Evolution in games with a continuous action space

Allowing for games with a continuous action space, we investigate how evolutionary stability, the existence of a uniform invasion barrier, local superiority and asymptotic stability relate to each other. This is done without restricting the populations of which we want to investigate the stability to monomorphic population states or to strategies with finite support. The authors have benefitted from careful and precise comments by Gerard van der Laan, Jan van Mill, the editor and an anonymous referee. Matthijs van Veelen gratefully acknowledges financial support by the Netherlands’ Organization for Scientific Research (NWO).