Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Abstract

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.