Evolutionary Stochastic Games

We extend the notion of Evolutionarily Stable Strategies introduced by Maynard Smith and Price (1973) for models ruled by a single fitness matrix A, to the framework of stochastic games developed by Lloyd Shapley (1953) where, at discrete stages in time, players play one of finitely many matrix games, while the transitions from one matrix game to the next follow a jointly controlled Markov chain. We show that this extension from a single‐state model to a multistate model can be done on the assumption of having an irreducible transition law. In a similar way, we extend the notion of Replicator Dynamics introduced by Taylor and Jonker (1978) to the multistate model. These extensions facilitate the analysis of evolutionary interactions that are richer than the ones that can be handled by the original, single‐state, evolutionary game model. Several examples are provided.