Computational Complexity of Multi-player Evolutionarily Stable Strategies

In this paper we study the computational complexity of computing an evolutionary stable strategy (ESS) in multi-player symmetric games. For two-player games, deciding existence ESS is complete for $$\mathrm {\Sigma }^\mathrm {p}_2$$ , second level polynomial time hierarchy. We show that a game closely connected to real Namely, problem hard class denote as $$\exists ^\mathrm {D}\cdot \forall \mathbb {R}$$ and member where former restrict latter by having existentially quantified variables be Boolean rather then real-valued. As special case our results it follows whether given $$\forall .