Evolutionary games in finite populations

Abstract

The classical replicator dynamics for evolutionary games in infinite populations formulated by Taylor and Jonker is invariant when all the payoff values are shifted by a constant. We demonstrate that this is not the case in finite populations. We show that both deterministic and stochastic evolutionary game dynamics based on the original model of Taylor and Jonker depend on the actual payoff values. We present a variant of Maynard Smith 's evolutionary stability criteria for finite populations that are large ( and possibly of unknown size). We give a full description for the case of a two strategy game. Our main contribution is a statement that an evolutionarily stable strategy as originally defined by M aynard Smith still works for large populations provided that it does well against itself.