Matrix games with payoffs of belief structures

Imprecise matrix games, such as interval-valued matrix games and fuzzy matrix games, have attracted much interest for a long time. Most of the previous studies on imprecise matrix games mainly focus on the fuzzy uncertainty of payoffs. However, the uncertainties of nonspecificity and discord involved in payoffs are not well addressed so far. The purpose of this paper is to study the matrix game with such types of uncertainties. In order to achieve that purpose, we present a matrix game model with payoffs of belief structures so as to integrate discord and nonspecificity. The proposed model can be used to express more imprecise interactions between players in the reality. Besides, as another main contribution of the study, an effective method for solving matrix games with belief structures payoffs is developed to help us find the equilibrium points of the kind of games. At last, an example is given to illustrate the proposed model and method.