Static Stability in Symmetric and Population Games

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). Examples of static notions of stability include evolutionarily stable strategy (ESS) and continuously stable strategy (CSS), both of which are meaningful or justifiable only for particular classes of symmetric and population games, such as games with multilinear payoff functions or with unidimensional strategy spaces. This paper presents a general notion of static stability in symmetric -player games and population games with non-discrete strategy spaces, of which ESS and CSS are essentially special cases. JEL Classification: C72.