SFB 303 Discussion Paper No. A - 340

Author: Hart, Sergiu, Salvatore Modica, and David Schmeidler
Title: A Neo Bayesian Foundation of the Maximin Value for Two-Person Zero-Sum Games
Abstract: A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows and n columns). Preferences over acts are complete, transitive, continuous, monotonic and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the corresponding m * n utility matrix (viewed as a two-person zero-sum game). An alternative statement of the result deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.
Creation-Date: April, 1991
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