped equilibrium. The
gross payo¤ matrices for platforms A and B under this treatment are presented in
tables 7 and 8 respectively. Again, players get higher net payo¤s in the B platform
tipped equilibrium than in the other tipped equilibrium and all level-k players for
k
1 go to market B in the unique equilibrium according to the CH model.
Table 7: Di¤erentiated I: T Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
6
6
1
10
9
2
13
12
Table 8: Di¤erentiated I: T Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
1
2
0
3
3
1
9
8
2
12
11
The Di¤erentiated I sessions consisted of 60 rounds but were otherwise the same
as the Baseline sessions. Sessions 9 and 11 were N T N T while sessions 10 and 12 used
25
the opposite presentation order.
5.1.2
Results
Figure 5 presents a time series of the percentages of subjects going to the cheaper
platform in all sixty periods for the Di¤erentiated I sessions. The …gure shows that
in the T N T N presentation ordering (Sessions 9 and 11), the market converges to
the cheaper platform fairly quickly and remains that way. In contrast, when the N
treatment is presented …rst (Sessions 10 and 12), the market “almost” converges to
the cheaper platform in the …rst 15 periods but never gets 100% subjects choosing the
cheaper market. Ultimately, in that set, around 94% of the subjects choose platform
B. This occurs because one of the 4-player groups in session 11 fails to converge to
any speci…c outcome in the …rst 15 periods. After the reshu- e of groups and type
allocation, all 4 groups converge to platform B very quickly and the entire market
remained that way for the rest of the session. Interestingly, the aforementioned group
did not converge to the A platform tipped or non-tipped Nash equilibrium. It simply
failed to converge to anything.
Figure 6 combines all the four sessions in this setting and presents the percentages
of subjects that chose the cheaper platform in periods 1 to 15 for the eight sets of
15-period non-tipped (N ) and tipped (T ) games. As was the case with homogeneous
platforms, the subjects quickly converged to the platform o¤ering the higher net payo¤
and remained there throughout the session. The presence of an equilibrium where
coexistence was possible appeared to have no attractive e¤ect to subjects nor were
there any groups that managed to converge to a QWERTY outcome of coordinating
on the platform yielding lower net payo¤s.
As with homogeneous markets, the behavior is consistent with the CH model as
well as with the cheaper platform heuristic and the Pareto criterion. In the next two
sections, we examine treatments with the power to distinguish among these three
possibilities.
26
5.2
5.2.1
Di¤erentiated II Sessions
Description
In sessions 13 to 16, unlike the Di¤erentiated I sessions, we reduced the access fee for
platform A such that it also o¤ered the higher net surplus among tipped equilibria
while still having a higher access fee. Thus, under cheaper platform heuristic, subjects should coordinate on platform B while under the Pareto criterion, they should
coordinate on platform A:
For all treatments, the access fees were pA = 3 and pB = 2. The gross payo¤
matrices for platforms A and B under the N treatment are presented in tables 9 and
10 respectively. The more expensive platform A gives subjects higher gross payo¤s.
When players exhibit cognitive sophistication according to the CH model, then there
is a unique Nash equilibrium where all level-k players for k
1 go to platform
A. Although platform B is cheaper, it is not cheap enough given that platform A
provides a signi…cantly higher level of gross payo¤s. Only in sessions 13 to 16 the
market should tip to the more expensive platform according to the CH model.
Table 9: Di¤erentiated II: N Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
4
4
1
11
8
2
13
12
27
Table 10: Di¤erentiated II: N Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
1
2
0
4
4
1
8
6
2
11
10
As before, there are three Nash equilibria with rational players with the above
payo¤ matrices. Players get higher net payo¤s on the A platform tipped equilibrium
than on the B platform tipped equilibrium. In the non-tipped equilibrium, players
who go to platform A get higher net payo¤s but the market impact e¤ects are enough
to preclude a pro…table deviation.
The gross payo¤ matrices for platforms A and B under the T treatment are
presented in tables 11 and 12 respectively. Players get higher net payo¤s in the A
platform tipped equilibrium than in the B platform tipped equilibrium. All levelk players for k
1 go to the more expensive market A in the unique equilibrium
according to the CH model.
