Evolution, games theory and polyhedra.
The problem of finding an Evolutionary Stable Strategy (ESS) for an animal species is defined. It is shown how such strategies are a subset of the equilibrium solutions for a particular non-zero sum game. These equilibrium solutions are then shown to arise from the vertices of a particular convex polyhedron. A method of finding these equilibrium solutions through the vertices and then the ESS solutions is given. This is illustrated by a number of numerical examples taken from the literature. Finally an alternative approach based on solving a Linear Complementarity Problem is discussed.
Williams
H P
HP
Faculty of Mathematics, University of Southampton, UK.
D000818:Animals; D005075:Biological Evolution; D005716:Game Theory; D008433:Mathematics; D008957:Models, Genetic; D011336:Probability