求收益模糊的贝叶斯纳什均衡解的结构元方法

Solution of Bias Static Game with Fuzzy Profit by Making Use of the Method of Structured Element

主要目的是利用结构元方法求解收益模糊的贝叶斯纳什均衡.首先,在原有结构元理论基础上,给出了多元模糊值函数的定义及其结构元表示;其次,给出了在混合策略下,收益模糊的贝叶斯纳什均衡的定义,并证明了其存在性定理;然后,利用结构元理论,将该博弈模型等价地转化为一个经典的博弈模型,简化了原问题的求解.最后的应用实例说明了该方法的有效性.

The main goal of this paper is to solve bias static game with fuzzy profit by making use of the structured element theory. Firstly, in the based on the original structural element theory, the authors define the multiple fuzzy value function, and use structural element to express it; secondly, under the mixed strategy, the authors define the bias Nash equilibrium with fuzzy profit and proof its existence; then, the authors transform bias static game with fuzzy profit into a classical bias static game by using the structured element theory, and simplify the original problem. At last, the application example illustrates the effectivity.