求解矩阵对策的直接线性规划法

求解矩阵对策的直接线性规划法 Direct Linear Programming Algorithm for Solving Matrix Games 白国仲 BAI Guozhong1 1 first-author 朱小琨 ZHU Xiaokun2 2 广东商学院数学系 广东商学院数学系 Department of Mathematics,Guangdong University of Business Studies Department of Mathematics,Guangdong University of Business Studies 华中师范大学学报编辑部 华中师范大学学报编辑部 Editorial Department of Journal,Huazhong Normal University Editorial Department of Journal,Huazhong Normal University 证明了一个矩阵对策问题的解等价于一个线性规划问题的最优解.提出了求解矩阵对策的一种新方法,即直接线性规划法.该方法根据所给问题建立一个特殊的线性规划模型,然后求解,可直接得到矩阵对策的值和两个局中人的最优策略,不需作变量变换,也不要求对策值大于零.给出了直接线性规划法在求解对称对策问题中的应用. By introducing a corresponding linear programming problem this paper establishes the equivalence between the optimal solutions of the linear programming and the solutions of the matrix games.In this paper,a new method for solving the matrix games is given,that is the direct linear programming algorithm.According to the direct linear programming algorithm,we must establish a special linear programming model based on the given matrix game,and solve the linear programming problem,then without making any transform we can directly obtain the value of the matrix game and each player’s optimal strategies no matter whether the value of the game is larger than zero or not.Also,an application of the direct linear programming algorithm in a symmetric game problem is presented. 矩阵对策 直接线性规划法 解 matrix games direct linear programming algorithm solution 10.14188/j.1671-8836.2010.05.001 O225 国家自然科学基金资助项目（70871050） 2010-05-01 2021-04-01 5 56