Stochastic replicator dynamics: A theoretical analysis and an experimental assessment

Abstract

We study the dynamics of strategic choice in an environment where payoffs are perturbed by strategy-specific noise and strategy revision is governed by the simple proportional imitation protocol. Applying the stochastic replicator dynamic to a two-by-two symmetric game, we derive the steady-state frequencies of the strategies and show that the dominated strategy can persist in equilibrium if the variance of the payoff shocks exceeds a critical value. Additionally, the rate of decay of the dominated strategy decreases with increasing variance. The behaviours of our experimental subjects accord with these tendencies. Our findings add to the growing experimental literature that demonstrates that evolutionary models of human behaviour with simple adaptive rules have predictive ability, even in complex, volatile environments.