Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals

✍ Scribed by Ichiro Nishizaki; Masatoshi Sakawa

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 168 KB
• Volume: 111
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00455-2

✦ Synopsis

When the game theory is applied to real world problems such as decision making in public and managerial problems, on occasions it is di cult to assess payo s exactly because of inaccuracy of information and fuzzy understanding of situations by experts. In such cases, games with fuzzy payo s, in which payo s are represented as fuzzy numbers, are often considered. In this paper, we consider equilibrium solutions in multiobjective bimatrix games with fuzzy payo s. We introduce fuzzy goals for payo s in order to incorporate ambiguity of a player's judgements and assume that the player tries to maximize degrees of attainment of the fuzzy goals. The fuzzy goals for payo s and the equilibrium solution with respect to the degree of attainment of the fuzzy goal are deÿned. Two basic methods, one by weighting coe cients and the other by a minimum component, are employed to aggregate multiple fuzzy goals. When membership functions of fuzzy payo s and fuzzy goals are all linear and the fuzzy decision in terms of the intersection is employed, the necessary conditions that pairs of strategies be the equilibrium solutions is obtained. When membership functions of fuzzy payo s are quadratic functions, those of fuzzy goals are linear, and the fuzzy decision in terms of the convex combination is employed, we also derive the necessary conditions that pairs of strategies be the equilibrium solutions.