Replicator Dynamics with Frequency Dependent Stage Games

We analyze evolutionary games with replicator dynamics that have frequency dependent stage games. In such an evolutionary game, the payoffs of a strategy at any point in time are functions of the strategy shares given by the players' strategy choices at that time. This framework is suited to model feedback effects between population variables and individual incentives, indirect network effects, and behavior under social norms. We show that the replicator dynamics with frequency dependent stage games is well behaved, i.e. has unique solutions and is simplex invariant for all initial strategy states. Moreover, we present an extension of Liapunov's Theorem that facilitates the analysis of evolutionary equilibria for frequency dependent evolutionary games