S. Hart et al., A NEO2 BAYESIAN FOUNDATION OF THE MAXMIN VALUE FOR 2-PERSON ZERO-SUM GAMES, International journal of game theory, 23(4), 1994, pp. 347-358
Citations number
15
Categorie Soggetti
Social Sciences, Mathematical Methods","Mathematical, Methods, Social Sciences
A joint derivation of utility and value for two-person zero-sum games
is obtained using a decision theoretic approach. Acts map states to co
nsequences. The latter are lotteries over prizes, and the set of state
s is a product of two finite sets (m rows and n columns). Preferences
over acts are complete, transitive, continuous, monotonic and certaint
y-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 r
anked according to the maxim value of the corresponding m x n utility
matrix (viewed as a two-person zero-sum game). An alternative statemen
t of the result deals simultaneously with all finite two-person zero-s
um games in the framework of conditional acts and preferences.