On Evolutionarily Stable Strategy

Abstract

Theory of evolutionarily stable strategy (ESS) emerged as an application of the game theoretic concept to the Darwinian theory of evolution. In this paper, we provide a brief review of ESS theory. The purpose is to fill gaps that are left open in the literature. We provide necessary and sufficient conditions along with an algorithm that can be used to find all ESS. We also describe results related to the bounds on the maximum number of ESS. Link of ESS theory to a dynamical system is also briefly described. The concept is also extended to the multi-player case and its dynamic formulation is also described. We provide result describing the equilibrium points for the game dynamics, which were not discussed before.