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Evolutionarily stable strategy (ESS) is an important solution concept in gametheory which has been applied frequently to biological models. Informally anESS is a strategy that if followed by the population cannot be taken over by amutation strategy that is initially rare. Finding such a strategy has beenshown to be difficult from a theoretical complexity perspective. We present analgorithm for the case where mutations are restricted to pure strategies, andpresent experiments on several game classes including random and arecently-proposed cancer model. Our algorithm is based on a mixed-integernon-convex feasibility program formulation, which constitutes the first generaloptimization formulation for this problem. It turns out that the vast majorityof the games included in the experiments contain ESS with small support, andour algorithm is outperformed by a support-enumeration based approach. Howeverwe suspect our algorithm may be useful in the future as games are studied thathave ESS with potentially larger and unknown support size.

Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations