A characterization of sequential equilibrium in terms of AGM belief revision

In [G. Bonanno, Rational choice and AGM belief revision, Artificial Intelligence, 2009] a semantics for one-stage AGM belief revision was proposed based on choice frames, borrowed from the rational choice literature. In this paper we extend the semantics of choice frames to deal with iterated belief revision and use the corresponding structures to analyze extensive-form games. Choice frames can be used to represent a player's initial beliefs and disposition to change those beliefs when informed that it is her turn to move. If the frame satisfies AGM-consistency and a natural postulate for iterated belief revision, then it is rationalizable by a total pre-order on the set of histories. We show that three properties of this total pre-order, together with the hypothesis of agreement among players, provide a characterization of the notion of consistent assessment, which is the central component of the notion of sequential equilibrium proposed by Kreps and Wilson [Econometrica, 1982].Choice function, AGM belief revision, extensive-form game, sequential equilibrium, iterated belief revision, backward induction.

Semantic structures for one-stage and iterated belief revision

Semantic structures for belief revision and iterated belief revision are proposed. We start with one-stage revision structures that generalize the notion of choice function from rational choice theory. A correspondence between these one-stage structures and AGM belief revision functions is established. We then add branching time and consider more general structures that accommodate iterated revision. AGM temporal belief revision structures are defined and a syntactic axiomatization is provided

Revealed preference, iterated belief revision and dynamic games

In previous work (G. Bonanno, Rational choice and AGM belief revision, Artificial Intelligence, 2009) a semantics for AGM belief revision was proposed based on choice frames, borrowed from the rational choice literature. In this paper we discuss how to use choice frames to analyze extensive-form games. Given an extensive form with perfect recall, a choice frame can be used to represent a player\u27s initial beliefs and her disposition to change those beliefs when she is informed that it is her turn to move. When some players move more than once along some play of the game, the issue of iterated belief revision arises. We provide a semantics for iterated belief revision in terms of choice frames and provide an outline of how to use choice frames to analyze solution concepts for extensive-form games

Belief Revision in Science: Informational Economy and Paraconsistency

In the present paper, our objective is to examine the application of belief revision models to scientific rationality. We begin by considering the standard model AGM, and along the way a number of problems surface that make it seem inadequate for this specific application. After considering three different heuristics of informational economy that seem fit for science, we consider some possible adaptations for it and argue informally that, overall, some paraconsistent models seem to better satisfy these principles, following Testa (2015). These models have been worked out in formal detail by Testa, Cogniglio, & Ribeiro (2015, 2017)

Extending the Harper Identity to Iterated Belief Change

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators

AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties.

We provide a general notion of perfect Bayesian equilibrium which can be applied to arbitrary extensive-form games and is intermediate between subgame-perfect equilibrium and sequential equilibrium. The essential ingredient of the proposed definition is the qualitative notion of AGM-consistency, which has an epistemic justification based on the AGM theory of belief revision.belief revision, plausibility order, consistency, subgame-perfect equilibrium, sequential equilibrium, Bayesian updating.