A Solution Concept of Matrix Game with Random Fuzzy Payoffs

Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. We present a new methodology for the analysis of random fuzzy payoffs matrix games. The main difficulty then appears in the study of these games is the comparison between the payoff values associated to the strategies of the players because these payoffs are random fuzzy quantities. The purpose of this paper is to introduce a two-person zero-sum matrix game in which the elements of payoff are characterized as random fuzzy variables. Based on expected value operator, an expected minmax equilibrium strategy to the proposed game is defined and the existence of the strategy is proved. Finally, an example is given to illustrate the effectiveness of the proposed game.