Collusive equilibria with switching costs: The effect of consumer concentration

• Date: 01 February 2021
• Published date: 01 February 2021
• Author: Guillem Roig
• DOI: http://doi.org/10.1111/jems.12398

J Econ Manage Strat. 2021;30:100–121.wileyonlinelibrary.com/journal/jems100

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© 2020 Wiley Periodicals LLC

Received: 22 February 2019

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Revised: 27 May 2020

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Accepted: 21 July 2020

DOI: 10.1111/jems.12398

ORIGINAL ARTICLE

Collusive equilibria with switching costs: The effect of

consumer concentration

Guillem Roig

Faculty of Economics, Casa Pedro Fermín

Calle 12 C # 4 ‐59, Universidad del

Rosario, Bogotá, Colombia

Correspondence

Guillem Roig, Faculty of Economics,

Casa Pedro Fermín Calle 12 C # 4 ‐59,

Universidad del Rosario, Bogotá 111711,

Colombia.

Email: guillem.roig@urosario.edu.co

Abstract

I study the ability of two competing firms to set collusive prices in markets

where consumers have switching costs. In consumer markets (with a small

number of consumers), I find an antifolk result in which collusion, in the

presence of switching costs, does not arise with patient firms. Patient firms

compete aggressively and consumers expect a large utility. A collusive equili-

brium is unstable because a deviating firm incorporates the future consumer

utility in its deviating price. Also, consumers have a strategic impact so, with

the prospects of large utility, they decide to switch to destabilize the firms'

collusive agreement. These results do not eventuate in markets with a large

number of consumers. In mass markets (a continuum of consumers), a single

consumer lacks a strategic impact to destabilize a collusive agreement and a

deviating firm cannot appropriate the consumer utility when deviating from

collusion. Collusion, then, becomes straightforward to achieve. We show that

for any number of consumers, switching costs make collusion easy to sustain.

1|INTRODUCTION

Switching costs are the costs that a consumer incurs as a result of changing brands, suppliers, or products. The

development of new industries and services creates switching costs. For instance, recent developments in online

financial services have increased transaction switching costs. This is especially true where consumers have: (a) set

default values in software connected to their current supplier (e.g., Quicken linked to Bank of America), (b) registered

credit cards for automatic online purchases, or (c) programmed their checking account to autopayments to other

suppliers (e.g., autopay monthly utility bills). In digital markets, customers may be dissuaded from switching to another

platform by the prospect of losing their photos, contacts, search history, apps, or other personal data.

1

Also, choosing

and switching among different digital portals entails cognitive costs; Amazon and Google acquired a dominant position

partly due to their users' aversions to the cognitive costs of switching.

2

Consumer switching costs have sparked interest in the study of market competition as consumers do not react to

price cuts as postulated by traditional competition models. Several antitrust cases have considered the effects of such

price stickiness in the likelihood of coordinated agreements among firms. For example, in 2005, the Chilean Com-

petition Authority filed a lawsuit against the five largest private health insurance providers for violation of antitrust law,

accusing them of collusion, propelled, among other things, by switching costs (Agostini, Saavedra, & Willington, 2008).

Also, in the early stages of competition after Korean telecom deregulation (a period in which consumers had important

switching costs), the Korea Fair Trade Commission and a court in Korea ruled as collusive the agreement between KT

and Hanaro Telecom in which the latter was to raise its monthly fixed fee in return for a transfer of market shares or

money from KT in the local calls market (Nam, 2016). This paper is motivated by these antitrust cases and demonstrates

that in addition to the level of switching costs, the consumer concentration determines the firms' abilities to achieve a

collusive outcome.

To study a collusive equilibrium in industries with switching costs, I consider a simple, infinitely competitive model

in which two symmetric firms, initially, have an equal market share and sell a homogeneous, nondurable good over an

infinite number of periods. Forward‐looking consumers, with unit demand, are identical and have the same switching

costs. I analyze how switching costs, and the concentration of consumers in the market, affect the sustainability of

collusion. I consider an imperfect monitoring model in which the buyers can observe both the firms' prices, but each

firm only knows its own price and not that of its rival. Imperfect monitoring gives strategic power to consumers as

firms' strategies are based on outcomes rather than actions. Then, firms set a collusive price as long as they serve half

the market; however, if, at some point in the game, a firm serves less than half the market, they start retaliatory

behaviors.

