A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

Zero-Sum Two Person Games

A satisfactory strategy of multiobjective two person matrix games with fuzzy payoffs

The multiobjective two person matrix game problem with fuzzy payoffs is considered in this paper. It is assumed that fuzzy payoffs are triangular fuzzy numbers. The problem is converted to several multiobjective matrix game problems with interval payoffs by using the $alpha$-cuts of fuzzy payoffs. By solving these problems some $alpha$-Pareto optimal strategies with some interval outcomes are o...

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

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...

Two-Person Zero-Sum Stochastic Games with Semicontinuous Payoff

Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f i...