Econometrica: Nov, 1995, Volume 63, Issue 6

Evolutionary Selection in Normal-Form Games

https://doi.org/0012-9682(199511)63:6<1371:ESING>2.0.CO;2-X
p. 1371-1399

Jorgen W. Weibull, Klaus Ritzberger

This paper investigates stability properties of evolutionary selection dynamics in normal-form games. The analysis is focused on deterministic dynamics in continuous time and on asymptotic stability of sets of population states, more precisely of faces of the mixed-strategy space. The main result is a characterization of those faces which are asymptotically stable in all dynamics from a certain class, and we show that every such face contains an essential component of the set of Nash equilibria, and hence a strategically stable set in the sense of Kohlberg and Mertens (1986).