Co‐evolutionary dynamics and Bayesian interaction games

Recently there has been a growing interest in evolutionary models of play with endogenous interaction structure. We call such processes co‐evolutionary dynamics of networks and play. We study a co‐evolutionary process of networks and play in settings where players have diverse preferences. In the class of potential games we provide a closed‐form solution for the unique invariant distribution of this process. Based on this result we derive various asymptotic statistics generated by the co‐evolutionary process. We give a complete characterization of the random graph model, and stochastically stable states in the small noise limit. Thereby we can select among action profiles and networks which appear jointly with non‐vanishing frequency in the limit of small noise in the population. We further study stochastic stability in the limit of large player populations.