General features of Nash equilibria in combinations of elementary interactions in symmetric two-person games

Abstract 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 macroscopic behavior these systems. In this paper, general features investigated systematically within framework matrix decomposition for n strategies. This approach distinguishes four types elementary interactions that each possess different characteristics. possible discussed separately also their combinations. A relation is established between existence infinitely mixed zero-eigenvalue eigenvectors payoff matrix.