A fuzzy game theoretic approach to multi-agent coordination

Game theoretic decision making is a practical approach to multi-agent coordination. Rational agents may make decisions based on different principles of rationality assumptions that usually involve knowledge of how other agents might move. After formulating a game matrix of utility entries of possible combination of moves from both agents, agents can reason which combination is the equilibrium. Most previous game theoretic works treat the utility values qualitatively .(i. e. consider only the order of the utility values). This is not practical since the utility values are usually approximate and the differences between utility values are somewhat vague. In this paper, we present a fuzzy game theoretic decision making mechanism that can deal with uncertain utilities. We thus construct a fuzzy-theoretic game framework under both the fuzzy theory and the game theory. The notions of fuzzy dominant relations, fuzzy Nash equilibrium, and fuzzy strategies are defined and fuzzy reasoning are carried out in agent decision making. We show that a fuzzy strategy can perform better than a mixed strategy in traditional game theory in dealing with more than one Nash equilibrium games.