Reputation in the Presence of Noisy Exogenous Learning

Abstract

This paper studies the reputation effect in which a long-lived player faces a sequence of uninformed short-lived players and the uninformed players receive informative but noisy exogenous signals about the type of the long-lived player.We provide an explicit lower bound on all Nash equilibrium payoffs of the longlived player. The lower bound shows when the exogenous signals are sufficiently noisy and the long-lived player is patient, he can be assured of a payoff strictly higher than his minmax payoff.

Reputations in Repeated Games

“…This section is based on Hu (2014), which provides a general analysis; Wiseman's (2009) original analysis considered the chain store example. Section 4.2.7 explained why this result must be interpreted carefully, with an emphasis on keeping track of which limits are taken in which order.…”

Promoting a reputation for quality

“…Cripps et al's (2004) observation has led to a large body of literature on when a firm can have a persistent reputation or when a firm's reputation cycles. Liu (2011), Liu and Skrzypacz (2014), Hu (2015) and Dilmé (2014) consider models similar to the standard reputation model with commitment types, and show that with some modifications to the environment reputations no longer vanish. Dilmé (2014) adds switching costs which add some persistence to the firm's action.…”

“…Liu (2011) considers an environment where it is costly for consumers to observe the history. In Liu and Skrzypacz (2014) and Hu (2015), consumers only observe part of the history. This new information structure enhances reputation building by making it more difficult, or impossible, for consumers to eventually detect strategic types.…”

“…In the reputation literature, information is treated as exogenous. Liu (2011), Liu and Skrzypacz (2014), Hu (2015) and Board and Meyer-ter-Vehn (2013) show how the information consumers see influences a firm's incentives to build and maintain reputation. However, firms often have a great deal of control over the information consumers are able to observe.…”

Reputations in Repeated Games

“…This section, considering the impact of exogenously informative signals, provides a further illustration of the subtleties that can arise in taking limits. This section is based on Hu (2013), which provides a general analysis; Wiseman's (2009) original analysis considered the chain store example.…”