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On the folk theorem with one-dimensional payoffs and different discount factors

  • Guéron, Yves
  • Lamadon, Thibaut
  • Thomas, Caroline D.

Proving the folk theorem in a game with three or more players usually requires imposing restrictions on the dimensionality of the stage-game payoffs. Fudenberg and Maskin (1986) assume full dimensionality of payoffs, while Abreu et al. (1994) assume the weaker NEU condition ("nonequivalent utilities"). In this note, we consider a class of n-player games where each player receives the same stage-game payoff, either zero or one. The stage-game payoffs therefore constitute a one-dimensional set, violating NEU. We show that if all players have different discount factors, then for discount factors sufficiently close to one, any strictly individually rational payoff profile can be obtained as the outcome of a subgame-perfect equilibrium with public correlation.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 73 (2011)
Issue (Month): 1 (September)
Pages: 287-295

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Handle: RePEc:eee:gamebe:v:73:y:2011:i:1:p:287-295
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  2. Fudenberg, Drew & Levine, David, 1983. "Subgame-perfect equilibria of finite- and infinite-horizon games," Journal of Economic Theory, Elsevier, vol. 31(2), pages 251-268, December.
  3. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
  4. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
  5. Chen, Bo, 2008. "On effective minimax payoffs and unequal discounting," Economics Letters, Elsevier, vol. 100(1), pages 105-107, July.
  6. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-48, July.
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