On solution of constraint matrix games under rough interval approach

The aim of this article is to propose an effective technique for solving constraint matrix games with rough interval payoffs, which are a class of non-cooperative two-person matrix games with rough interval payoffs and the strategies of the players are constrained. Since the payoffs of the rough constraint matrix games are rough intervals, then its game value is also a rough interval. In this technique, we derived four linear programming problems, which are used to obtain the upper–lower bound, lower–lower bound, lower–upper bound and upper–upper bound of the rough interval game values of the players in rough constraint matrix games. Moreover, the expected value operator and trust measure of rough interval have been used to obtain the α-trust equilibrium strategies and the expected equilibrium strategies of the problem under study. In addition, the different advantages of the proposed technique over those existing are discussed. Finally, a numerical experiment of market share game model is given and solved by the three mentioned methods to illustrate the effectiveness and practicality of the proposed method.