基于灰混合策略的灰矩阵博弈模型的解

Solution of Grey Matrix Game Based on Grey Mixed Strategy

最大最小灰博弈值与灰混合策略的灰鞍点问题是基于灰混合策略的灰矩阵博弈的关键问题 ,本文运用灰色系统理论证明了最大最小灰博弈值定理 ,从而奠定了灰矩阵博弈的理论基础。在此基础上 ,提出了灰混合策略的灰鞍点的概念 ,并且证明了灰鞍点存在的充分必要条件和灰混合最优策略的可交换性定理。

How to solve the problems of maximum-minimum value of grey matrix game and the grey saddle point of grey mixed strategy in the grey matrix game is the key problem of grey matrix game based on the grey mixed strategy. Applying the grey system theory, the maximum-minimum value theorem of grey matrix game is proved, which lays a theory foundation of the grey matrix game. Then, the conception of the grey saddle point of the grey mixed strategy is presented, and the sufficient and necessary condition of the existence on grey saddle point in the grey matrix game, and an interchangeable theorem of the grey mixed optimum strategy are proved.