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Platform competition and consumer’s decisions:
An ABM simulation of pricing with different
behavioral rules
Juan Manuel S´anchez-Cartas
Universidad Polit´ecnica de Madrid, Center of Support to Technology Innovation
(CAIT), Campus de Montegancedo, Madrid, Spain,
e-mail: juanmanuel.sanchez@upm.es
Abstract. I use an agent-based model (ABM) to study how consumer’s
behavior influences prices and how common simplifying assumptions con-
straints the explanatory power of classical models. I simulate an ABM
in which two multi-sided platforms compete for attracting buyers and
sellers. I use as a framework a theoretical market model in which the
difference among behavioral rules is overestimated because of the “mar-
ket covered” assumption that is necessary to make the model tractable.
Making realistic assumptions about the adoption process point out that
the difference among behavioral rules is not so extreme as theory says.
I find that assumptions regarding the spread of information, such as the
network topology, are more relevant in accounting for price differences
than behavioral rules.
Keywords: boundedly rationality, agent-based models, price competi-
tion, multi-sided markets
1 Introduction
Theoretical economic models make simplifying assumptions to be tractable, but
that may compromise their insights; a clear example of those assumptions is the
fully informed rational consumer. Although the consequences of incorporating
psychologically more realistic assumptions are well-known1, the interaction of
these assumptions with other simplifying assumptions – the fixed market size
or the full information – remains unanswered because the tractability may be
compromised. This is especially relevant for multi-sided markets2, in which cus-
tomers’ decisions depend on how many other different customers are on the
platform. For example, the number of consumers of Uber or Lyft depends on
the number of drivers, and vice versa. In this sense, the use of agent-based mod-
els and artificial intelligence allows us to address more realistic market models
1See, for example, the work of the Nobel prize winner Richard Thaler.
2In these markets, companies are platforms that coordinate the demands of several
consumer groups that need each other in some way, sellers and buyers, users and
developers, etc.
2 J. Manuel S´anchez-Cartas
without compromising their tractability.
Up to now, the study of multi-sided digital platforms (MSP) has focused on
the different equilibria that may appear with fully informed rational consumers.
Recently, some authors have started paying attention to different behaviors that
emerge when consumers make less informed decisions regarding the consumption
of digital platforms, see [2] for a theoretical approach, and [4] for an ABM ap-
proach. However, there is a gap in the literature regarding how those behaviors
interact with other assumptions. Especially, with the “market covered” assump-
tion that implies all consumers know and want to adopt at least one platform.
The model I propose is similar to those of [2] and [4]. On the one hand, I analyze
the role of behavioral economics on platforms competition using an ABM as [4],
but instead of building an ad-hoc setting, I adopt an assumption-relaxed version
of the [2]’s setting, which is a common framework in the MSP literature.
I consider six different behaviors: three behaviors from the behavioral economics
(BE) literature, and the other three from the classical industrial organization
(IO) literature. I address the differences between those behaviors in the [2]’s
setting and then, I compare those behaviors by relaxing the “market covered”
assumption. To do so, I consider that not all consumers know the platforms,
and even among those who know them, not all of them are willing to adopt
the platforms. In this sense, I assume there is a diffusion of information process
that determines who knows about the platforms combined with one of the six
behavioral rules, which determines who adopts which platform.
I find that, because of the market covered assumption, theoretical models tend
to overestimate the differences in equilibrium prices. I find similar prices levels
among the six types of behaviors once the market covered assumption is relaxed.
Additionally, the higher the prices, the lower the adoption. But, independently
of the demand or the prices, all the cases provide a similar profit level to the
platforms. Lastly, I find evidence following previous works that shows that the
network topology is essential to explain the observed differences in prices. In fact,
network topology seems to be the most relevant exogenous variable in terms of
price differences. The paper proceeds as follows. In Section 2, I present the mar-
ket, consumers, and their behaviors, while Section 3 is devoted to how prices are
set. In Section 4, I present the simulation results, and Section 5 gathers some
final remarks.
