Evolution in Partnership Games, an Equivalence Result

A partnership game is a two person game in which both players necessarily receive the same payoff. For symmetric partnership games it is shown that asymptotic stability with respect to the replicator dynamics, evolutionary stability (Maynard Smith and Price [1973], Thomas [1985]) and equilibrium evolutionary stability (Swinkels [1992]) are equivalent concepts. This equivalence result is also derived for asymmetric partnership games, both in the asymmetric contest (Selten [1980]) and in the two population setting (Balkenborg and Schlag [1994]). A side result shows for general games that equilibrium evolutionary stability is weaker than evolutionary stability