A Neo^{2} Bayesian Foundation of the Maxmin Value for TwoPerson
ZeroSum Games
Sergiu Hart, Salvatore Modica and David Schmeidler
Abstract
A joint derivation of utility and value for twoperson zerosum
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 certaintyindependent (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 NeumannMorgenstern utility function, and (ii) each act
is ranked according to the maxmin value of the corresponding m
× n utility matrix (viewed as a twoperson zerosum game). An
alternative statement of the result deals simultaneously with
all finite twoperson zerosum games in the framework of
conditional acts and preferences.

International Journal of Game Theory 23 (1994), 4, 347358