Travelling waves and dominance of ESS's
- Cite this article as:
- Hutson, V.C.L. & Vickers, G.T. J. Math. Biol. (1992) 30: 457. doi:10.1007/BF00160531
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.