A cognitive hierarchy model of behavior in the action commitment game

We apply the cognitive hierarchy model of Camerer, Ho and Chong (2004)—where players have different levels of reasoning—to Huck, Müller and Normann’s (2002) discrete version of Hamilton and Slutsky’s (1990) action commitment game—a duopoly with endogenous timing of entry. We show that, for empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in Huck, Müller and Normann (2002). In order to gauge the success of cognitive hierarchy model in fitting the data, we compare it to a noisy Nash model in the spirit of McKelvey and Palfrey (1998). We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model. JEL Classification Numbers: C72, D43, L13.