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The Folk Theorem in Dynastic Repeated Games

Author

Listed:
  • Luca Anderlini

    (Georgetown University)

  • Dino Gerardi

    (Yale University)

  • Roger Lagunoff

    (Georgetown University)

Abstract

A canonical interpretation of an infinitely repeated game is that of a “dynastic” repeated game: a stage game repeatedly played by successive generations of finitely-lived players with dynastic preferences. These two models are in fact equivalent when the past history of play is observable to all players. 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) 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. Our results stem from the fact that, in equilibrium, a player may be unable to communicate effectively relevant information to his successor in the same dynasty. This, in turn implies that following some histories of play the players’ equilibrium beliefs may violate “Inter-Generational Agreement.”

Suggested Citation

  • Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2004. "The Folk Theorem in Dynastic Repeated Games," Game Theory and Information 0410001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0410001
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    References listed on IDEAS

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    Cited by:

    1. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2004. "The Folk Theorem in Dynastic Repeated Games," Levine's Bibliography 122247000000000577, UCLA Department of Economics.
    2. Egorov, Georgy & Sonin, Konstantin, 2005. "The Killing Game: Reputation and Knowledge in Non-Democratic Succession," CEPR Discussion Papers 5092, C.E.P.R. Discussion Papers.
    3. 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.
    4. Georgy Egorov & Konstantin Sonin, 2005. "The Killing Game: Reputation and Knowledge in Politics of Succession," Game Theory and Information 0505003, University Library of Munich, Germany.
    5. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "A `Super Folk Theorem' in Dynastic Repeated Games," Levine's Bibliography 321307000000000926, UCLA Department of Economics.

    More about this item

    Keywords

    Dynastic Repeated Games; Private Communication; Folk Theorem;

    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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