Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations

TL;DR

This paper introduces a novel mixed-integer non-convex optimization algorithm to find evolutionarily stable strategies (ESS) against pure mutations, addressing a complex problem in game theory with applications in biological models.

Contribution

It presents the first general optimization formulation for computing ESS against pure mutations, expanding the toolkit for analyzing stability in game-theoretic models.

Findings

Most tested games have ESS with small support

The algorithm is outperformed by support-enumeration in current experiments

Potential future usefulness for games with larger ESS support

Abstract

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy that is initially rare. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. We present an algorithm for the case where mutations are restricted to pure strategies, and present experiments on several game classes including random and a recently-proposed cancer model. Our algorithm is based on a mixed-integer non-convex feasibility program formulation, which constitutes the first general optimization formulation for this problem. It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach. However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size.