Cognitive hierarchies in adaptive play

Inspired by the behavior in repeated guessing game experiments, we study adaptive play bypopulations containing individuals that reason with different levels of cognition. Individualsplay a higher order best response to samples from the empirical data on the history of play, wherethe order of best response is determined by their exogenously given level of cognition. As inYoung''s model of adaptive play, (unperturbed) play still converges to a minimal curb set. However,with the random perturbations of this (higher order) best response dynamic, the stochasticallystable states obtained may now be different, but in a deterministic manner. Perhapscounter-intuitively, higher cognition may actually be bad for both the individual with highercognition and his parent population.