Consistency of beliefs and epistemic conditions for Nash and correlated equilibria
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Cited by (21)
Lexicographic agreeing to disagree and perfect equilibrium
2023, Journal of Mathematical EconomicsCommon priors under endogenous uncertainty
2021, Journal of Economic TheoryTwo definitions of correlated equilibrium
2020, Journal of Mathematical EconomicsCitation Excerpt :We leave such questions for possible future research. The epistemic analysis of Nash equilibrium (e.g. Aumann and Brandenburger, 1995; Perea, 2007; Barelli, 2009; Bach and Tsakas, 2014; Bonanno, 2017; Bach and Perea, 2019) has unveiled a correct beliefs assumption as the decisive epistemic property of Nash equilibrium. In fact, a correct beliefs property also features implicitly in the one-theory-per-choice condition (Remark 5): the reasoner believes that his opponents are correct about his theories, believes that his opponents believe that their opponents are correct about his theories, etc.
Generalized Nash equilibrium without common belief in rationality
2020, Economics LettersCitation Excerpt :Furthermore, the approaches by Aumann and Brandenburger (1995), Barelli (2009), as well as Bach and Tsakas (2014) are state-based, whereas we employ a one-person perspective approach by modelling all epistemic conditions within the mind of the reasoner only. The elementary epistemic operator in Aumann and Brandenburger (1995) as well as in Barelli (2009) is knowledge, while we use the weaker epistemic notion of belief. In contrast to Perea’s (2007) epistemic conditions for Nash equilibrium, Corollary 1 does not imply that a player believes his opponents to be correct about his full belief hierarchy: our conditions only imply that a player believes his opponents to be correct about his first-order belief, i.e. the first layer in his belief hierarchy.
Epistemic Game Theory
2015, Handbook of Game Theory with Economic ApplicationsPairwise epistemic conditions for Nash equilibrium
2014, Games and Economic BehaviorCitation Excerpt :The contribution of the previous result to the epistemic foundation of Nash equilibrium is twofold. Firstly, we relax the epistemic conditions of Barelli (2009), and a fortiori also the standard conditions by Aumann and Brandenburger (1995), by no longer requiring neither mutual belief in rationality, nor mutual belief in payoffs, nor action-consistency. Finally, note that Barelli's extension of Aumann and Brandenburger (1995) is based on weakening the common prior assumption.