TWO-PERSON ZERO-SUM GAMES WITH RANDOM PAYOFFS

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...

Zero-Sum Two Person Games

A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs

We concentrate on discussing a class of two-person zero-sum games with rough payoffs. Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy and r-trust maximin equilibrium strategy are defined. Five cases whether the game exists r-trust maximin equilibrium strategy are discussed, and the technique of genetic algorithm is applied to find...

Zero - Sum Games with Vector - Valued Payoffs

In this lecture we formulate and prove the celebrated approachability theorem of Blackwell, which extends von Neumann's minimax theorem to zero-sum games with vector-valued payoffs [1]. (The proof here is based on the presentation in [2]; a similar presentation was given by Foster and Vohra [3].) This theorem is powerful in its own right, but also has significant implications for regret minimiz...

Part II . Two - Person Zero - Sum Games