Evolution of populations playing mixed multiplayer games

We study temporal evolution of monomorphic populations of individuals which, at each time step participate in one of the prescribed k-player stage games, k = 2, 3,…,n. We introduce replicator equations for such systems, and investigate the effect of playing different stage games on the number and stability of stationary states of the populations. When the probabilities of the stage games depend on time, we introduce a system of replicator equations in a properly modified simplex of the game, and discuss stationary states for such populations.