Composite and combined games in evolutionary dynamics in finite populations

Evolutionary game theory connects dynamics to strategy by assuming few behavioral strategies, modeling costs and benefits from interactions via a payoff matrices, then casting these into replicator equations (in infinite populations) resp. stochastic processes (in finite populations) which comprise a “physics of behaviour” model of the collective decision dynamics (which may include cyclic oscillations). We build on previous results (PRL 95, 238701 and PRL 100, 058104 and subsequent) and discuss combinations of 2- and 3 strategy games in the context of different replicator dynamics, and stochastic processes derived from agent interaction models. We demonstrate how the previous concepts of drift reversal - how an attracting fixed point resulting from a Hopf bifurcation loses stabilty below a critical population size, applies to the combined games.