A neo Bayesian foundation of the maxmin value for two-person zero-sum games

A neo Bayesian foundation of the maxmin value for two-person zero-sum games

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Article ID: iaor19952238
Country: Germany
Volume: 23
Start Page Number: 347
End Page Number: 358
Publication Date: Apr 1994
Journal: International Journal of Game Theory
Authors: , ,
Keywords: Bayesian modelling
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, and satisfy a new axiom which the authors 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.

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