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A 'Super' Folk Theorem for Dynastic Repeated Games

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  • Luca Anderlini
  • Dino Gerardi
  • Roger Lagunoff

Abstract

We analyze "dynastic" repeated games. A stage game is repeatedly played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. When all players observe the past history of play, the standard repeated game and the dynastic game are equivalent In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize entirely when a Sequential Equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a Subgame Perfect Equilibrium of the standard repeated game. For this to be the case it must be that the players' equilibrium beliefs violate a condition that we term "Inter-Generational Agreement."
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Suggested Citation

  • Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2006. "A 'Super' Folk Theorem for Dynastic Repeated Games," Levine's Bibliography 784828000000000664, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:784828000000000664
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    Cited by:

    1. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2008. "A “Super” Folk Theorem for dynastic repeated games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(3), pages 357-394, December.
    2. Chihiro Morooka, 2020. "Inefficiency in alternately repeated coordination games with dynastic preferences," Economics Bulletin, AccessEcon, vol. 40(4), pages 3167-3170.
    3. Pablo Casas-Arce, 2010. "Dismissals and quits in repeated games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 67-80, April.
    4. Daron Acemoglu & Matthew O. Jackson, 2015. "History, Expectations, and Leadership in the Evolution of Social Norms," Review of Economic Studies, Oxford University Press, vol. 82(2), pages 423-456.
    5. Daniel Monte & Maher Said, 2014. "The value of (bounded) memory in a changing world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 59-82, May.
    6. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "A `Super Folk Theorem' in Dynastic Repeated Games," Levine's Bibliography 321307000000000926, UCLA Department of Economics.
    7. Francesco Lancia & Alessia Russo, 2016. "Cooperation in Organization through Self-Commitment Actions," Vienna Economics Papers vie1605, University of Vienna, Department of Economics.
    8. Francesco Lancia & Alessia Russo, 2016. "Cooperation in Organization through Self-Commitment Actions," Vienna Economics Papers 1605, University of Vienna, Department of Economics.
    9. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "Social Memory and Evidence from the Past," Levine's Bibliography 321307000000000850, UCLA Department of Economics.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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