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Pairwise epistemic conditions for Nash equilibrium

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  • Bach, Christian W.
  • Tsakas, Elias

Abstract

We introduce a framework for modeling pairwise interactive beliefs and provide an epistemic foundation for Nash equilibrium in terms of pairwise epistemic conditions locally imposed on only some pairs of players. Our main result considerably weakens not only the standard sufficient conditions by Aumann and Brandenburger (1995), but also the subsequent generalization by Barelli (2009). Surprisingly, our conditions do not require nor imply mutual belief in rationality.

Suggested Citation

  • Bach, Christian W. & Tsakas, Elias, 2014. "Pairwise epistemic conditions for Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 85(C), pages 48-59.
    • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:48-59
    DOI: 10.1016/j.geb.2014.01.017
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    References listed on IDEAS

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    1. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    2. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
    3. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
    4. Barelli, Paulo, 2009. "Consistency of beliefs and epistemic conditions for Nash and correlated equilibria," Games and Economic Behavior, Elsevier, vol. 67(2), pages 363-375, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Bach, Christian W. & Perea, Andrés, 2020. "Generalized Nash equilibrium without common belief in rationality," Economics Letters, Elsevier, vol. 186(C).
    2. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    3. Bach, Christian W. & Perea, Andrés, 2020. "Two definitions of correlated equilibrium," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 12-24.
    4. Florian Brandl & Felix Brandt, 2023. "A Robust Characterization of Nash Equilibrium," Papers 2307.03079, arXiv.org, revised Jun 2024.
    5. Tsakas, Elias, 2013. "Pairwise epistemic conditions for correlated rationalizability," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 379-384.
    6. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    7. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    8. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    9. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Nash equilibrium; Pairwise common belief; Pairwise mutual belief; Pairwise action-consistency; Rationality; Conjectures; Biconnected graph; Epistemic game theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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