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Impermanent Types and Permanent Reputations

  • Mehmet Ekmekci
  • Olivier Gossner
  • Andrea Wilson

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1511.

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Date of creation: Apr 2010
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Handle: RePEc:nwu:cmsems:1511
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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  1. Bar-Isaac, Heski & Tadelis, Steven, 2008. "Seller Reputation," Foundations and Trends(R) in Microeconomics, now publishers, vol. 4(4), pages 273-351, August.
  2. Martin W. Cripps & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," PIER Working Paper Archive 04-031, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2004.
  3. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, vol. 57(4), pages 759-78, July.
  4. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  5. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Imperfect Monitoring and Impermanent Reputations," Econometrica, Econometric Society, vol. 72(2), pages 407-432, 03.
  6. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
  7. Wiseman, Thomas, 2008. "Reputation and impermanent types," Games and Economic Behavior, Elsevier, vol. 62(1), pages 190-210, January.
  8. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
  9. D. Fudenberg & D. K. Levine, 1999. "Maintaining a Reputation when Strategies are Imperfectly Observed," Levine's Working Paper Archive 571, David K. Levine.
  10. Bernardita Vial, 2008. "Competitive Equilibrium and Reputation under Imperfect Public Monitoring," Documentos de Trabajo 327, Instituto de Economia. Pontificia Universidad Católica de Chile..
  11. George J. Mailath & Larry Samuelson, 2000. "Who Wants a Good Reputation?," CARESS Working Papres sell-rep, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, March.
  13. Harold L. Cole & James Dow & William B. English, 1994. "Default, settlement, and signalling: lending resumption in a reputational model of sovereign debt," Staff Report 180, Federal Reserve Bank of Minneapolis.
  14. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  15. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
  16. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy bounds on Bayesian learning," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 24-32, January.
  17. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  18. Mailath, George J & Samuelson, Larry, 2001. "Who Wants a Good Reputation? Erratum," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 714, July.
  19. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy Bounds on Bayesian Learning," Economics Papers from University Paris Dauphine 123456789/6067, Paris Dauphine University.
  20. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  21. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  22. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
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