Predicting Genetic Drift in 2×2 Games

For the analysis of the dynamics of game playing populations, it is common practice to assume infinitely large populations. Infinite models yield predictions of fixed points and their stability properties. However, these models cannot demonstrate the influence of genetic drift, caused by stochastic sampling in small populations. Instead, we propose Markov models of finite populations for the analysis of genetic drift in games. With these exact models, we can study the stability of evolutionary stable strategies, and measure the influence of genetic drift in the long run. We show that genetic drift can introduce significant differences in the expectations of long term behavior.