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A Partial Folk Theorem for Games with Private Learning

Author

Listed:
  • 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. Olivier Gossner & Tristan Tomala, 2012. "Repeated Games with Complete Information," PSE-Ecole d'économie de Paris (Postprint) hal-00712075, HAL.
    2. Gossner, Olivier & Vieille, Nicolas, 2003. "Strategic learning in games with symmetric information," Games and Economic Behavior, Elsevier, vol. 42(1), pages 25-47, January.
    3. Alp E. Atakan & Mehmet Ekmekci, 2012. "Reputation in Long-Run Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 451-480.
    4. repec:dau:papers:123456789/6379 is not listed on IDEAS
    5. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    6. 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.
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    Citations

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    Cited by:

    1. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    2. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    3. Piotr Evdokimov & Umberto Garfagnini, 2022. "Higher-order learning," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1234-1266, September.
    4. 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.
    5. 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.
    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 12062r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2013.
    7. Yuichi Yamamoto, 2014. "We Can Cooperate Even When the Monitoring Structure Will Never Be Known," PIER Working Paper Archive 17-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 08 Apr 2017.
    8. Françoise Forges, 2012. "Folk theorems for Bayesian (public good) games," Post-Print hal-02447604, HAL.
    9. Yuichi Yamamoto, 2014. "Stochastic Games with Hidden States, Second Version," PIER Working Paper Archive 15-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jun 2015.
    10. 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.
    11. Yamamoto, Yuichi, 2019. "Stochastic games with hidden states," Theoretical Economics, Econometric Society, vol. 14(3), July.
    12. Pathikrit Basu & Kalyan Chatterjee & Tetsuya Hoshino & Omer Tamuz, 2018. "Repeated Coordination with Private Learning," Papers 1809.00051, arXiv.org.
    13. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    14. Yuichi Yamamoto, 2014. "Stochastic Games With Hidden States, Fourth Version," PIER Working Paper Archive 16-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Nov 2017.
    15. 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.
    16. Basu, Pathikrit & Chatterjee, Kalyan & Hoshino, Tetsuya & Tamuz, Omer, 2020. "Repeated coordination with private learning," Journal of Economic Theory, Elsevier, vol. 190(C).
    17. 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.
    18. 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.
    19. Tristan Tomala, 2013. "Belief-Free Communication Equilibria in Repeated Games," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 617-637, November.
    20. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    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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