Table 11: Di¤erentiated II: T Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
4
4
1
11
10
2
13
12
28
Table 12: Di¤erentiated II: T Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
5.2.2
1
2
0
4
4
1
8
6
2
11
10
Results
Figure 7 presents a time series of the percentages of subjects going to the more
expensive platform in all sixty periods for the Di¤erentiated II sessions. Looking at
treatment N T N T (sessions 13 and 15) and treatment T N T N (sessions 14 and 16)
separately in Figure 7, we see that the market tips to the more expensive platform
in treatment T N T N fairly early in the …rst 15 periods. However, in the treatment
N T N T , the market seems to converge to an outcome where around 75% of the
subjects (24 out of 32 in sessions 13 and 15 combined) go to the more expensive
platform A and the remaining 25% of the subjects go to the cheaper platform B
in the …rst 15 periods. In the remaining 45 periods, in all four sessions of the two
treatments, the market converges to the more expensive platform quickly. This is
also evident in Figure 8, which presents the percentages of subjects that chose the
more expensive platform in periods 1 to 15 for the eight sets of non-tipped (N ) and
tipped (T ) games.
Figure 7 suggests that the two treatments fare di¤erently only in the …rst set
of 15 periods. In fact, we fail to reject the hypothesis that the subjects behaved
di¤erently when a non-tipped equilibrium existed using a Wilcoxon signed-rank test
when we look at the last 30 periods for all four sessions. In all cases, the simple
“choose the cheapest platform” heuristic receives little support. Instead, the results
are more closely approximated by the CH model or the Pareto re…nement. It is,
29
however, instructive to look more closely at the …rst rounds of the N T N T sessions.
In these periods, the market does not tip to the more expensive platform and even
seems to reach a non-tipped outcome. Looking individually at each of the eight 4player groups that formed a market in sessions 13 and 15 in those periods, we see that
the aggregation here is misleading. Each of these small markets actually tipped— to
the more e¢ cient platform three quarters of the time and to the ine¢ cient platform
one-quarter of the time. Here at last is some evidence that, with su¢ cient platform
di¤erentiation, local interactions can lead to tipping with QWERTY outcomes. However, once we reshu- ed the groups after the end of period 15, all eight new markets
converged quickly to the e¢ cient equilibrium. There is, moreover, still no behavioral
evidence in favor of equilibrium coexistence.
Even in this relatively complicated setting, we cannot experimentally reach a
non-tipped equilibrium. Nevertheless, super…cially, the overall market looks rather
non-tipped— at least at the early stages of each session. This presents an interesting
idea, if players in a market are su¢ ciently segregated that populations of both types
can be segmented into partitions in a way that members of partition i of one type are
only interested in members of partition j of the other type and vice versa, the market
may look non-tipped even though at a deeper level the smaller markets are tipped.
This may be a useful description of US online dating markets which, at an aggregate
level, appear to o¤er support for platform coexistence, but might, at a more local
level, re‡ect mainly locally tipped markets.
5.3
5.3.1
Di¤erentiated III Sessions
Description
In both of the previous di¤erentiated platforms settings, the unique equilibrium suggested by the cognitive hierarchy model is also the Pareto dominant equilibrium.
One possible explanation for our results can be subjects intuitively converge to the
Pareto dominant equilibrium. To examine this possibility, we modify the gross payo¤
matrices so that the Pareto dominant equilibrium is di¤erent from the equilibrium
predicted by the CH model.
30
In sessions 17 to 20, the access fees were set to pA = 3 and pB = 2. The gross
payo¤ matrices for platforms A and B under the N treatment are presented in tables
13 and 14 respectively. The equilibrium where all players go to the more expensive
platform A Pareto dominates all other equilibria. On the other hand, the unique
equilibrium in the CH model is for all level-k players for k
1 to use platform B.
