EVOLUTIONARY CONSUMERS IMPLY MONOPOLIES EXIT

• DOI: http://doi.org/10.1111/iere.12318
• Author: Patrick Hummel,R. Preston McAfee
• Published date: 01 November 2018
• Date: 01 November 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 4, November 2018 DOI: 10.1111/iere.12318

EVOLUTIONARY CONSUMERS IMPLY MONOPOLIES EXIT∗

BYPATRICK HUMMEL AND R. PRESTON MCAFEE1

Google Inc., U.S.A.; Microsoft Corp.,U.S.A.

We address the question of how a monopolist should price when facing evolutionary consumers who gradually

move in the direction of following their optimal strategy but may make temporary suboptimal choices. We show

that under a broad generalization of the most commonly used model of evolution, the monopolist will set a path

of prices such that all consumers eventually stop purchasing the monopolist’s product.

1. INTRODUCTION

Although a standard rationalist paradigm assumes that individuals optimize instantaneously,

the assumption of full rationality on the part of economic agents has been widely questioned

in the literature (see Camerer et al., 2004, for an extensive collection of essays related to this).

For most people, optimizing is costly, and even with good intentions, mistakes are made. Many

people are not on the optimal cell phone plan given their usage, use credit cards with dominated

terms (Ausubel, 1991), and do not save enough for retirement (Bernheim et al., 2001). Product

adoptions often follow an “S-shaped” pattern, reflecting a period in which the adoption rate

increases as awareness increases, followed by a diminishing rate as the set of people available

to adopt dwindles.

The fact that the assumption of full rationality may not be satisfied has prompted an exami-

nation of alternative models. Evolutionary models have been a particularly popular choice, as

they provide a compelling framework for understanding how people actually behave. These

models typically have the property that individual decisions are eventually optimal and, in a

static environment, improve over time. Evolutionary models have been extensively studied as a

model of game play since Maynard Smith and Price (1973) introduced the concept of evolution-

arily stable strategies, and the literature is generally supportive of their use in modeling game

play. For instance, evolutionary models have been applied to a wide range of problems such

as crime (Cressman et al., 1998), firm market shares (Mazzucato, 1998), industrial dynamics

(Klarl, 2008), livestock management (Gramig and Horan, 2011), portfolio selection (Bomze,

2000), the prisoner’s dilemma (Epstein, 1999), public goods (Brandt et al., 2006), technological

innovation (Windrum, 1999), tourism (Accinelli et al., 2009), and value chains (Cantner et al.,

2016).

As noted in Weibull (1998a), the most widely used model of evolution in the literature is

the replicator dynamics, which was first developed by Taylor and Jonker (1978).2Under the

replicator dynamics, the rate at which the fraction of players who employ a particular strategy

changes is directly proportional to the difference between the average payoff obtained by

players who employ that strategy and the average payoff of all the players. Such evolutionary

models based on the replicator dynamics have been used successfully in a myriad of applications

∗Manuscript received March 2017; revised July 2017.

1We thank the editor and the anonymous referee for comments and suggestions. Please address correspon-

dence to: Patrick Hummel, Google Inc., 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA. E-mail:

phummel@google.com.

2Cressman and Tao (2014) also note that “the replicator equation is the first and most important game dynamics

studied in connection with evolutionary game theory.”

1733

C

(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association