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Learning from Private Information in Noisy Repeated Games

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  • Fudenberg, Drew
  • Yamamoto, Yuichi

Abstract

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.

Suggested Citation

  • Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from Private Information in Noisy Repeated Games," Scholarly Articles 9962008, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:9962008
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tristan Tomala, 2013. "Belief-Free Communication Equilibria in Repeated Games," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 617-637, November.
    2. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2018. "Belief-free price formation," Journal of Financial Economics, Elsevier, vol. 127(2), pages 342-365.
    3. 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.
    4. Yuichi Yamamoto, 2014. "Stochastic Games with Hidden States, Fifth version," PIER Working Paper Archive 18-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 19 May 2018.
    5. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    6. Pathikrit Basu & Kalyan Chatterjee & Tetsuya Hoshino & Omer Tamuz, 2018. "Repeated Coordination with Private Learning," Papers 1809.00051, arXiv.org.
    7. 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.
    8. Berliant, Marcus, 2020. "Daily commuting," MPRA Paper 100169, University Library of Munich, Germany.
    9. Basu, Pathikrit & Chatterjee, Kalyan & Hoshino, Tetsuya & Tamuz, Omer, 2020. "Repeated coordination with private learning," Journal of Economic Theory, Elsevier, vol. 190(C).
    10. 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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