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The Folk Theorem in Dynastic Repeated Games

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  • Luca Anderlini
  • Dino Gerardi
  • Roger Lagunoff

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.”

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000577.

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Date of creation: 04 Oct 2004
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Handle: RePEc:cla:levrem:122247000000000577

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Citations

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Cited by:
  1. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2006. "A 'Super' Folk Theorem for Dynastic Repeated Games," Levine's Bibliography 784828000000000664, UCLA Department of Economics.
  2. George Egorov & Konstantin Sonin, 2005. "The Killing Game: Reputation and Knowledge in Non-Democratic Succession," Economics Working Papers 0054, Institute for Advanced Study, School of Social Science.
  3. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2004. "The Folk Theorem in Dynastic Repeated Games," Game Theory and Information 0410001, EconWPA.
  4. Georgy Egorov & Konstantin Sonin, 2005. "The Killing Game: Reputation and Knowledge in Politics of Succession," Game Theory and Information 0505003, EconWPA.
  5. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "A `Super Folk Theorem' in Dynastic Repeated Games," Levine's Bibliography 321307000000000926, UCLA Department of Economics.

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