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A 'Super' Folk Theorem for Dynastic Repeated Games

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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.” Classification-JEL Codes: C72, C73, D82

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Bibliographic Info

Paper provided by Georgetown University, Department of Economics in its series Working Papers with number gueconwpa~06-06-01.

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Date of creation: 01 Jun 2006
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Handle: RePEc:geo:guwopa:gueconwpa~06-06-01

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Postal: Georgetown University Department of Economics Washington, DC 20057-1036
Phone: 202-687-6074
Fax: 202-687-6102
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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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Web: http://econ.georgetown.edu/

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Keywords: Dynastic Repeated Games; Private Communication; Folk Theorem;

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References

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  1. 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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  3. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2008. "Communication and Learning," Levine's Bibliography 122247000000001868, UCLA Department of Economics.
  4. Luca Anderlini (Georgetown University), Dino Gerardi (Yale University), Roger Lagunoff (Georgetown University), 2004. "The Folk Theorem in Dynastic Repeated Games," Working Papers gueconwpa~04-04-09, Georgetown University, Department of Economics.
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Cited by:
  1. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "Social Memory and Evidence from the Past," Working Papers gueconwpa~07-07-01, Georgetown University, Department of Economics.
  2. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "A `Super Folk Theorem' in Dynastic Repeated Games," Levine's Bibliography 321307000000000926, UCLA Department of Economics.
  3. Pablo Casas-Arce, 2010. "Dismissals and quits in repeated games," Economic Theory, Springer, vol. 43(1), pages 67-80, April.
  4. 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.
  5. Daron Acemoglu & Matthew O. Jackson, 2011. "History, Expectations, and Leadership in the Evolution of Social Norms," NBER Working Papers 17066, National Bureau of Economic Research, Inc.

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