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

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

Abstract

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.

Suggested Citation

  • Guéron, Yves & Lamadon, Thibaut & Thomas, Caroline D., 2011. "On the folk theorem with one-dimensional payoffs and different discount factors," Games and Economic Behavior, Elsevier, vol. 73(1), pages 287-295, September.
    • Handle: RePEc:eee:gamebe:v:73:y:2011:i:1:p:287-295
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    References listed on IDEAS

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    1. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    2. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-954, July.
    3. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    4. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    5. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    6. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    7. Chen, Bo, 2008. "On effective minimax payoffs and unequal discounting," Economics Letters, Elsevier, vol. 100(1), pages 105-107, July.
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    Cited by:

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    4. Marina Agranov & Jeongbin Kim & Leeat Yariv, 2023. "Coordination with Differential Time Preferences: Experimental Evidence," Working Papers 2023-10, Princeton University. Economics Department..
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