Intuitively, a level 1 CH player ascribes signi…cant probability to the outcome
where both players of the other type use platform B while no player of her own type
uses that platform. This yields an extremely attractive payo¤ of 22. Once the level
1 players select platform B; then, owing to the market size e¤ect, it is optimal for all
more sophisticated types to follow suit and also select platform B.
Table 13: Di¤erentiated III: N Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
4
4
1
11
8
2
13
12
Table 14: Di¤erentiated III: N Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
1
2
0
4
4
1
8
6
2
22
10
31
The gross payo¤ matrices for platforms A and B under the T treatment are
presented in tables 15 and 16 respectively. Again, coordination on platform A is
Pareto dominant while the CH model and risk-dominance predicts coordination on
platform B.
Table 15: Di¤erentiated III: T Payo¤ Matrix for Platform A
Number of players of the player's
own type (including herself) in
platform A
Number of
players of the
opposite type
in platform A
1
2
0
4
4
1
11
10
2
13
12
Table 16: Di¤erentiated III: T Payo¤ Matrix for Platform B
Number of players of the player's
own type (including herself) in
platform B
Number of
players of the
opposite type
in platform B
5.3.2
1
2
0
4
4
1
8
6
2
22
10
Results
Figure 9 presents a time series of the percentages of subjects going to the cheaper
platform in all sixty periods for the four Di¤erentiated III sessions separately. It
is readily apparent from the …gure that subject choices di¤ered substantially across
sessions. In session 17 (the N T N T ordering), subjects rapidly coordinated on the less
e¢ cient platform B— consistent with the predictions of the CH model and contrary
32
to the Pareto re…nement. In session 18 (the T N T N ordering), there is no evidence of
convergence at the aggregate level. In sessions 19 and 20 there are some convergence
at the aggregate level only towards the end of the session. However, over the four
sessions, N and T treatments do not look so di¤erent and we cannot reject the
null hypothesis that subjects behave similarly under these two treatments using a
Wilcoxon signed-rank test even when we consider all periods. Figure 10 presents the
percentages of subjects that chose the cheaper platform in periods 1 to 15 for the
eight sets of non-tipped (N ) and tipped (T ) games and shows that although we do
not see any converging trends in 15-period games under either treatments when look
at all four sessions together, there is no clear distinction in the two treatments with
di¤erent market-impact e¤ects.
Overall, results from Di¤erentiated III sessions are very nuanced. This may have
resulted from the fact that to create di¤ering predictions from the CH model and
Pareto criterion, we had to make the payo¤ function from platform B extremely
lop-sided. The payo¤ from going to this platform when both players of the other
type goes to platform B but the competing player of the own type goes to plat
form A is 22, much higher than the second highest possible payo¤ of 10. This may
have led to the divergent results from these sessions. Very few markets succeeded in
converging within a 15-period set and there does not seem to be any clear pattern in
the di¤erences between sessions. Nevertheless, none of 4-player markets ever chose the
non-tipped equilibrium outcome for more than three periods in a row even when this
was an equilibrium. Interestingly, all markets in session 17 converged to the Pareto
ine¢ cient equilibrium predicted by the CH model by the 20th period and stayed
that way while session 19 converged to the Pareto dominant (but not predicted by
the CH model) equilibrium toward the end of the session. On the other hand, two
2-player markets went for the cheaper platform as predicted by the CH model and
the remaining two markets tipped to the Pareto e¢ cient more expensive platform.
Many of the 4-player markets never converged to any particular equilibrium (or
non-equilibrium) outcome in the 15-period games. If they did converge, the markets
tipped to either of the platforms. As a result, although the overall market looks non-
33
tipped as in Di¤erentiated II sessions, individual markets within the session actually
never reached a non-tipped equilibrium. But it is hard to say that the tipping was
more prevalent towards the cheaper or more expensive market. Thus, neither CH
model or Pareto criterion does overwhelmingly better than the other.
