Violations of monotonicity in evolutionary models with sample-based beliefs

•Not all evolutionary models exhibit the property of monotonicity.•Violations of monotonicity arise when agents form beliefs by sampling.•This is a consequence of the Central Limit Theorem.

This paper considers a class of evolutionary game-theoretic models, namely those in which agents form beliefs about the behavior of others on the basis of random samples from the population. It shows that the dynamics of these models violate the property of monotonicity, which many authors have argued any well-specified evolutionary model should possess.