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. However, it is difficult to know the exact values of payoffs and we could only know the values of payoffs approximately. In such situations, it is useful to model the problems as games with fuzzy payoffs. In this case, since the expected payoffs of the game should be fuzzy-valued, there are no concepts of equilibrium strategies to be accepted widely. So, it is an important task to define the concept of equilibrium strategies and investigate their properties. In this paper, we consider fuzzy bimatrix games, namely, the games where the number of players are two and fuzzy payoffs. For such a game, we shall define three kinds of concepts of minim ax equilibrium strategies.