Evolution in Games with a Continuous Action Space

This discussion paper resulted in a publication in <A href="http://link.springer.com/article/10.1007%2Fs00199-008-0338-8">'Economic Theory'</A>, 2009, 39(3), 355-376. Allowing for games with a continuous action space, we deal with the question whether and when static conceptslike evolutionary stability can shed any light on what happens in the dynamical context of a population playingthese games. The continuous equivalents of theorems for the finite case are either harder to prove or simplyuntrue. 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 itmakes quite a difference what kind of shocks we consider to be likely.