Bad Reputation under Bounded and Fading Memory
I relax the full memory assumption in Ely and Valimaki's (2003) mechanic game, where reputation is bad for all players. First I consider "bounded memory," where only finitely many recent periods are observed. For long memory, reputation is still bad. Shortening memory avoids bad reputation but only by making it "useless." There is no "happy middle:" reputation is either useless or reduces equilibrium payoffs for any memory length. I find a qualitatively different result for "fading memory," where players randomly sample past periods with probabilities "fading" toward zero. Unlike bounded memory, reputation is not bad but remains useful under sufficiently fast fading. This result extends to a more general class of both good and bad reputation games, suggesting reputation leaves long-run player behavior unaffected in some realistic word-of-mouth environments.
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- Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
- George J. Mailath & Wojciech Olszewski, 2008.
"Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring,"
PIER Working Paper Archive
08-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
- George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
- Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
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