Humans differ in their strategic reasoning abilities and in beliefs about others’ strategic reasoning abilities. Studying such cognitive hierarchies has produced new insights regarding equilibrium analysis in economics. This paper investigates the effect of cognitive hierarchies on long run behavior. Despite short run behavior being highly sensitive to variation in strategic reasoning abilities, this variation is not replicated in the long run. In particular, when generalized risk dominant strategy profiles exist, they emerge in the long run independently of the strategic reasoning abilities of players. These abilities may be arbitrarily low or high, heterogeneous across players and evolve over time.