Evolutionary Selection in Normal Form Games

Abstract: This paper investigates stability properties of evolutionary selection dynamics in normal form games. The analysis is focused on aggregate monotonic selection (AMS) dynamics in continuous time. While it is already known that virtually onlystrict equilibria are asymptotically stable in such selection dynamics, we emphasize asymptotic stability of sets of population states, more precisely of boundary faces of the mixed-strategy space. Our main result is a characterization of those boundary faces which are asymptotically stable in AMS dynamics, and we show that every such boundary face contains an essential component of Nash equilibria, and hence a strategically stable set of Nash equilibria.;