5.4
Discussion
The di¤erentiated platforms setting, in addition to being more realistic, also leads to
some interesting results. First, we …nd that the markets take much longer to converge
to some outcome. Especially, they frequently failed to converge within the 15 periods
in the third di¤erentiated platform setting. Given that one of the platforms have a
very lopsided gross payo¤ function in these sessions, we may ignore that setting. Still,
we do …nd that when platforms vary in two dimensions— matching e¢ ciency and entry
fees, as is common in the real world, convergence to a particular outcome becomes
more di¢ cult. Second, disconnected market segments within the larger market may
tip to di¤erent platforms. This market segmentation is di¤erent from those suggested
by The …rst two observations suggests that even when a large market seems nontipped from a distance, when we look at it closely, we may …nd that it is because
di¤erent disconnected segments of the market have tipped to di¤erent platforms or
some market segments have not yet reached a steady state. This is di¤erent from the
segmentation inside a connected market suggested by Damiano and Li (2005) where
lower-quality agents go to one market and higher quality agents go to the other.
Our result resembles more the observation that online dating markets and online
auction markets are somewhat geographically segmented. Third, we …nd tipping to
the platform o¤ering lower net payo¤s, a QWERTY-like outcome, can occur in the
di¤erentiated platforms setting. Finally, even though slow convergence and market
segmentation may lead to apparent non-tipping in markets, market impact e¤ect as
suggested by Ellison and Fudenberg (2003) and Ellison, Fudenberg and Möbius (2004)
seems to be ine¤ective even in the di¤erentiated markets setting. The results also
lead to an empirically testable implication— a market with homogenous platforms is
more likely tip than market where platforms are more di¤erentiated.
34
6
Conclusions
Success stories in platform competition— Google, Yahoo, Microsoft, eBay— have created spectacular amounts of wealth for shareholders. In all of these situations, size
e¤ects, combined with various other advantages, worked to produce markets where
the market shares of the “winners”versus the “losers”among platforms are vastly unequal. Existing theory models dating as far back as Schelling (1972) can account for
the possibility of tipping, but have little to say about how to tell the winners from the
losers before the fact. More recent theoretical work has suggested that compensating
market impact e¤ects— the competitive e¤ect of the introduction of another player
onto an existing platform— can lead to coexistence between platforms in equilibrium,
even if market shares are vastly unequal.
Testing such models using …eld data is inherently di¢ cult. It is easy to perceive
after the fact that the computer operating system market has tipped to Windows
or that online auctions in the US have tipped to eBay, but a much more di¢ cult
proposition to identify what factors, if any, might have led to a di¤erent outcome.
Retrospective evaluations of the evolutions of these markets have the ‡avor of “just
so”stories— that is, theory can be made to …t the facts, but the data are insu¢ cient
to examine the counterfactual implications of these same theories.
For this reason, we think that laboratory experiments have an essential role to play
in adding to understanding of when markets tip. Moreover, laboratory experiments
o¤er a useful middle ground between the theory models, many of which are static,
and the real-world markets for online dating, online auctions, and so on, which are
inherently dynamic. Our experimental setup bridges this gap by choosing payo¤s
such that a static analysis is possible while studying dynamic interactions by a set of
participants in platform competition. Thus, we see our approach as somewhat in the
spirit of the pioneering experimental work done by Smith, Plott and many others in
connecting real world market institutions with the abstraction of competitive markets
o¤ered by theory.
The title of our paper asks the question when do markets tip. A useful starting
point is the contrary statement— when don’t markets tip? One possible answer to
35
this question o¤ered by the extant theory literature is that markets do not tip when
there exists an equilibrium where both platforms can coexist. This usually happens
when the market impact e¤ect is large enough. We …nd no evidence to support this.
Another answer is that markets don’t tip when platforms are su¢ ciently di¤erentiated
that individual groups of agents interacting with one another can end up coordinating
on either platform. We …nd some evidence of this, but overwhelmingly, disparate
groups of subjects seem to coordinate on the same platform. Only when matching
e¢ ciency of a platform is lopsidedly distributed we …nd that markets take a long time
to converge; but, they still do not converge to a non-tipped outcome. Taken together,
the evidence from the experiments suggests that in the overwhelming majority of
situations where size e¤ects are present and the e¢ ciency di¤erences between two
platforms are somewhat monotonic, the market will tip.
