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.