# SFB 303 Discussion Paper No. B - 314

**Author**: Balkenborg, Dieter, and Karl H. Schlag

**Title**: Evolutionary Stability in Asymmetric Population Games

**Abstract**: We extend the notions of evolutionary stability and, for the first
time, that of neutral stability to asymmetric games played between two
populations. Stability with respect to simultaneous entry of a small
proportion of mutants into both populations is considered. Allocations where
neither mutant can ever spread are called neutrally stable. For bimatrix
games, neutral stability in the asymmetric population game is found to be a
weaker concept than neutral stability in the asymmetric contest. Moreover
existence is guaranteed for 2 x 2 bimatrix games. Sets of neutrally stable
strategy pairs such that for any pair of mutants not in the set at least one
mutant is driven out are called evolutionary stable. Evolutionarily stable
sets are shown to be equivalent to strict equilibrium sets.
Additionally, uniformity considerations are investigated.

**Keywords**: evolutionarily stable set, evolutionarily stable strategy, neutral
stability, strict equilibrium, mixed strategy model, asymmetric contest

**JEL-Classification-Number**: C79

**Creation-Date**: May 1995

**URL**: ../1995/b/bonnsfb314.ps
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