That being the case, the next logical question is to which platform will the market
tip? How can one determine the winners from the losers before the fact that tipping
has taken place? The standard solution concept, Nash equilibrium, o¤ers no answer
to this question. Indeed, a matter of some considerable interest to social scientists
is the possibility that such markets will tip to the “wrong” platform and then get
stuck there, what we term in the paper the QWERTY e¤ect. While we occasionally
observe the QWERTY e¤ect in our experiments, it appears to be very much the exception. Indeed, subjects seem remarkably good at coordinating on the more e¢ cient
equilibrium.
This would seem to suggest using the Pareto re…nement to select among equilibria.
While this is indeed quite useful in characterizing outcomes with homogeneous platforms, it is known to be a poor predictor in a wide variety of other coordination games.
Therefore, we o¤er an alternative solution concept— cognitive hierarchies. Modeling
agents as having heterogeneous cognitive levels and then best responding given their
beliefs yields a unique equilibrium that suggests not only that tipping is inevitable
but also to which platform the market will tip. With homogeneous platforms, the CH
model does well to predict subject behavior, but su¤ers from the weakness that its
predictions are identical to the Pareto re…nement and a simple heuristic strategy—
36
choose the platform with the cheaper access fee. With di¤erentiated platforms, we
constructed payo¤ parameters to distinguish the competing theories and …nd, overall, the predictions of either models are far from perfect. Certainly, subjects to not
instantly coordinate in a game, coordination seems to take time and some shared
history. However, once subjects achieve coordination, they remain coordinated on
that platform. Moreover, in the sternest test of the CH model, settings where the CH
model di¤ers from the Pareto re…nement, we sometimes observed subject behavior
that was chaotic and not well predicted by any existing theory of which we are aware.
Although we do not have strong support to reject either the CH model or Pareto criterion, we can easily reject the hypothesis that equilibrium coexistence occurs from
the market impact e¤ect.
One of the lessons about the industrial organization of two-sided markets we
learn from this experiment is that these markets are naturally prone to tipping— even
when markets divide itself into di¤erent disconnected segments, the segments seem
to tip, perhaps to di¤erent platforms. Moreover, markets usually tip to the more
e¢ cient platform when the net di¤erences between platforms are clear. However,
when platforms di¤er in multiple dimensions, tipping to the less e¢ cient platform
becomes more likely to happen. Unlike many coordination game experiments, we …nd
that subjects succeed in coordinating to the best outcome in many sessions and the
group size does not seem to a¤ect the coordination problem. Both cognitive hierarchy
model of analytical sophistication and the Pareto criterion succeed in explaining the
overall results although neither clearly does a better job than the other in that respect.
While we have explored a number of avenues of platform competition and tipping,
there remains vast area to be explored. First, we treated the access price for each
platform as exogenous. In reality, platform pricing is a key component of competitive
strategy by platforms. (Witness the price competition in online auctions in the late
1990s with the entry of Amazon and Yahoo into this space.) One interesting avenue is
to make the platform provider itself a strategic player along the lines of Caillaud and
Jullien (2003). The agents of any given type were homogenous in our experiments.
Markets where agents have heterogeneous preferences might be more likely to reach
37
a non-tipped outcome. A third avenue is multi-homing. In most theory models and
in our experiments, subjects were required to single-home— choose to access only a
single platform. Yet, in many markets multi-homing is possible and in some (like
credit cards) it is the norm; thus, this would seem a fruitful area to investigate.
Fourth, for many of these markets, there is both a history of past market shares as
well as a continuing in‡ux of new agents coming into the market. Indeed, many of
the QWERTY-type arguments are based on the idea that an early player can gain an
advantage and, owing to its substantial share of existing agents, it can easily attract
new agents even in the face of superior competing platforms. On the other hand,
Google has taken over the mantle most prominent search engine despite entering after
yahoo and AltaVista had established their search engines solidly. A natural question
is how much more e¢ cient a newly entrant platform has to be to tip a tipped market
towards itself. Thus, examining platform competition and the presence of tipping
in an overlapping generations type of setting would also appear to be an extremely
useful next step.
