Using decision trees and a-cuts for solving matrix games with fuzzy payoffs

Making decisions plays an important role in human life. At any stage of our life we make decisions about what to do, how to do, necessities and un-necessities. Game Theory has an important role in decision issues such as economy and management. Selecting effective strategies in decisions is the base for being successful in the games. The player formulates his decisions using uncertain information in hand. We use fuzzy numbers for determining the profit rate because of un-certainty in real cases. In this article zero-sum 2-player games in fuzzy environments are investigated. In order to research the existence of Pareto Nash equilibrium strategy in fuzzy matrix games, we use the concept of crisp parametric bi-matrix games. By solving these two parameter matrix games we reach (weak) Pareto Nash equilibrium in fuzzy matrix games. In this article we use α-cuts for comparison fuzzy payoffs of the players in decision trees and determine the Nash equilibrium points by min-max strategy. For affecting the rate of risk of people on game decisions, we can decrease or increase the risk with different levels of α. We can also determine optimum risk with POSS (Pareto Optimal Security Strategy) by selecting the value of α.