Managing competition on a two‐sided platform

• DOI: http://doi.org/10.1111/jems.12311
• Author: Martin Peitz,Paul Belleflamme
• Published date: 01 January 2019
• Date: 01 January 2019

Received: 20 August 2018

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Accepted: 20 August 2018

DOI: 10.1111/jems.12311

Managing competition on a two‐sided platform

Paul Belleflamme

1

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Martin Peitz

2

1

Aix‐Marseille University, CNRS, EHESS,

Centrae Marseille, AMSE, Aix and

Marseille, France, KEDGE Business

School and CESifo

2

Department of Economics and MaCCI,

University of Mannheim, Mannheim,

Germany, CEPR, CESifo, and ZEW

Correspondence

Martin Peitz, Department of Economics

and MaCCI, University of Mannheim,

68131 Mannheim, Germany, CEPR,

CESifo, and ZEW.

Email: martin.peitz@gmail.com

Funding information

Deutsche Forschungsgemeinschaft, Bonn,

Germany, Grant/Award Number: CRC

TR 224

Abstract

On many two‐sided platforms, users on one side not only care about user

participation and usage levels on the other side, but they also care about

participation and usage of fellow users on the same side. Most prominent is the

degree of seller competition on a platform catering to buyers and sellers. In this

paper, we address how seller competition affects platform pricing, product

variety, and the number of platforms that carry trade.

KEYWORDS

Imperfect competition, intermediation, network effects, platform competition, pricing, two‐sided

markets

JEL CLASSIFICATION

D43, L13, L86

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INTRODUCTION

Many platforms enable or facilitate trade between buyers and sellers. Probably since the Stone Age, people gather at

central places to exchange goods and provide services. Medieval trade fairs brought buyers and sellers into contact. The

offline world features many platforms including stock exchanges, currencies, flea markets, shopping malls, newspapers,

magazines, and broadcasters. Electronic payment systems, software platforms, and digital marketplaces are more recent

prominent platforms allowing two distinct groups of participants to interact and exchange goods or services.

Starting with the seminal papers by Caillaud and Jullien (2003), Rochet and Tirole (2003), and Armstrong (2006), the

economic literature on two‐sided platforms focuses on cross‐group external effects. Such focus seems natural as cross‐

group effects directly stem from the desire of the two groups of agents to interact and, thereby, give their raison d’être to

two‐sided platforms. However, in many economic environments, platforms have to factor in the fact that the

attractiveness of a platform for the members of one group also depends on the participation of the members of the very

same group. That is, there exist within‐group external effects, which platforms have to take into account when choosing

their strategies. Let us describe a number of settings in which such effects are present.

Negative within‐group effects appear when the members of one group compete with one another to interact with the

other group. For instance, given a set of buyers on the platform, the expected profits of sellers on Ebay decrease in

response to the entry of competing sellers. Similarly, if an additional competing shop opens in a shopping mall, the

expected profits of existing shops decrease given a set of buyers in the mall. Another example is dating apps. These are

characterized by positive cross‐group external effects, as the app becomes more attractive the more it is used by people

of the opposite gender. However, they are also characterized by negative within‐group external effects, as more people

of the same gender make it less likely that a match materializes for a particular person. Different from a buyer–seller

context, there is typically no monetary transaction between users on a dating app.

Negative within‐group effects may also arise because of congestion problems—for instance, sellers may compete for

buyer attention, which is scarce. Consumption externalities are another instance of negative within‐group effects. For

J Econ Manage Strat. 2019;28:5–22. wileyonlinelibrary.com/journal/jems © 2019 Wiley Periodicals, Inc.

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ORIGINAL ARTICLE

instance, referring to Airbnb visitors, Slee (2016) reports that “as their numbers grow, they erode the very atmosphere in

which they bask and threaten the livability of the city for residents.”This arguably also applies to fellow visitors.

