Reputation Effects under Short Memories

TL;DR

This paper examines how limited consumer memory affects reputation dynamics in a seller-consumer game, showing that short memories can still sustain seller commitment and influence welfare outcomes.

Contribution

It introduces a model where consumers have limited memory of seller actions, revealing how memory length impacts reputation and welfare in equilibrium.

Findings

Seller can secure commitment payoff with minimal memory.

Welfare can be optimized depending on consumers' memory length.

Longer memory can both enable punishment and weaken incentives.

Abstract

I analyze a novel reputation game between a patient seller and a sequence of myopic consumers, in which the consumers have limited memories and do not know the exact sequence of the seller's actions. I focus on the case where each consumer only observes the number of times that the seller took each of his actions in the last K periods. When payoffs are monotone-supermodular, I show that the patient seller can approximately secure his commitment payoff in all equilibria as long as K is at least one. I also show that the consumers can approximately attain their first-best welfare in all equilibria if and only if their memory length K is lower than some cutoff. Although a longer memory enables more consumers to punish the seller once the seller shirks, it weakens their incentives to punish the seller once they observe him shirking