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The Folk Theorem in Dynastic Repeated Games

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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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Paper provided by Georgetown University, Department of Economics in its series Working Papers with number gueconwpa~04-04-09.

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Date of creation: 09 Apr 2004
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Handle: RePEc:geo:guwopa:gueconwpa~04-04-09

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Postal: Georgetown University Department of Economics Washington, DC 20057-1036
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Web page: http://econ.georgetown.edu/

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Postal: Marcia Suss Administrative Officer Georgetown University Department of Economics Washington, DC 20057-1036
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Keywords: Dynastic Repeated Games; Private Communication; Folk Theorem;

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Citations

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Cited by:
  1. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2004. "The Folk Theorem in Dynastic Repeated Games," Game Theory and Information 0410001, EconWPA.
  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, 2008. "A “Super” Folk Theorem for dynastic repeated games," Economic Theory, Springer, vol. 37(3), pages 357-394, December.
  4. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "A `Super Folk Theorem' in Dynastic Repeated Games," Levine's Bibliography 321307000000000926, UCLA Department of Economics.
  5. Georgy Egorov & Konstantin Sonin, 2005. "The Killing Game: Reputation and Knowledge in Politics of Succession," Game Theory and Information 0505003, EconWPA.

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