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Impermanent Types and Permanent Reputations

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  • Mehmet Ekmekci
  • Olivier Gossner
  • Andrea Wilson

Abstract

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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Bibliographic Info

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

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: Reputation; repeated games; replacements; disappearing reputations JEL Classification Numbers: D80; C73;

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  1. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy bounds on Bayesian learning," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 24-32, January.
  2. Mailath, George J & Samuelson, Larry, 2001. "Who Wants a Good Reputation?," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 415-41, April.
  3. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," PIER Working Paper Archive 04-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  4. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2002. "Imperfect Monitoring and Impermanent Reputations," PIER Working Paper Archive 03-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 30 May 2003.
  5. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  7. Bar-Isaac, Heski & Tadelis, Steven, 2008. "Seller Reputation," Foundations and Trends(R) in Microeconomics, now publishers, vol. 4(4), pages 273-351, August.
  8. David Kreps & Robert Wilson, 1999. "Reputation and Imperfect Information," Levine's Working Paper Archive 238, David K. Levine.
  9. Bernardita Vial, 2008. "Competitive Equilibrium and Reputation under Imperfect Public Monitoring," Documentos de Trabajo 327, Instituto de Economia. Pontificia Universidad Católica de Chile..
  10. Drew Fudenberg & David K. Levine, 1995. "Reputation and Equilibrium Selection in Games with a Patient Player," Levine's Working Paper Archive 103, David K. Levine.
  11. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
  12. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  13. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
  14. Gossner, Olivier & Tomala, Tristan, 2008. "Entropy Bounds on Bayesian Learning," Economics Papers from University Paris Dauphine 123456789/6067, Paris Dauphine University.
  15. Fudenberg, D., 1991. "Maintaining a Reputation when Strategies are Imperfectly Observed," Working papers 589, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, September.
  17. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
  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. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
  20. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
  21. Wiseman, Thomas, 2008. "Reputation and impermanent types," Games and Economic Behavior, Elsevier, vol. 62(1), pages 190-210, January.
  22. Cole, Harold L & Dow, James & English, William B, 1995. "Default, Settlement, and Signalling: Lending Resumption in a Reputational Model of Sovereign Debt," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(2), pages 365-85, May.
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Cited by:
  1. Ju Hu, 2013. "Reputation in the Presence of Noisy Exogenous Learning," PIER Working Paper Archive 13-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Daron Acemoglu & Alexander Wolitzky, 2012. "Cycles of Distrust: An Economic Model," Levine's Working Paper Archive 786969000000000502, David K. Levine.
  3. Renault, Jerome & Solan, Eilon & Vieille, Nicolas, 2012. "Dynamic Sender-Receiver Games," Les Cahiers de Recherche 966, HEC Paris.
  4. Rick Harbaugh & Ted To, 2008. "Opportunistic Discrimination," Working Papers 2008-07, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.

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