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Consistency of beliefs and epistemic conditions for Nash and correlated equilibria

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  • Barelli, Paulo

Abstract

A consistency condition (action-consistency) on the interim beliefs of players in a game is introduced. Action-consistency is weaker than common priors and, unlike common priors, is characterized by a "no-bets" condition on verifiable events. Using action-consistency, we provide epistemic conditions to Nash and correlated equilibria weakening the common knowledge restrictions in Aumann and Brandenburger [Aumann, R., Brandenburger, A., 1995. Epistemic conditions for Nash equilibrium. Econometrica 63, 1161-1180] and Aumann [Aumann, R., 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55, 1-18].

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  • 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.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:363-375
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    Cited by:

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    2. Bach, C.W. & Tsakas, E., 2012. "Pairwise interactive knowledge and Nash equilibrium," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Bach, Christian W. & Perea, Andrés, 2020. "Generalized Nash equilibrium without common belief in rationality," Economics Letters, Elsevier, vol. 186(C).
    4. Satoshi Fukuda, 2024. "On the consistency among prior, posteriors, and information sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 521-565, September.
    5. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    6. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
    7. Bach, Christian W. & Perea, Andrés, 2020. "Two definitions of correlated equilibrium," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 12-24.
    8. Alex Boulatov & Dan Bernhardt, 2015. "Robustness of equilibrium in the Kyle model of informed speculation," Annals of Finance, Springer, vol. 11(3), pages 297-318, November.
    9. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.
    11. Paulo Barelli, 2010. "Consistent Beliefs in Extensive Form Games," Games, MDPI, vol. 1(4), pages 1-7, October.
    12. 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.
    13. Giacomo Bonanno, 2021. "Rational play in games: A behavioral approach," Working Papers 344, University of California, Davis, Department of Economics.
    14. Hellman, Ziv, 2013. "Weakly rational expectations," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 496-500.
    15. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    16. Bach, Christian W. & Tsakas, Elias, 2014. "Pairwise epistemic conditions for Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 85(C), pages 48-59.

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