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Knowing the informed player's payoffs and simple play in repeated games

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  • Habu, Takuma
  • Lipnowski, Elliot
  • Ravid, Doron

Abstract

We revisit the canonical model of repeated games with two patient players, observable actions, and one-sided incomplete information, and make the substantive assumption that the informed player's preference is state independent. We show the informed player can attain a payoff in equilibrium if and only if she can attain it in the simple class of equilibria first studied by Aumann, Maschler, and Stearns (1968), in which the initial stages are used only for revealing information, and no further information is revealed after the initial stages. This sufficiency result does not extend to the uninformed player's equilibrium payoff set.

Suggested Citation

  • Habu, Takuma & Lipnowski, Elliot & Ravid, Doron, 2024. "Knowing the informed player's payoffs and simple play in repeated games," Journal of Economic Theory, Elsevier, vol. 221(C).
  • Handle: RePEc:eee:jetheo:v:221:y:2024:i:c:s0022053124000942
    DOI: 10.1016/j.jet.2024.105888
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    References listed on IDEAS

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    1. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    2. Archishman Chakraborty & Rick Harbaugh, 2010. "Persuasion by Cheap Talk," American Economic Review, American Economic Association, vol. 100(5), pages 2361-2382, December.
      • Archishman Chakraborty & Rick Harbaugh, 2006. "Persuasion by Cheap Talk," Working Papers 2006-10, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy, revised Oct 2009.
    3. Elliot Lipnowski & Doron Ravid, 2020. "Cheap Talk With Transparent Motives," Econometrica, Econometric Society, vol. 88(4), pages 1631-1660, July.
    4. Forges, F., 1984. "Note on Nash equilibria in infinitely repeated games with incomplete information," LIDAM Reprints CORE 573, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Martin W. Cripps & Jonathan P. Thomas, 2003. "Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 433-462, August.
    6. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
    7. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    8. Françoise Forges, 2020. "Games with Incomplete Information: From Repetition to Cheap Talk and Persuasion," Annals of Economics and Statistics, GENES, issue 137, pages 3-30.
    9. Sergiu Hart, 1985. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 117-153, February.
    10. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    11. Françoise Forges, 2020. "Games with incomplete information: from repetition to cheap talk and persuasion," Post-Print hal-03537868, HAL.
    12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    More about this item

    Keywords

    Repeated games; Incomplete information; Transparent motives;
    All these keywords.

    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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