# 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.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: April, 1991

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