Cognitive hierarchy and multi-stage I.O. games

The concept of cognitive hierarchy (Camerer et.al (2004)) is extended to multistage games. In a multi-stage game we will assume that the rationality level of a player indicates the number of stages of the game where he puts cognitive effort to calculate optimal actions. A player of rationality level k plays optimaly in the last k stages of the game and randomizes uniformly in the first m − k, where m is the number of stages of the game. We apply this concept to a Hotelling twostage model and we show that firms with rationality above or equal to 2 choose to locate in the center of a set of locations; so minimum differentiation across different rationality levels is achieved.