A cognitive hierarchy model of behavior in the action commitment game

Abstract

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861–898, 2004)—where players have different levels of reasoning—to Huck et al. (Games Econ Behav 38:240–264, 2002) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29–46, 1990) action commitment game—a duopoly with endogenous timing of entry. We show that, for an 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 (2002). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model.