Long run equilibria in social games with coordination reward

We study the interaction between two different types of players in the presence of uncertainty in the payoffs. In particular, we examine a scenario where there is a reward for coordinating with the players of the other type and investigate how the players behave when they interact repeatedly under a simple selection model. The recurring interactions between the players are modeled as an ergodic Markov chain that has a unique stationary distribution. We then look for equilibria on which the stationary distribution of the Markov chain will concentrate as the frequency at which players change their actions decreases. Such equilibria are called long run equilibria.