Reputation Effects under Short Memories
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
- Publication:
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arXiv e-prints
- Pub Date:
- July 2022
- DOI:
- 10.48550/arXiv.2207.02744
- arXiv:
- arXiv:2207.02744
- Bibcode:
- 2022arXiv220702744P
- Keywords:
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- Economics - Theoretical Economics