基于纯策略的灰矩阵二人有限零和博弈模型研究

运用灰色系统理论分析和研究了基于纯策略的灰矩阵二人有限零和最保守博弈决策问题。研究了灰博弈损益值矩阵的特性，构建了该问题的数学模型．提出并证明了该PI题的局中人各单方面和整体的灰矩阵二人有限零和最保守博弈决策有解的充分必要条件，提出了该问题解的灰鞍点概念。在此基础上，用该灰矩阵博弈理论来解决某单位冬季取暖用煤的采购决策问题，取得了良好效果。

Grey Matrix Game Model Based on Pure Strategy

The classical matrix game theories can be used to solve the matrix game problems described by classical mathematics. However, in the real life, there are many problems of the game, for example some grey elements in the payoff matrix, which cannot be pictured by the classical mathematics. This paper studies the problems of grey matrix game based on pure strategy applying grey system theories. The properties of the gains and loss matrix of grey matrix game are analyzed. Then a mathematical model for the problem is built. The necessary and sufficient conditions for the solution of the mono-side and the whole-side grey matrix game are proposed and proved. The conception of the grey saddle point of the solution is put forward. Furthermore, a practical grey matrix game problem, in which some department stocks coal for warm oneself in the winter, is solved by the grey matrix game theories.