Evolutionary optimal strategies in stochastic dynamic games

We will consider a class of games that arise in mathematical economics. I will introduce the notion of an evolutionary optimal strategy, which is a strategy such that the proportion of players using it remains separated from zero with probability 1 over an infinite time horizon, regardless of strategies used by other players. The main results consist in proving the existence of such strategies in the class of games under consideration and obtaining an estimate of closeness of strategies with this property to each other in a certain sense.