How can fuzzy logic determine game equilibriums better?

Abstract

Classical game theory is concerned with how rational players make decisions when they are faced with known payoffs. In the past decade, fuzzy logic has been widely used to manage uncertainties in games. In this paper, we employ fuzzy logic to determine the priority of a payoff to other payoffs. A new term is introduced to measure the preference of one payoff to others. By this means a fuzzy preference relation is constructed and using a least deviation method, the priority of every payoff for each player is calculated and the relation of this value with the degree of being Nash is discussed. In the second part of the paper, games with fuzzy payoffs and fuzzy satisfaction functions (SF), satisfaction degree from each payoff, are considered and a new method for analyzing these games is proposed. In this regard we calculate the similarity between SF and payoffs and make a crisp game from the fuzzy game and apply our mentioned method to analyze that game. Compared to the previous generalization, our method has more sensitivity to the slight alternation of payoffs and yields more realistic results. We also studied the effect of playerspsila greediness, modeled by the SF, on the gamepsilas equilibriums.