Equilibrium Solutions in Bimatrix Games with Fuzzy Payoffs

Abstract

When game theory is applied to real world problems such as decision making in public and managerial problems, there are occasions when it is difficult to assess exact payoffs because of inaccuracy in information and uncertainty of describing states. To analyze such situations, games with fuzzy payoffs, in which payoffs are represented as fuzzy numbers, are often employed.In this paper, we consider equilibrium solutions in bimatrix games with fuzzy payoffs. First, we examine the case where there is no information on the preferences of players. The equilibrium solutions are defined from a viewpoint of possibility and necessity, and existence conditions of these solutions are investigated. Second, we examine the case where the preferences of the players are represented by fuzzy goals to the payoffs of the players and consider equilibrium solutions with respect to the attainment of each of their goals. Third, we assume that each player maximized the mean of the fuzzy expected payoff and minimizes its spread, and then consider equilibrium solutions of the games with fuzzy payoffs in which the players optimize these objectives in accordance with their preferences.