Evolutionary dynamics on measurable strategy spaces: Asymmetric games

The theory of evolutionary dynamics in asymmetric games has been mainly studied for games with a finite strategy space. In this paper we introduce an evolutionary dynamics model for asymmetric games where the strategy sets are measurable spaces (separable metric spaces). Under this hypothesis the replicator dynamics is in a Banach Space. We specify conditions under which the replicator dynamics has a solution. Furthermore, under suitable assumptions, a critical point of the system is stable. Finally, an example illustrates our results.