The evolution game: A simple algorithm for the determination of an evolutionary stable strategy

Abstract

As a result of the complex nature of genetic models used to describe intricate survival strategies of living organisms during the process of evolution, principles of game theory are often used as an alternative. In such cases it is important to be able to determine which strategy – out of a set of possible strategies – would be optimal, in the sense that populations of which all members are using this strategy, can not be invaded by individuals following any other possible strategy from the feasible set. Such a strategy is known as an Evolutionary Stable Strategy (ESS), and much research has been done on the properties of an ESS, as far as it could be associated with mathematical population growth models. In this article we discuss a simple algorithm by which an ESS can be calculated in the case of non linear discrete models with a single strategy variable. We also give the theoretical basis of the algorithm, and show that it can be used even in the case of fairly complicated population situations.