A Syntactic Framework with Probabilistic Beliefs and Conditionals for the Analysis of Strategic Form Games

Authors:
Thorsten Clausing
Affiliations:
Faculty of Management and Economics, University of Magdeburg, Postfach 4120, 39016 Magdeburg, Germany. E-mail: thorsten.clausing@ww.uni-magdeburg.de
Venue:
Journal of Logic, Language and Information
Year:
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).