Two-person games are used in many multi-agent mathematical models to describe pair interactions. The type (pure or mixed) and the number of Nash equilibria affect fundamentally the macroscopic behavior of these systems. In this paper, the general features of Nash equilibria are investigated systematically within the framework of matrix decomposition for n strategies. This approach distinguishes four types of elementary interactions that each possess fundamentally different characteristics. The possible Nash equilibria are discussed separately for different types of interactions and also for their combinations. A relation is established between the existence of infinitely many mixed Nash equilibria and the zero-eigenvalue eigenvectors of the payoff matrix.

在许多多主体数学模型中使用两人游戏来描述配对互动。纳什均衡的类型（纯或混合）和数量从根本上影响这些系统的宏观行为。本文在n种策略的矩阵分解框架内，系统地研究了纳什均衡的一般特征。这种方法区分了四种基本交互类型，每种基本交互特性都不同。对于不同类型的相互作用及其组合，分别讨论了可能的Nash平衡。在存在无限多个混合Nash均衡与收益矩阵的零特征值特征向量之间建立关系。