Deep and Shallow Thinking in the Long Run

Humans differ in their strategic reasoning abilities and in beliefs about others' strategic reasoning abilities. Models of cognitive hierarchies that express these differences have produced new insights regarding equilibrium analysis in economics. This paper investigates the effect of cognitive hierarchies on long run behavior. It is shown that, 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 a generalized risk dominant strategy profile exists, it emerges in the long run independently of the strategic reasoning abilities of the players. These abilties may be arbitrarily low or high, may be heterogeneous across players and may evolve over time