A two-sided reputation result with long-run players
We establish reputation results, under two sided incomplete information, for a class of repeated games. We consider a repeated game that satisfies the assumptions of either Atakan and Ekmekci (2012)  or Cripps et al. (2005)  and we assume that both players are Stackelberg types with positive probability. If the stage game is not a common interest game, then equilibrium play converges to the unique equilibrium of a continuous time war of attrition as the stage game is repeated arbitrarily frequently. Alternatively, if the stage game is a common-interest game, then the playersʼ equilibrium payoffs converge to their highest payoffs as the stage game is repeated arbitrarily frequently.
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- Kreps, David M. & Wilson, Robert, 1982.
"Reputation and imperfect information,"
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- Dilip Abreu & Faruk Gul, 2000.
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- Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, March.
- Cripps, Martin W. & Dekel, Eddie & Pesendorfer, Wolfgang, 2005. "Reputation with equal discounting in repeated games with strictly conflicting interests," Journal of Economic Theory, Elsevier, vol. 121(2), pages 259-272, April.
- Dilip Abreu & David Pearce, 2007. "Bargaining, Reputation, and Equilibrium Selection in Repeated Games with Contracts," Econometrica, Econometric Society, vol. 75(3), pages 653-710, 05.
- Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, December.
- Cripps, Martin W. & Thomas, Jonathan P., 1997. "Reputation and Perfection in Repeated Common Interest Games," Games and Economic Behavior, Elsevier, vol. 18(2), pages 141-158, February.
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