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Games 2016, 7(4), 35; doi:10.3390/g7040035

Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium

Department of Economics, University of California, Davis, CA 95616-8578, USA
I am grateful to two anonymous reviewers for helpful comments and suggestions.
Academic Editor: Paul Weirich
Received: 9 August 2016 / Revised: 1 November 2016 / Accepted: 4 November 2016 / Published: 10 November 2016
(This article belongs to the Special Issue Epistemic Game Theory and Logic)
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Abstract

In (Bonanno, 2013), a solution concept for extensive-form games, called perfect Bayesian equilibrium (PBE), was introduced and shown to be a strict refinement of subgame-perfect equilibrium; it was also shown that, in turn, sequential equilibrium (SE) is a strict refinement of PBE. In (Bonanno, 2016), the notion of PBE was used to provide a characterization of SE in terms of a strengthening of the two defining components of PBE (besides sequential rationality), namely AGM consistency and Bayes consistency. In this paper we explore the gap between PBE and SE by identifying solution concepts that lie strictly between PBE and SE; these solution concepts embody a notion of “conservative” belief revision. Furthermore, we provide a method for determining if a plausibility order on the set of histories is choice measurable, which is a necessary condition for a PBE to be a SE. View Full-Text
Keywords: plausibility order; minimal belief revision; Bayesian updating; independence; sequential equilibrium plausibility order; minimal belief revision; Bayesian updating; independence; sequential equilibrium
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Bonanno, G. Exploring the Gap between Perfect Bayesian Equilibrium and Sequential Equilibrium. Games 2016, 7, 35.

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