On Nash Equilibrium Strategy of Two-person Zero-sum Games with Trapezoidal Fuzzy 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...

Two-Person Non Zero-Sum Bimatrix Game with Fuzzy Payoffs and Its Equilibrium Strategy

Since seminal works by Neumann-Morgenstern(J.VonNeunann, 1994) and Nash(J.F.Nash., 1950 & J.F.Nash., 1951), Game theory has played an important role in the fields of decision making theory such as economics, management, and operations research, etc. When we apply the game theory to model some practical problems which we encounter in real situations, we have to know the values of payoffs exactly...

Nash Equilibrium Strategy for Bi-matrix Games with L-R Fuzzy Payoffs

In this paper, bi-matrix games are investigated based on L-R fuzzy variables. Also, based on the fuzzy max order several models in non-symmetrical L-R fuzzy environment is constructed and the existence condition of Nash equilibrium strategies of the fuzzy bi-matrix games is proposed. At last, based on the Nash equilibrium of crisp parametric bi-matrix games, we obtain the Pareto and weak Pareto...

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 Two Person Games