A Neo[superscript]2 Bayesian Foundation of the Maxmin Value for Two-Person Zero-Sum Games.
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 x n utility matrix (viewed as a two-person zero-sum game). An alternative statement of the result details simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.
Year of publication: |
1994
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Authors: | Hart, Sergiu ; Modica, Salvatore ; Schmeidler, David |
Published in: |
International Journal of Game Theory. - Springer. - Vol. 23.1994, 4, p. 347-58
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Publisher: |
Springer |
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