2 The market framework. Hagiu and Halaburda’s model
I adopt the same setting as [2], in which two platforms, j= 1,2 compete in
prices for sellers and buyers that are uniformly distributed in a line. Platforms
are at the extreme of that line. Initially, all buyers (sellers) obtain a stand-alone
value when being on a platform. This value is represented by θ. To guarantee
that all consumers buy at least one platform, the theoretical model assumes that
all consumers have an identical (and sufficiently high) stand-alone value. How-
ever, each buyer (seller) values each platform differently, and it is represented
by the distance between the buyer (seller) –xi– and the platform, lj. That dis-
Platform competition and consumer’s decisions 3
tance between platforms and consumers (sellers and buyers) –|lj−xi|– is called
“horizontal differentiation”, and it represents that, at the same level of prices,
some consumers prefer one platform, but other consumers prefer the competitor.
For example, at the same price, some consumers may prefer Coke over Pepsi.
The relevance of this differentiation in the utility is weighted by what is called
the transportation cost, t. The larger the t, the larger the relevance of the dif-
ferentiation in the decision-making process. In the extreme case in which tis
so high that only a platform provides positive utility, the model converges to a
monopolistic one. In this way, the expression t∗ |lj−xi|represents the disutility
of having a product that does not fit buyers’ (sellers’) tastes perfectly. All buy-
ers (and sellers) pay a price for using the platform. That price is the same for
all buyers (sellers) and depends on each platform, pb,j (ps,j). Lastly, each buyer
(seller) values the number of sellers (buyers) that can find on the platform. The
intuition is that the large the number of sellers (buyers) that a buyer (seller) can
find on the platform, the higher the utility. That is controlled by δbne
s,(δsne
b),
where ne
s(ne
b) is the expected number of sellers (buyers) on the platform, and
δis a parameter that controls for the relevance of such number. Implicitly, this
specification assumes that a buyer (seller) values all the sellers (buyers) on the
other side of the platform. Therefore, once on a platform, the buyer (seller) can
connect with all the sellers (buyers) on the other side3. Thus, the utility of the
i-buyer who adopts the platform jis as follows4
Uij =θb
i,j −tb∗ |lj−xi| − pb,j +δbne
s(1)
Buyers and sellers choose the platform that maximizes their utilities, so the
number of consumers that choose the same platform forms the demand for that
platform. However, such decision is subjected to six behavioral rules:
1. Rational: An i-agent is capable of forecasting the impact of any change
in price on the demands of any group of agents. Therefore, prices influence
his/her utility directly (via prices) and indirectly (via expectations).
2. Wary: Agents do not know the price that the other side pays, but they
assume platforms set an optimal price. Similar to the previous one, but it
changes how expectations are formed because agents only observe their price.
3. Passive: Agents do not know the price that the other side pays, and they
assume everything will remain equal. Thus, they do not form new expecta-
tions.
4. Heterogeneous: They are a 50% mix between Rational and Passive
5. Satisfaction rule: Agents choose randomly among the platforms that gen-
erate them a non-negative utility.
6. “Where my friends are”: This is a modification of the majority rule.
Agents choose the platforms with the largest number of neighbors on it, but
without considering the number of agents of the other group.
3The parameter δbcontrols how buyers value the presence of an additional seller. For
simplicity’s sake and without loss of generality, I assume that this value is constant
and equal for all buyers and sellers, δb=δs=δ.
4Symmetrically for sellers.
4 J. Manuel S´anchez-Cartas
The Rational, Wary and Heterogeneous are the “rational” rules from the IO
literature, and the Satisfaction rule, the Local Rationality, and the Passive are
the “behavioral rules” from the BE literature. Lastly, it is necessary to relax
some of the simplifying assumptions of the original theoretical model:
–Originally, the stand-alone value (θ) is constant and high for all consumers.
The ABM assumes θ∼N(−0.3,0.25). In this way, some consumers may not
use any platform at all.
–The theoretical model assumes a fully-connected network with fully informed
consumers (Covered Market assumption). The ABM assumes either a small-
world or a preferential attachment network with informed and uninformed
consumers5.
The two platforms compete in prices in fifty periods to attract buyers and sellers.
