ASYMMETRY OF CUSTOMER LOSS AND RECOVERY UNDER ENDOGENOUS PARTNERSHIPS: THEORY AND EVIDENCE*

• Date: 01 February 2016
• Author: Stefan Jonsson,Henrich R. Greve,Takako Fujiwara‐Greve
• Published date: 01 February 2016
• DOI: http://doi.org/10.1111/iere.12146

INTERNATIONAL

ECONOMIC

REVIEW

February 2016

Vol. 57, No. 1

ASYMMETRY OF CUSTOMER LOSS AND RECOVERY UNDER ENDOGENOUS

PARTNERSHIPS: THEORY AND EVIDENCE∗

BYTAKAKO FUJIWARA-GREVE,HENRICH R. GREVE,AND STEFAN JONSSON 1

Keio University, Japan; INSEAD, Singapore; Uppsala University, Sweden

This article is inspired by real-world phenomena that firms lose customers based on imprecise information and

take a long time to recover. If consumers are playing an ordinary repeated game with fixed partners, there is no clear

reason why recovery happens slowly. However, if consumers are playing an endogenously repeated game, a class of

simple efficient equilibria exhibits the asymmetry of fast loss and slow recovery of customers after a bad signal. Exit

is systematic, but formation of a new partnership is random. We also give empirical evidence of our equilibria at an

individual-firm level.

1. INTRODUCTION

This article is inspired by real-world phenomena where consumers punish firms based on

imprecise information, and the dynamic path of the customer measure of a punished firm takes

a certain form: fast loss after a bad signal, followed by slow recovery. To give a rationale for

the phenomena, we create a new model of endogenously repeated games and show that even

under imperfect monitoring, firms’ constant effort and consumers’ grim-trigger type strategies

constitute efficient sequential equilibria. The equilibria display immediate loss of customers and

slow recovery. To support our equilibria, we also provide empirical evidence that consumers

quickly withdrew from a seller with a bad image but returned slowly, even though the seller’s

performance was no worse than the rivals’.

There are many real-world episodes of “undeserved loss” of customers that take a long time

to recover. For example, Audi in the United States was badly hit by allegations of “unintended

accelerations” in 1986. The bad press coverage continued intermittently until around 1989, when

it was established that the incidents were mostly the result of driver mistakes. Yet, it took 15

years for the sales of Audi to gradually recover to the level of 1985 (see Figure 1).2The average

re-purchase cycle of regular passenger cars is 7.8 to 8.7 years;3thus 15 years is a very long time.

∗Manuscript received August 2013; revised September 2014.

1This is a substantial revision of the paper originally titled “Asymmetry of Reputation Loss and Recovery under

Endogenous Partnerships: Theory and Evidence.” We are grateful to the co-editor Masaki Aoyagi for valuable advice

that improved the paper considerably. We are also grateful to three anonymous referees, Kiminori Matsuyama, Pei-yu

(Melody) Lo, Ichiro Obara, Sergei Severinov, and Anne-Marie Carrick for helpful comments, and to Premiepensions-

myndigheten (PPM) and especially to Marcela Cohen Birman for generously providing data. Takako Fujiwara-Greve

gratefully acknowledges the financial support from Keio Gijuku Academic Development Funds and Keio Economic So-

ciety. Usual disclaimer applies. Please address correspondence to: Takako Fujiwara-Greve, Department of Economics,

Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan. E-mail: takakofg@econ.keio.ac.jp.

2Source: Audi press releases.

3For more details, see Winter (2010).

3

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

4FUJIWARA-GREVE,GREVE,AND JONSSON

FIGURE 1

AUDI U.S.SALES IN 1979–2001

It is natural to ask whether this is “irrational,” emotional behavior of nervous customers or

whether there is any rationale for it (Aizcorbe et al., 2004).4

To formulate a situation where consumers receive imprecise information about actions by

firms/sellers and may switch among them, we extend the model of endogenously repeated games

(e.g., Datta, 1996; Ghosh and Ray, 1996; Kranton, 1996; Carmichael and MacLeod, 1997; Rob

and Yang, 2008; Fujiwara-Greve and Okuno-Fujiwara, 2009; McAdams, 2011). The literature

of endogenously repeated games has two features: (i) The stage game is simultaneous-move

and played by a uniform population, and (ii) a player’s action is observed only by the current

partner (“no information flow” assumption). We extend the existing model to a two-population

model of consumers and firms playing the Trust game (Kreps, 1990), an extensive-form game of

one-sided moral hazard. Consumers’ choices are which firm to trust/invest in, and firms’ choices

are whether to make an effort or to shirk. Even if all firms make an effort, however, one firm

may get a bad signal (which we call the relative standing signal), and this is observed only by its

customers.5Our model has a technically new aspect that a firm’s customer measure depends not

only on its history of signals but also on all other firms’ customer measure, because customers

of other firms may choose to move to this firm. Therefore it is not a trivial extension of the

existing model.

We construct the following customer-efficient Markov equilibria. All firms make an effort

after any private history. Consumers are uninformed when they enter the market and choose

a firm at random. They stay with the same firm as long as they continue to experience no bad

signal. As soon as they experience a bad signal, however, they switch with a positive probability

to an alternative firm at random and stay there as long as they experience no bad signal.

Whenever the consumers switch firms, they may return to the firm(s) they left previously. This

strategy is of the grim-trigger type because a bad signal triggers (with a positive probability)

a punishment of immediate withdrawal from a repeated transaction that lasts at least until

another incidence of a bad signal at a new firm. In ordinary repeated games, a grim-trigger

strategy means eternal punishment and not gradual recovery. On the other hand, the grim-

trigger firm-switching strategy in our model yields the fast drop of customer measures after a

bad signal and slow recovery thereafter.

Our equilibria have many good features. First, they are informationally constrained efficient.

Firms’ random loss of customers cancels out over time by other firms’ random loss. Because all

4We also found a very similar pattern of Japanese beef production data in 1985–2013 with a large drop in 2001 (BSE

cows were found in Japan) and slow recovery. Around 2001, only a few cows for milk production were diagnosed as

having BSE, and thus the reaction in the meat market can be viewed as a result of imperfect monitoring.

5We distinguish the general term consumers from customers of a firm.