Evolution in Games with a Continuous Action Space

Allowing for games with a continuous action space, we deal with the question whether and when static concepts like evolutionary stability can shed any light on what happens in the dynamical context of a population playing these games. The continuous equivalents of theorems for the finite case are either harder to prove or simply untrue. In some cases that fall within the latter category, sensible additional assumptions can repair the damage. Apart from that it turns out that we can no longer ignore the mutation process; with a continuous action space it makes quite a difference what kind of shocks we consider to be likely.