Asymmetric Games in Monomorphic and Polymorphic Populations

Evolutionary game theory is an increasingly important way to model the evolution of biological populations. Many early models were in the form of matrix games, or bi-matrix games in asymmetric situations when individuals occupy distinct roles within the contest, where rewards are accrued through independent contests against random members of the population. More recent models have not had the simple linear properties of matrix games, and more general analysis has been required. In this paper we carry out a general analysis of asymmetric games, comparing monomorphic and polymorphic populations. We are particularly interested in situations where the strategies that individuals play influence which role that they occupy, for example in a more realistic variant of the classical Owner-Intruder game. We both prove general results and consider specific examples to illustrate the difficulties of these more complex games.