Cognitive hierarchies in adaptive play

Inspired by the behavior in repeated guessing game experiments, we study adaptive play by populations containing individuals that reason with di erent levels of cognition. Indi- viduals play a higher order best response to samples from the empirical data on the history of play, where the order of best response is determined by their exogenously given level of cognition. As in Young'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 stochastically stable states obtained may now be di erent, but in a deterministic manner. Perhaps counter-intuitively, higher cognition may actually be bad for both the individual with higher cognition and his parent population.