区间值双矩阵博弈的均衡策略

The Equilibrium Strategies of Bi-matrix Games with Interval-valued Payoffs

基于区间值偏序关系理论,研究了区间值双矩阵博弈均衡策略的确定问题。利用区间值的相对优势函数和模糊偏好比刻画和度量局中人对区间值支付的模糊偏好,提出了区间值双矩阵博弈满足不同序关系的均衡策略概念。针对局中人具有模糊偏好和不同的风险态度的博弈环境,建立了模糊优势支付矩阵和风险模糊优势支付矩阵,给出了该环境下均衡策略确定的方法,为现实博弈均衡的确定提供了有效的途径。最后通过算例予以说明。

Based on the existing works on comparing and ranking to any two interval numbers on the real line, this paper puts forward an approach of solving the equilibrium strategies. Here, we study mainly on the interval-valued bi-matrix games, namely, two-person non-zero-sum games with interval-valued payoffs. Under many conditions, real numbers are inadequate in modeling matrix games systems, since players can not estimate their payoffs with an exact number value except interval-valued numbers. First, we shall measure and describe the player＇s fuzzy preference to interval-valued payoffs, and then gives the ratio of fuzzy preference and the fuzzy optimal function. The concepts of equilibrium strategies are also defined by using different ordering relations on interval-valued payoffs. Second, after taking full thought of players＇ fuzzy preference and their risk attitudes, we construct the fuzzy preference payoff matrix and venture fuzzy optimal payoffs matrix, in addition, give the equilibrium strategies. Finally, a numeric example is raised to illustrate the proposed method＇s effectiveness and feasibility.