Congestion effects may also be present on digital platforms with limited bandwidth such that, for example, the delivery

of research result is slowed down—this would imply that the stand‐alone utility of the platform suffers from a lot of

buyer participation. In the offline world, congestion problems appear when the platform’s physical venue is too

crowded; for instance, shoppers may get stuck in a crowded shopping mall and, as a result, make fewer purchase

attempts.

1

In this paper, we focus on competition in a buyer–seller context, and we examine how such competition affects

outcomes in platform markets. We consider a two‐sided platform that enables trade between buyers and sellers—these

sellers make nondiscriminatory take‐it‐or‐leave‐it offers to buyers. Imperfect competition between sellers has the

standard property that an additional seller on the platform leads to lower per‐buyer profit for each seller already on the

platform—a negative within‐group external effect. It also often leads to lower prices and more variety, which buyers

like. Thus, the additional seller may generate more participation on the buyer side, which, in turn, will benefit all sellers

—the combination of two positive cross‐group external effects. Our objective is to analyze how platforms take these

conflicting effects into account when choosing their price and non-price strategies.

One way to carry out such analysis is to augment standard two‐sided platform models by adding a parameter that

measures a negative effect within the group of sellers and to study the allocative effects in response to a change of this

parameter; we review below some papers that follow this path (e.g., Belleflamme & Toulemonde, 2009). However, in

light of the argument above, such comparative statics can be misconceived, as seller competition also affects how buyers

and sellers value the interaction with each other. For instance, an increase in seller competition drives down per‐

consumer profits and, thus, increases the strength of the negative within‐group external effect on the seller side. At the

same time, the per‐seller consumer benefit is affected and, thus, the strength of the cross‐group external effect exerted

by sellers on consumers changes as well. Hence, an increase in seller competition affects two parameters in the reduced

form model at the same time. This implies that these parameters should not be treated as primitives of the model. We

need instead to couple standard two‐sided platform models with microfoundations of seller competition and buyer–

seller relationships. This is the route that we take in this paper.

2

This paper is organized as follows. First, we consider seller competition on a monopoly platform and its effect on

prices and product variety. Second, we study platform competition; in particular, we generalize the two‐sided single‐

homing model of Armstrong (2006) to allow for seller competition. Third, we examine the influence of seller

competition on the number of platforms carrying positive volume of trade. Our objective is to synthesize existing

literature, which will be referenced in the main text.

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PRICES AND PRODUCT VARIETY ON A MONOPOLY PLATFORM

In this section, we focus on a single platform that facilitates the interaction between buyers and competing sellers. We

first develop a baseline model to derive the main intuitions. We then extend the analysis by reviewing the extant

literature.

2.1

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A baseline model

Let us define the seller and buyer net surplus of visiting the platform (gross of any opportunity cost), respectively, as

vrπnn m=+(,)−

ss bs

s

and

vrunn m=+(,)−

bb bs b

. Here,

r

g

is the stand‐alone utility on side

gbs{, }∈

and mgis the

fixed membership or subscription fee charged by the platform to side g. The general functions πn n(,

)

bs

and

un n(,

)

bs

represent the net gains from trade for any seller and any buyer on the platform. They both potentially depend on the

number of buyers and on the number of sellers who are present on the platform, meaning that any form of cross‐group

and within‐group external effects are permitted. We assume that both functions are twice continuously differentiable in

their two arguments. In this paper, we focus on fixed fees per participant and do not allow the platform to charge usage

fees. This is reasonable in situations in which monitoring transactions is prohibitively costly or in which consumers can

bypass the platform at negligible cost.

3

We consider a model with three stages: First, the monopoly platform sets the

fixed fees; second, buyers and sellers simultaneously decide to enter (alternatively, the platform admits a certain

number of buyers of sellers on the platform and fees then clear the market); and, third, participating sellers play an

oligopoly game. We analyze the properties of the subgame‐perfect Nash equilibrium.

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BELLEFLAMME AND PEITZ