38
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41
Appendix: Instructions to Subjects in the Baseline Sessions
Date: XXX
Name:
Student ID:
Instructions
General Rules
This session is part of an experiment in the economics of decision making. If you follow
the instructions carefully and make good decisions, you can earn a considerable amount
of money. You will be paid in private and in cash at the end of the session.
There are sixteen people in this room who are participating in this session. They have all
been recruited in the same way as you and are reading the same instructions as you are
for the first time. It is important that you do not talk to any of the other participants in the
room until the session is over.
The session will consist of 40 periods, in each of which you can earn points. At the end of
the experiment you will be paid based on your total point earnings from all 40 periods.
Each point is worth 50 cents. Thus, if you earn y points from the experiment then your
total income will be HKD y/2. Notice that the more points you earn, the more cash you
will receive.
Description of a Period
At the start of period 1, you will be randomly matched with exactly three other subjects
in the room and will be designated as either a square or a triangle player. You and these
three others form a “market” consisting of exactly two triangle players and two square
players. During periods 1 through 10 you will be playing with the same three other
people and retain the same type (square or triangle). At the start of period 11, you will be
randomly matched with three other people in the room and randomly designated the types
square or triangle and will play in a new market. The same thing will happen at the start
of periods 21 and 31. Thus, the people with whom you are participating will change
every ten periods and your type may also change.
In each period, you will decide between joining either one of two competing firms
(labeled “firm %” and “firm #”). If you join firm #, you pay a subscription fee of 4 points
and if you join the firm %, you pay a subscription fee of 2 points. The three other players
in your market will also individually decide on which firm to join at the same time as
you. On your screen, click on the firm (% or #) that you want to join. After you click
“OK,” a new box will pop up to confirm that you are certain about your choice. If you
want to stay with your choice, please click “yes” and click “no” otherwise. If you click
“no,” you will go back to the initial box that allows you to choose one of the firms. When
all the players in the market have made their decisions, you will learn your payoffs.
42
At the end of the period, for each firm, you will learn the number of players of each type
that joined that firm in that period. Your net payoff depends on the numbers of players of
each type in the firm that you join as well as that firm’s subscription fee. Once you join a
firm, before paying the subscription fee, in rounds 1-10, you will earn a gross payoff
according to Table 1. The two columns present your gross payoffs when the number of
players of your type (including yourself) in the firm you choose is 1 and 2 respectively.
The three rows present your gross payoffs when the number of players of your opposite
type in the firm you choose is 0, 1 or 2 respectively. You will be able to see the table on
your screen during these periods.
Table 1. Gross payoffs before paying the subscription fee in periods 1-10 and 21-30
Number of players of your own type
(including yourself) in the firm you joined
1
2
Number of players of
0
5
5
the opposite type in
1
9
6
the firm you joined
2
12
11
The subscription fee is 2 for firm % and 4 for firm #. At the end of the period, you will
see your net payoff (your gross payoff minus your firm’s subscription fee) in points from
that period. At the end of every 10 periods, you will see your net payoffs from all
previous periods.
Differences between periods
At the start of period 11, your payoffs will change. Specifically, in rounds 11-20, you will
earn gross payoffs (before paying the subscription fee) according to the following table:
Table 2. Gross payoffs before paying the subscription fee in periods 11-20 and 31-40
Number of players of your own type
(including yourself) in the firm you joined
1
2
Number of players of
0
5
5
the opposite type in
1
9
8
the firm you joined
2
12
11
Once again, you will be able to see the table on your screen during these periods. Also,
remember that the subscription fee is 2 for firm % and 4 for firm #.
The payoffs in periods 21-30 are calculated in the same way as in periods 1-10 using
Table 1. The payoffs in periods 31-40 are calculated in the same way as in periods 11-20
using Table 2.
