A Neo2 Bayesian Foundation of the Maxmin Value for Two-Person Zero-Sum Games'
نویسندگان
چکیده
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 NeumannMorgenstern 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 deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.
منابع مشابه
A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS
In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...
متن کاملRepeated Games with Bounded Entropy
We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of the maximizer’s strategies while the other player is unrestricted. We will show that if the Ž . bound h n , a function of the number of repetitions n, satisfies the condition Ž . Ž . nŽ Ž .. Ž .Ž . h n rn a g n a ` , then the maxmin value W h n converges to ...
متن کاملThe value of two-person zero-sum repeated games with incomplete information and uncertain duration
It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist [1]. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players’ information about the uncertain number of repetitions is asy...
متن کاملZero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture $\operatorname{maxmin}=\operatorname{lim}v_n$
Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528–1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum repeated game, the asymptotic value exists, and the second one is that, when Player 1 is more informed than Player 2, in the long run Player 1 is able to guaran...
متن کاملComputing Maxmin Strategies in Extensive-form Zero-sum Games with Imperfect Recall
Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative theoretical results: a Nash equilibrium does not have to exist, computing maxmin strategies is NP-hard, and they may require irrational numbers. We present the fir...
متن کامل