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Generalized Nash equilibrium without common belief in rationality

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  • Bach, Christian W.
  • Perea, Andrés

Abstract

We provide an existence result for the solution concept of generalized Nash equilibrium, which can be viewed as the direct incomplete information analogue of Nash equilibrium. Intuitively, a tuple consisting of a probability measure for every player on his choices and utility functions is a generalized Nash equilibrium, whenever some mutual optimality property is satisfied. This incomplete information solution concept is then epistemically characterized in a way that common belief in rationality is neither used nor implied. For the special case of complete information, an epistemic characterization of Nash equilibrium ensues as a corollary.

Suggested Citation

  • Bach, Christian W. & Perea, Andrés, 2020. "Generalized Nash equilibrium without common belief in rationality," Economics Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:ecolet:v:186:y:2020:i:c:s0165176519302502
    DOI: 10.1016/j.econlet.2019.108526
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    References listed on IDEAS

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    1. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    2. 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..
    3. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    4. Ben Polak, 1999. "Epistemic Conditions for Nash Equilibrium, and Common Knowledge of Rationality," Econometrica, Econometric Society, vol. 67(3), pages 673-676, May.
    5. Bach, Christian W. & Tsakas, Elias, 2014. "Pairwise epistemic conditions for Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 85(C), pages 48-59.
    6. 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.
    7. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    8. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    9. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
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    Cited by:

    1. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    2. Yuwei Yan & Xiaomeng Ma & Yi Song & Ajay Kumar & Ruixian Yang, 2023. "Exploring the interaction and choice behavior of organization and individuals in the crowd logistics," Annals of Operations Research, Springer, vol. 320(2), pages 1021-1040, January.

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    More about this item

    Keywords

    Common belief in rationality; Complete information; Epistemic characterization; Epistemic game theory; Existence; Generalized Nash equilibrium; Incomplete information; Interactive epistemology; Nash equilibrium; Solution concepts; Static games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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