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 of an ESS is complete for Σ2p, the second level of the polynomial time hierarchy. We show that deciding existence of an ESS of a multi-player game is closely connected to the second level of the real polynomial time hierarchy. Namely, we show that the problem is hard for a complexity class we denote as ∃ D· ∀ R and is a member of ∃ ∀ R, where the former class restrict the latter by having the existentially quantified variables be Boolean rather then real-valued. As a special case of our results it follows that deciding whether a given strategy is an ESS is complete for ∀ R.
CITATION STYLE
Blanc, M., & Hansen, K. A. (2021). Computational Complexity of Multi-player Evolutionarily Stable Strategies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12730 LNCS, pp. 1–17). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-79416-3_1
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