Ending the session
At the end of period 40, you will see a screen displaying your total earnings for the
experiment. Recall that, if you earn y points in total from the experiment, your total
income from the experiment would be HKD y/2. You will be paid this amount in cash.
43
Table 17: Subjects' Platform Choices at Different Stages of the Sessions in
The Homogenous Platform setting
Percentages of Players in the Cheaper Platform
Baseline Sessions
Jumbo Sessions
Last 5 Periods of the First Set
96.9%
99.7%
Last 5 Periods of the Second Set
99.6%
100.0%
Last 5 Periods of the Third Set
99.8%
100.0%
Last 5 Periods of the Fourth Set
99.8%
100.0%
The Entire Session
96.7%
98.2%
44
Percentages of Subjects in
the Cheaper Firm
Figure 1: Time Series of Market Choice for the NonTipped and Tipped Games in the Benchmark Setting
Actual Numbers in the
Non-Tipped Game
Actual Numbers in the
Tipped Game
CH Prediction
100%
80%
60%
Non-tipped Equilibrium
Prediction
40%
1
2
3
4
5
6
7
8
9
10
Period
Percentages of Subjects in
the Cheaper Firm
Figure 2: Time Series of Market Choice Throughout the
Sessions and the Presentation Effect
110%
100%
90%
Sessions 1, 3 and 5
Sessions 2, 4 and 6
80%
70%
60%
1
5
9 13 17 21 25 29 33 37
Period
45
Percentage of Subjects in
the Cheaper Firm
Figure 3: Time Series of Market Choice
in the 8-Player Setting
110%
100%
90%
Session 7
Session 8
CH Prediction
80%
70%
60%
50%
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57
Period
Percentages of Subjects
in the Cheaper Firm
Figure 4: Time Series of Market Choice for the NonTipped and Tipped Games in the 8-Player Setting
Actual Numbers in the
Non-Tipped Game
Actual Numbers in the
Tipped Game
CH Prediction
100%
80%
60%
Non-tipped Equilibrium
Prediction
40%
1
3
5
7
9
11
13
Period
46
15
Percentage of Subjects in
the Cheaper Firm
Figure 5: Time Series of Market Choice
in the Differentiated Firms Setting I
110%
100%
90%
Sessions 9 and 11
Sessions 10 and 12
CH Prediction
80%
70%
60%
50%
1
6 11 16 21 26 31 36 41 46 51 56
Period
Figure 6: Time Series of Market Choice for the NonTipped and Tipped Games in Differentiated Firms Setting
I
Actual Numbers in the
Non-Tipped Game
Actual Numbers in the
Tipped Game
CH Prediction
Percentages of
Subjects in the
Cheaper Firm
100%
80%
60%
Non-tipped Equilibrium
Prediction
40%
1
3
5
7
9
11
13
Period
47
15
Percentage of Subjects in
the More Expensive Firm
Figure 7: Time Series of Market Choice
in the Differentiated Firms Setting II
110%
100%
90%
Sessions 13 and 15
Sessions 14 and 16
CH Prediction
80%
70%
60%
50%
1
6 11 16 21 26 31 36 41 46 51 56
Period
Percentages of
Subjects in the More
Expensive Firm
Figure 8: Time Series of Market Choice for the NonTipped and Tipped Games in Differentiated Firms Setting
II
Actual Numbers in the
Non-Tipped Game
Actual Numbers in the
Tipped Game
CH Prediction
100%
80%
60%
Non-tipped Equilibrium
Prediction
40%
1
3
5
7
9
11
13
Period
48
15
Figure 9: Time Series of Market Choice
in the Differentiated Firms Setting III
Percentage of Subjects in
the Cheaper Firm
1.2
1
0.8
Session 17
Session 18
Session 19
Session 20
0.6
0.4
0.2
0
1
4
7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
period
Percentage of Subjects
in the Cheaper Firm
Figure 10: Time Series of Market Choice for the NonTipped and Tipped Games in Differentiated Firms Setting
III
0.75
0.7
Actual Numbers in the NonTipped Game
0.65
Actual Numbers in the Tipped
Game
0.6
0.55
0.5
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Period
49