An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize minimize his her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends. In this paper, we utilize fuzzy set theory in order to incorporate the players’ heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.