That is enough to reach stability in demands and prices6. At each moment,
buyers and sellers can be in three different awareness states: Those who do not
know any platform, those who know one platform only, and those who know
both platforms. 5% of buyers and sellers know the platforms at the beginning
of the simulations. These people represent the “innovators”. They can “infect”
other buyers and sellers with their information7. The process of adoption follows
an infection process as in [5] or [1]. Once buyers (or sellers) know one platform,
there is a probability of infecting other buyers in his/her network with that
information. The infection process depends on consuming the platform: buyers
and sellers have to consume to infect other agents with their information about
platforms. However, if a buyer (seller) knows one platform only, he/she will
spread the information about that platform only. If that buyer (seller) knows the
two platforms, he/she will only spread information about the platform he/she
consumes. Lastly, if they know one or two platforms, but they do not consume
any platform, they will not spread the information8.
3 The price competition algorithm
Although the ABM uses as a framework the [2]’s model, it omits the use of the
equilibrium equations to compute prices because they rely on theoretical assump-
tions that may influence the equilibrium, and relaxing any of those assumptions
5Both the preferential and the small-world networks were created with the default
primitives of the Netlogo NW extension that are based on the BarabsiAlbert al-
gorithm and Watts-Strogatz small-world network. Buyers and sellers have separate
networks, although both are either preferential or small-world.
6A period is an iteration in the simulation model.
7The probability depends on the normalized degree of each node. The higher the
degree, the higher the chance of being infected. The degree of each agent is divided
by 4. In this way, the most connected node will only be infected in 1 out of 4 cases.
8The infection process assumes either the innovators are scattered or clustered. The
insights remain valid in both cases. The only change is the adoption level that is
lower when clustered.
Platform competition and consumer’s decisions 5
implies solving the model again, which may be analytically intractable. To deal
with this issue, the ABM considers a price competition algorithm that simulates
the platforms’ strategic behavior. This algorithm has been previously used to
address the role of “influencers” in the launching of digital platforms and to
solve theoretical microeconomic models. However, despite its potential to sim-
ulate companies’ price-competing behaviors, it has not been used to address
companies’ behavior with boundedly rational consumers yet.
The price competition algorithm encompasses two sub-algorithms: the consumers’
and the companies’ ones, see Fig. 1. The ABM considers the consumers’ behav-
ioral rules, and platforms set prices by following a gradient-like pricing rule that
takes into account those behaviors9. It allows us to simulate the price competition
without using the equilibrium equations. Buyers and sellers choose the platform
that maximizes their utility functions but following the behavioral rules, and
platforms evaluate the impact on their profits of a small change (0.1) in prices.
If that change is profitable, they will increase or decrease the price by that
quantity. If not, they will maintain the current price10. In this setting, platforms
behave as fully informed and rational agents that contemporaneously choose the
best action to improve their profits.
4 Platform optimal prices and consumers’ behaviour
The ABM run in NetLogo 5.3.1 with 314 buyers and 314 sellers, and two plat-
forms11, [7]. The simulations are carried out by considering a specific set of
parameter values, however, other values can be considered without loss of gen-
erality. The parameter values considered are the following:
–θu,s
ivN(−0.3,0.25)
–tu=ts= 0.31
–δu=δs= 0.31
–probability of infecting (Pi), PivN(0.05,0.05)
Initially, the ABM run the theoretical model without relaxing the market covered
assumption, but with the six behavioral rules on the users’ side12. In Fig 2,
prices behave as expected in theory. The less rational, the higher the prices. [2]
finds this same result by solving the model analytically. However, [2] omits the
analysis with the “satisfaction” and “where my friends are” rules, but the results
intuitively are the same as expected in the literature.
9See [6] for a full description of the algorithm.
10 Profitability is measured in terms of net profits. In this framework, it is the sum of
the revenues on buyers’ and sellers’ sides. Formally: ns∗ps,j +nb∗pb,j.
11 The number of buyers and sellers is arbitrarily selected. Conclusions will not change
with a different number of agents.
12 To avoid that different behavioral rules from the sellers’ side may influence the results
on buyers’ side, sellers behave as rational agents in all the simulations.
