Static Stability in Symmetric and Population Games

Igal Milchtaich

Abstract

Static stability in strategic games differs from dynamic stability in only considering the players’ incentives to change their strategies. It does not rely on any assumptions about the players’ reactions to these incentives and it is thus independent of the law of motion (e.g., whether players move simultaneously or sequentially). This paper presents a general notion of static stability in symmetric N-player games and population games, of which evolutionarily stable strategy (ESS) and continuously stable strategy (CSS) are essentially special cases. Unlike them, the proposed stability concept does not depend on the existence of special structures in the game such as multilinear payoff functions or unidimensional strategy spaces.

JEL classification

C72

Keywords

Static stability; Evolutionarily stable strategy; Continuously stable strategy; Risk dominance; Potential games