The concept of minimax variational inequality was proposed by Huy and Yen (Acta Math Vietnam 36, 265–281, 2011). This paper establishes some properties of monotone affine minimax variational inequalities and gives sufficient conditions for their solution stability. Then, by transforming a two-person zero sum game in matrix form (Barron in Game Theory. An Introduction, 2nd edn, Wiley, New Jersey, 2013) to a monotone affine minimax variational inequality, we prove that the saddle point set in mixed strategies of the matrix game is a nonempty compact polyhedral convex set and it is locally upper Lipschitz everywhere when the game matrix is perturbed. The rate of convergence of the extragradient method of Korpelevich applied to the matrix game is also discussed.

最小极大变分不等式的概念由Huy和Yen提出（Acta Math Vietnam 36，265–281，2011）。建立了单调仿射极小极大不等式的一些性质，并为其解的稳定性提供了充分的条件。然后，通过将矩阵形式的两人零和游戏（游戏理论中的巴伦，前言，第二版，威利，新泽西州，2013年）转化为单调仿射极小极大变分不等式，我们证明了混合点集上的鞍点矩阵博弈的策略是一个非空的紧凑多面凸集，当博弈矩阵受到扰动时，它在各处都是Lipschitz的局部。还讨论了将Korpelevich的超梯度方法应用于矩阵博弈的收敛速度。