6533b853fe1ef96bd12ac98e
RESEARCH PRODUCT
A Neo2 bayesian foundation of the maxmin value for two-person zero-sum games
Sergiu HartDavid SchmeidlerDavid SchmeidlerSalvatore Modicasubject
Statistics and ProbabilityComputer Science::Computer Science and Game TheoryEconomics and EconometricsTransitive relationVon Neumann–Morgenstern utility theoremMathematics (miscellaneous)Zero-sum gameExample of a game without a valueCardinal utilityStatistics Probability and UncertaintyTransferable utilityMathematical economicsFinite setSocial Sciences (miscellaneous)AxiomMathematicsdescription
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 andn columns). Preferences over acts are complete, transitive, continuous, monotonie 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 correspondingm × 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1994-12-01 | International Journal of Game Theory |