3

For the construction of the collusive equilibrium, I first characterize the firms' profits under a noncollusive out-

come, to which firms will revert in the punishment phase. Here, firms play a Markovian equilibrium in which a strategy

is, effectively, a mapping from the current market share to a price. When one firm has served all consumers in the

previous period, the market structure is reminiscent of a situation with one incumbent and one entrant who must pay

an entry cost equal to the switching cost. In this case, the stationary Markov Perfect Equilibrium is in pure strategies;

namely, the incumbent firm sets the price to keep consumers, while the rival sets a negative price to become the

incumbent. The difference of both prices is equal to the consumers' switching costs (see Lemma 1). In the equilibrium

path, no consumers switch, and the present discounted profits increase with the level of switching costs.

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As per the

finding of Biglaiser, Crémer, and Dobos (2013), firms can collect the switching cost only once.

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When both firms have a

positive market share, the stationary Markov Perfect Equilibrium requires randomization (with mixed strategies) and

the price distribution depends on the firms' proportions of the market share (see Proposition 1).

The main result of this paper is that in consumer markets (where a small number of consumers populate the

market), there is an antifolk result in which collusion does not arise with patient firms (see Proposition 2). Patient firms

compete aggressively, and consumers expect to receive a large utility in a noncollusive equilibrium. A large consumer

utility destabilizes the firms' collusive agreement because the firms foresee the future consumer utility and factor this

element into their current decision‐making. In particular, a deviating firm appropriates the future rent of consumers; a

forward‐looking consumer anticipates that by switching; consequently, the firm's retaliation begins, and the consumer

is willing to switch even if the deviating firm sets a hefty price. Contrary to existing results in the literature (e.g., Fong &

Liu, 2011; Padilla, 1995), a deviating firm does not need to pay the switching costs to attract its rival's consumers.

Additionally, in consumer markets, consumer strategic behavior is relevant. Because consumers have strategic mass,

any of them can trigger firms' retaliation from switching to the rival firm, which introduces an extra constraint beyond

the firms' standard incentive compatibility constraints.

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The utility a consumer expects with no‐collusion more than

compensates for the costs of switching and, therefore, a consumer decides to destabilize the collusive agreement.

The results above do not eventuate when more consumers populate the market. In the limit, with a continuum of

consumers, a single consumer has a negligible strategic impact such that his or her individual buying decisions do not

affect the level of competition in the continuation game. A consumer alone, then, cannot trigger a breaking of the

collusive agreement and the increase in competition between the firms, as a result of their patience, does not destabilize

the collusive agreement. Only the firms' standard incentive constraints are necessary and these are sufficient to

implement collusion. With the lack of consumer strategic mass, a deviating firm will offer a price discount equal to the

level of switching costs; a firm's deviating price does not increase with the firm's patience. As a result, the antifolk result

does not hold in mass markets (see Proposition 3). Then, a collusive agreement becomes easier to implement with an

increase in the number of consumers (see Corollary 2). With more consumers, the strategic impact of individual

consumers fades away. Also, the price cut needed to attract the rival's consumers, when deviating from the collusive

outcome, increases with a more significant number of consumers. This result is consistent with the discussion in The

National Economic Research Associates (2003, 7.36), which states that the likelihood of successful collusion diminishes

in line with the fewer number of buyers in the market.

In my model, and contrary to the results in the literature (see Anderson, Kumar, & Rajiv, 2004; Padilla, 1995),

switching costs make tacit collusion easier to sustain.

7

In mass markets, an increase in switching costs deters consumers

from destabilizing a collusive outcome as switching would become dearer. Also, an increase in switching costs makes

firms less aggressive, which reduces the expected utility of consumers in a noncollusive equilibrium; an increase in

switching costs reduces the deviation price and, thereby, firms have fewer incentives to deviate from collusion. When

more consumers populate the market, consumers' incentives to destabilize collusion also decrease with switching costs.

ROIG

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