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.
Highlights
Since its introduction in 1982 [1], sequential equilibrium has been the most widely used solution concept for extensive-form games
The first property identifies the set of decision histories that can be assigned positive conditional probability by the system of beliefs, while the second property imposes constraints on how conditional probabilities can be distributed over that set in order to guarantee “Bayesian updating as long as possible”30
The strengthening of the first condition is that the plausibility order that rationalizes the given assessment be choice measurable, that it, that there be a cardinal representation of it
Summary
Since its introduction in 1982 [1], sequential equilibrium has been the most widely used solution concept for extensive-form games. In this paper we continue the study of one such notion, introduced in [5], where it is shown that (a) the proposed solution concept is a strict refinement of subgame-perfect equilibrium; and (b) in general, the set of sequential equilibria is a proper subset of the set of perfect Bayesian equilibria This definition of PBE is based on two notions (besides sequential rationality): (1) the qualitative property of AGM-consistency relative to a plausibility.
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