Abstract
We consider a simple two strategy game in which each pure strategy is an evolutionarily stable strategy (ESS). Under the usual dynamical equations, the large-time behaviour of the system will depend upon the initial conditions and the pay-off matrix. If spatial effects are included to give a reaction-diffusion system, we prove that travelling wavefronts can occur which in effect replace one ESS by another. The ‘strength’ or ‘dominance’ of each ESS which decides the ‘winner’ in a precisely defined sense is determined by its pay-off and by its diffusion rate. Good strategies have large pay-offs and small diffusion rates.
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Hutson, V.C.L., Vickers, G.T. Travelling waves and dominance of ESS's. J. Math. Biol. 30, 457–471 (1992). https://doi.org/10.1007/BF00160531
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DOI: https://doi.org/10.1007/BF00160531