6 J. Manuel S´anchez-Cartas
Fig. 1. Decision Processes
Platform competition and consumer’s decisions 7
Fig. 2. Theoretical prices with each behavioural rule
Relaxing the market covered assumption leads to a mitigation of the dif-
ferences between the optimal prices. In Fig. 3, the ABM run two small-world
networks that link buyers and sellers (Clustering and Avg. path length of 0.5 and
3.8 respectively). Although the order between the more expensive and cheaper
cases holds, the magnitude of the difference is significantly smaller. Therefore,
it seems that the market covered assumption leads to an overestimation of the
impact of behavioral rules over the platform prices. Another simulation with
a preferential attachment network shows the same pattern, although the price
levels change. These two results reflect the relevance of considering the network
topology in pricing, which is even more relevant than consumers’ behavior. And
their effects are not limited to prices, it influences demands too, which depend on
those prices as well. As expected, the more expensive the platforms, the lower the
adoption. The network topology influences the diffusion of information, which is
an overall constraint of demands and prices that is independent of the behav-
ior, but that plays an essential role, see [3, Chapter 7]. Additionally, platforms
that face rational customers set cheaper prices and attract more customers, see
Fig. 4. This impact on demands is normally omitted in the literature because of
the market covered assumption that assumes a fixed market size formed by all
consumers. Comparing Fig. 3 and Fig. 4, cases with a higher price level corre-
spond to cases with a lower demand level. Multiplying these two factors on each
side, I find that, in the end, in all the behavioral cases, platforms reach the same
profit level approximately13. Platforms adapt themselves to achieve the maxi-
mum profit they can under the defined market structure. Only after changing
market environmental parameters such as the network topology, the degree of
differentiation, or the probability of infection, other profit levels are possible.
Lastly, all the previous results hold in the sellers’ case too. Although during all
13 Results available upon request.
8 J. Manuel S´anchez-Cartas
Fig. 3. Prices without the market covered assumption. Two network topologies
the simulations they behave as rational agents, buyers influence the price that
sellers pay and their demands. See for example the first graph of Fig. 3 and
Fig. 5. That implies the necessity not only of taking into account how many
groups are linked by the platform, but also how each group behaves because
there are behavioral externalities between one group to the other. Behavioral
rules indirectly influence the prices of other markets.
5 Conclusions
When buying a product, consumers follow different behavioural rules that de-
pend on how sophisticated they are and how much information they can use.
The theory points out that the less sophisticated and informed consumers tend
to pay significantly higher prices than informed and sophisticated consumers.
I challenge that intuition by simulating an agent-based model based on [2], in
Platform competition and consumer’s decisions 9
Fig. 4. Demands without the market covered assumption. Two network topologies
which I test different behavioral rules when the market size is fixed and all agents
have full information (“market covered” simplifying assumption), and when con-
sumers get aware of platforms by an infection process in two network topologies:
small-world and preferential attachment networks. The market covered assump-
tion implicitly implies a fully-connected network, and the ABM points out that
such an assumption is essential to explain the different prices of traditional
theoretical models. Under the market covered assumption, I find that profit-
maximizing platforms set higher prices when they face non-rational consumers,
the large the rational bias of consumers, the higher those prices, and the lower
the adoption. On the contrary, when I relax the market covered assumption,
price differences are less extreme, and the network topology that dominates the
infection process explains better the differences in prices. This result implies that
the market covered assumption, which is common in the literature, may bias our
intuitions regarding the impact of consumer behavior. In the end, what matters
10 J. Manuel S´anchez-Cartas
Fig. 5. Sellers prices without the market covered assumption. Small-World network
is the network topology and how the information spreads. Therefore, there is
a need to check whether or not other results based on the market covered as-
sumption are robust to other network topologies, and more importantly, there
is a need to study which network properties are key in influencing the final price
levels. In this work, only two topologies have been tested, but that is not enough
to set a pattern. Another potential consequence of the network topology that it
is not addressed in this work is that platforms may become expensive over time
because of market saturation and the creation of new links among consumers
and sellers and not because of a change in consumers’ behavior. Nonetheless, I
let this question for future research.
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