Stable Biased Sampling

This paper presents a model in which sampling biases are evolutionary stable. We consider the sampling best response dynamics for a two-strategy population game having a unique equilibrium that is in mixed strategies. Allowing players to use differing sampling procedures, we model evolutionary competition between such procedures with a variant of the replicator dynamics that discriminates on the basis of average fitness among players with the same procedure. Using results on slow-fast systems, we find that the sampling bias in stable procedures is generically non-zero, that the size of the bias is the more extreme the closer the mixed equilibrium is to the boundary of (0,1), and that, if sample size increases, then the bias eventually decreases. Based on these observations, we argue that the presence of biases can be explained by an evolutionary second-best effect correcting for suboptimal choices induced by playing best response to small samples.