A symmetrization for finite two-person games

A symmetrization for finite two-person games

The symmetrization method of Gale, Kuhn and Tucker for matrix games is extended for bimatrix games. It is shown that the equilibria of a bimatrix game and its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.

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...

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...

Computing Equilibria for Two-person Games

Computing Equilibria for Two-Person Games

This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games given in normal form or extensive form. The classical Lemke{Howson algorithm for nding one equilibrium of a bimatrix game is presented graph-theoretically as well as algebraically in terms of complementary pivoting. Common deenitions of degenerate games are shown as equivalent. Enumeration of a...