Stable biased sampling

This paper analyzes an indirect evolutionary model of sampling biases in probability estimates, which combines the sampling best response dynamics with the replicator dynamics. The arrival rate of revision opportunities in the best response dynamics is high, so that the resulting joint dynamical system is a slow-fast system and we can use Tikhonov's theorem to study its solutions, employing practical asymptotic stability as a stability criterion. For two-strategy population games with a unique Nash equilibrium that is in mixed strategies, we find that the stable sampling bias is generically non-zero and that it is highest when the equilibrium is most asymmetric, yet that the stable sampling bias vanishes in the sample size.