A new bi-matrix game model with fuzzy payoffs in credibility space

Uncertain theory based on expert's evaluation and non-additive measure is introduced to explore the bi-matrix game with the uncertain payoffs. The uncertainty space based on the axiom of the uncertain measures is presented. Some basic characteristics of uncertain events are described and the expected value of the uncertain variables is given in uncertainty space. A new model of bi-matrix game with uncertain payoffs is established and its equivalent strategy is given. Then, we develop an expected model of uncertain bi-matrix games and define the uncertain equilibrium strategy of uncertain bi-matrix games. By using the expected value of uncertain variable, we transform the model into a linear programming, the expected equilibrium strategy of the uncertain bi-matrix games is identified through solving linear equations.