A syntactic framework with probabilistic beliefs and conditionals for the analysis of strategic form games

Journal of Logic, Language and Information 11 (3):335-348 (2002)
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Abstract

In this paper, I develop a syntactic framework for the analysis ofstrategic form games that is based on a straightforward combination ofstandard systems of doxastic, probabilistic and conditionalpropositional logic. In particular, for the probabilistic part I makeuse of the axiomatization provided in Fagin and Halpern (1994). The use ofconditionals allows to represent a strategic form game by a logicalformula in a very natural way. Also expected utility maximization can benaturally captured. I use this framework to prove a version of a resulton Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995).

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References found in this work

The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Conditional Logic.Donald Nute - 1989 - Journal of Symbolic Logic 54 (4):1477-1479.
Fine-grained opinion, probability, and the logic of full belief.Bas C. van Fraassen - 1995 - Journal of Philosophical Logic 24 (4):349-377.

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