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A Partial Folk Theorem for Games with Private Learning

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  • Thomas E. Wiseman

    (University of Texas at Austin)

Abstract

The payoff matrix of a finite stage game is realized randomly, and then the stage game is repeated infinitely. The distribution over states of the world (a state corresponds to a payoff matrix) is commonly known, but players do not observe nature’s choice. Over time, they can learn the state in two ways. After each round, each player observes his own realized payoff (which may be stochastic, conditional on the state), and he observes a noisy public signal of the state (whose informativeness may vary with the actions chosen). Actions are perfectly observable. The result is that for any function that maps each state to a payoff vector that is feasible and individually rational in that state, there is a sequential equilibrium in which patient players learn the realized state with arbitrary precision and achieve a payoff close to the one specified for that state. That result extends to the case where there is no public signal, but instead players receive very closely correlated private signals of the vector of realized payoffs.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2011 Meeting Papers with number 181.

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Date of creation: 2011
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Handle: RePEc:red:sed011:181

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References

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  1. Gossner, Olivier & Vieille, Nicolas, 2003. "Strategic learning in games with symmetric information," Games and Economic Behavior, Elsevier, Elsevier, vol. 42(1), pages 25-47, January.
  2. Mehmet Ekmekci & Alp Atakan, 2009. "A two Sided Reputation Result with Long Run Players," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1510, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262011476, December.
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Cited by:
  1. Francoise Forges & Antoine Salomon, 2014. "Bayesian Repeated Games and Reputations," CESifo Working Paper Series 4700, CESifo Group Munich.
  2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(5), pages 1733-1769, September.
  3. Sonja Brangewitz & Gael Giraud, 2011. "Learning in Infinite Horizon Strategic Market Games with Collateral and Incomplete Information," Working Papers, Bielefeld University, Center for Mathematical Economics 456, Bielefeld University, Center for Mathematical Economics.
  4. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Lovo, Stefano & Tomala, Tristan & Hörner, Johannes, 2009. "Belief-free equilibria in games with incomplete information: characterization and existence," Les Cahiers de Recherche 921, HEC Paris.
  6. Sonja Brangewitz & Gaël Giraud, 2012. "Learning by Trading in Infinite Horizon Strategic Market Games with Default," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 12062r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2013.
  7. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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