On the Elimination of Dominated Strategies in Stochastic Models of Evolution with Large Populations

This paper analyzes a stochastic best reply evolutionary model with inertia in normal form games. The long-run behavior of individuals in this model is investigated in the limit where experimentation rates tend to zero, while the expected number of experimenters, and hence also population sizes, tend to infinity. Conditions on the learning-rate which are necessary and sufficient for the evolutionary elimination of weakly dominated strategies are found. The key determinant is found to be the sensitivity of the learning-rate to small payoff differences.