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A Partial Folk Theorem for Games with Private Learning

Author

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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.

Suggested Citation

  • Thomas E. Wiseman, 2011. "A Partial Folk Theorem for Games with Private Learning," 2011 Meeting Papers 181, Society for Economic Dynamics.
  • Handle: RePEc:red:sed011:181
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    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    2. Olivier Gossner & Tristan Tomala, 2012. "Repeated Games with Complete Information," Post-Print hal-00712075, HAL.
    3. Atakan, Alp E. & Ekmekci, Mehmet, 2013. "A two-sided reputation result with long-run players," Journal of Economic Theory, Elsevier, vol. 148(1), pages 376-392.
    4. Gossner, Olivier & Vieille, Nicolas, 2003. "Strategic learning in games with symmetric information," Games and Economic Behavior, Elsevier, vol. 42(1), pages 25-47, January.
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    Cited by:

    1. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    2. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    3. Brangewitz, Sonja & Giraud, Gael, 2016. "Learning in Infinite Horizon Strategic Market Games with Collateral and Incomplete Information," Center for Mathematical Economics Working Papers 456, Center for Mathematical Economics, Bielefeld University.
    4. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    5. 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.
    6. Yuichi Yamamoto, 2015. "Stochastic Games with Hidden States," PIER Working Paper Archive 15-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. 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.
    8. 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 12062r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2013.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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