Abstract

In traditional reputation models, the ability to build a reputation is good for the long-run player. In [Ely, J., Valimaki, J., 2003. Bad reputation. NAJ Econ. 4, 2; http://www.najecon.org/v4.htm. Quart. J. Econ. 118 (2003) 785–814], Ely and Valimaki give an example in which reputation is unambiguously bad. This paper characterizes a class of games in which that insight holds. The key to bad reputation is that participation is optional for the short-run players, and that every action of the long-run player that makes the short-run players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.” We allow a broad set of commitment types, allowing many types, including the “Stackelberg type” used to prove positive results on reputation. Although reputation need not be bad if the probability of the Stackelberg type is too high, the relative probability of the Stackelberg type can be high when all commitment types are unlikely.

Highlights

  • A long-run player playing against a sequence of short-lived opponents can build a reputation for playing in a specific way and so obtain the benefits of commitment power

  • In traditional reputation theory, reputation is good for the long-run player

  • The key properties are that participation is optional for the short-run players, and that every action of the long-run player that makes the short-run players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.” We broaden the set of commitment types, allowing many types, including the “Stackelberg type” used to prove positive results on reputation

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Summary

Introduction

A long-run player playing against a sequence of short-lived opponents can build a reputation for playing in a specific way and so obtain the benefits of commitment power. We define a class of “bad reputation” games, and show that in these games, reputation effects imply that the long-run player can do no better than if the short-run players choose not to participate This extends the EV example in a number of ways. Earlier research suggests that to attain the upper bound on the long-run player’s payoff, it can be important to include the “Stackelberg type” that is committed to the stage-game action the long-run player would choose in a Stackelberg equilibrium. By extending the EV example to a broad class of stage games we are able to more clearly identify the properties that are needed for the bad reputation result There are several such properties, notably that the short-run players can either individually or collectively choose not to participate. We illustrate the boundaries of bad reputation by giving a number of examples and classes of participation games that are not bad reputation games

The Dynamic Game
The Ely-Valimaki Example
Participation Games and Bad Reputation Games
The Theorem
Poor Reputation Games and Strong Temptations
Principal-Agent Entry Games
Games with Hidden Information
Multilateral Entry Games
B HT F for some vulnerable friendly action F with temptation bounds
Full Text
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