Platform market competition with endogenous side decisions

• Author: Jay Pil Choi,Yusuke Zennyo
• DOI: http://doi.org/10.1111/jems.12305
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 21 August 2018

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Accepted: 24 August 2018

DOI: 10.1111/jems.12305

Platform market competition with endogenous side

decisions

Jay Pil Choi

1,2

|

Yusuke Zennyo

3

1

Department of Economics, Michigan

State University, East Lansing, Michigan

2

School of Economics, Yonsei University,

Seoul, South Korea

3

Graduate School of Business

Administration, Kobe University, Kobe,

Japan

Correspondence

Jay Pil Choi, Department of Economics,

Michigan State University, East Lansing,

MI.

Email: choijay@msu.edu

Funding information

JSPS Grant‐in‐Aid for Young Scientists,

Grant/Award Number: 16K17126;

Grant‐in‐Aid for Scientific Research,

Grant/Award Number: 17H00959;

Ministry of Education of the Republic of

Korea and the National Research

Foundation of Korea, Grant/Award

Number: NRF‐2016S1A5A2A01022389;

Ministry of Education of the Republic of

Korea; National Research Foundation of

Korea

Abstract

This paper develops a framework to analyze platform competition in two‐sided

markets in which agents endogenously decide on which side of a platform to

join. We characterize the equilibrium pricing structure and perform a

comparative statics analysis on how the distribution of agents’preferences

affects the platforms’profits. We also show that the market equilibrium under

profit‐maximizing platforms leads to the first best social surplus, which

illustrates the importance of the price mechanism to induce more balanced

participation across the two sides. This framework can be applied to analyze

market competition for “rental”or “sharing”platforms. In addition, we extend

our analysis to consider an initial investment stage, which makes participants

the owner of some durable goods to rent out.

KEYWORDS

endogenous side decisions, indirect network externalities, platform market competition, sharing

economy, two‐sided markets

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INTRODUCTION

This paper analyzes platform pricing in two‐sided markets in which agents endogenously decide on which side of a

platform to join. The existing literature on two‐sided markets typically assumes that agents are exogenously preassigned

to a particular side of the market and derives the optimal pricing structure (Armstrong, 2006; Caillaud & Jullien, 2003;

Rochet & Tirole, 2003, 2006). This would be the case if there are two distinct groups of agents that represent each side,

as in the example of nightclubs or dating sites where male and female patrons constitute each side. Credit card markets

with merchants and card holders can be another example. However, there are other two‐sided markets where an agent

can be reasonably assumed to decide which side to participate in, such as eBay, crowdfunding platforms, and many

“rental”or “sharing”platforms. In sharing economy platforms, each agent can choose whether to provide services or

receive services. In the ride‐sharing platform market, for instance, Uber or Lyft users can decide whether to become a

driver or a passenger. Airbnb and TaskRabbit are other prominent examples of sharing economy platforms with similar

characteristics of endogenous side decisions. In crowdfunding platforms, users can be either on the side of fund‐raisers

or funders depending on their financial status and investment opportunities. To analyze such markets, we endogenize

economic agents’participation decision on which side to join and analyze the optimal pricing scheme for platforms. We

J Econ Manage Strat. 2019;28:73–88. wileyonlinelibrary.com/journal/jems © 2019 Wiley Periodicals, Inc.

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ORIGINAL ARTICLE

show how the classical result in Armstrong (2006) can be naturally modified to reflect the endogeneity of the side

choice.

More specifically, to analyze users’endogenous participation decisions, we extend the seminal paper of Armstrong

(2006) by introducing a parameter, denoted by θ, which represents a user’s preference for one of the two sides. A user

with a higher value of θhas a stronger preference towards Side 1 while a user with a lower value of θhas a stronger

preference towards Side 2. The users’preferences

θ

(

)

are assumed to be distributed according to cumulative distribution

function

Fθ()

with the corresponding probability density function

f

θ(

)

. This preference variable (along with the

platforms’prices) drives users’endogenous decisions on which side they will join.

We derive three main results. First, in equilibrium, the two‐sided optimal pricing is affected not only by the extent of

indirect network externalities but also by the distribution of users’preferences towards each side. Platforms have an

incentive to charge a lower price for the side that exerts the greater indirect network externalities to the other side, as in

Armstrong (2006). In addition, platforms need to adjust their prices to enhance the total number of transactions among

users, taking the users’endogenous side decisions into account. Platforms offer a greater discount to the side that is less

favored by the users. This mechanism leads to our second result that competing platforms receive a greater profit in the

market when the users’preferences are more biased towards one side. As the probability density function

f

θ(

)

is

skewed either positively or negatively, the two‐sided pricing is affected not only by the extent of indirect network

externalities but also by the balance between the number of users on each side. The platforms can effectively charge a

higher price for the side that is favored by more users, whereas a discount is offered to the other side. As a higher price

is charged on the side with more users while a lower price is offered to the side with less users in equilibrium, more

skewness in users’preferences towards one side can yield a greater profit for the platform.

Finally, we demonstrate that profit‐maximizing platforms can lead to first best social welfare. Profit‐maximizing

platforms adjust the prices for both sides to enhance the total number of transactions among users in an effort to

maximize their profits, in the process effectively increasing total benefits that users derive from transactions. This result

illustrates the importance of the price mechanism in inducing more balanced participation across the two sides.

1

This

result also implies that profit‐maximizing platforms can lead to a more socially desirable allocation compared to the

case in which the intermediation services of the platforms are provided for free, such as Linux and Wikipedia.

We contribute to the two‐sided market literature by building a model with endogenous decisions of agents on which

side they will join. Our framework is more appropriate in analyzing market competition for “rental”or “sharing”

platforms as well as online auction platforms such as eBay and Yahoo! auctions and crowdfunding platforms. To apply

our model to the sharing economy platforms, we also extend our analysis to consider an initial investment stage, which

makes participants the owner of some durable goods to rent out. One notable exception is Gao (2017) who analyzes a

general model for two‐sided markets in which a consumer may appear on different sides of the market. However, the

focus of his paper is very different from ours. In particular, he analyzes a monopolistic platform and shows the

monopolist platform’s incentive to bundle the services it provides to two sides.

The rest of the paper is organized as follows. Section 2 introduces the model that endogenizes the agents’choice of

which side as well as which platform to join. Section 3 characterizes the market equilibrium. Section 4 discusses the

properties of the market equilibrium derived and their implications. Section 5 concludes. Detailed proofs and some of

the other extensions that show the robustness of our results are relegated to the appendix.

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MODEL

We extend the two‐sided market model of Armstrong (2006) to incorporate users’endogenous choices of which side of

the market to join. There are two competing platforms (

j

A

B

=,) that intermediate interactions between users on two

sides (

i

=1,

2

). Each user on one side of a platform benefits from the interaction with users on the other side of the

platform. Platform

j

offers price

p

i

jfor users who join side

i

(

i

=1,

2

). Let nijdenote the number of users on side

i

of

platform

j

. Then, the benefit from interactions that users who join side

i

of platform

j

derive is given by

uαn p=−

ijii

j

i

j

−, where

α

irepresents the extent of indirect network externalities that a user on side

i

benefits from

interacting with users on the other side

i

−

. In addition, users obtain a stand‐alone benefit from joining either platform,

denoted by v, which is assumed to be the same for both platforms and large enough to ensure that the market is fully

covered.

We consider two types of user heterogeneity. First, as in Armstrong (2006), users are heterogeneous with respect to

their relative preferences towards the competing platforms, which is captured by the Hotelling specification. Users are

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CHOI AND ZENNYO