将求解一般0-1策略对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程组的问题.作为一种特殊而重要的情形,利用Pascal 矩阵,Newton矩阵(对角元素为Newton 二项式系数的对角矩阵)和Pascal-Newton 矩阵(Pascal 矩阵和Newton 矩阵的逆阵的乘积)将求解对称0-1 对策的完全混合Nash均衡的问题转化为求解根为正的纯小数的高次代数方程的问题,并给出第二问题的反问题(由完全混合Nash 均衡求解对称0-1 对策族)的求解方法.同时,给出了一些算例来说明对应问题的算法.

In this paper, the problem to solve completely mixed Nash equilibria in a general 0-1 strategy game is changed as the problem to solve a system of high degree algebraic equations whose roots are positive and pure decimals. As a special and important case, the problem to solve completely mixed Nash equilibria in a symmetrical 0-1 game is changed as the problem to solve a high degree algebraic equation whose roots are positive and pure decimals by Pascal matrix, Newtonian matrix (a diagonal matrix whose diagonal elements are Newtonian binomial coefficients), and Pascal-Newtonianmatrix (product of Pascalmatrix and converse of Newtonian matrix). The method of solving converse of the second problem that family of 0-1 symmetrical games is solved by their common completely mixed Nash equilibrium is also given. At the end of the paper, the some examples are given.