On some properties of Nash equilibrium points in two-person games

In modern game theory, a lot of attention is paid to the concept of Nash equilibrium. The paper is devoted to the study of some properties of the set $\mathfrak A$ of Nash equilibrium points in two-person games. In particular, the character of possible complexity of the set $\mathfrak A$ is investigated, and the stability of the set $\mathfrak A$ under small perturbations of payoff functions is analyzed.