Effects of Finite Populations on Evolutionary Stable Strategies

A strong assumption made in evolutionary game theory (EGT) [7] is that the evolving population is infinitely large. Recent simulations by Fogel, et al, [3, 4, 5] show that finite populations produce behavior that, at best, deviate with statistical significance from the evolutionary stable strategy (ESS) predicted by EGT. They conclude that evolutionary game theory loses its predictive power with finite populations. In this paper, we revisit the question of how finite populations affect EGT dynamics. By paying particular attention to the operation of the selection mechanisms used by Fogel, et al, we are able to account for the divergence between ESS predictions (based on infinite populations) and results observed in our own finite-population simulations. We then show that Baker's SUS [1] selection method corrects the divergence to a great extent. We thus conclude that the dynamics of EGT, and particularly ESSs, can indeed apply to finite-population systems.