A Bayesian cognitive hierarchy model with fixed reasoning levels

We propose a Bayesian cognitive hierarchy (BCH) model with fixed reasoning levels for two-person normal-form games. The model extends the previous static version of the cognitive hierarchy model to dynamic environments and combines the cognitive hierarchy model with one of the most advanced adaptive learning models. We estimate the proposed model and other models with five datasets of two-person repeated normal-form games. The results indicate that the fixed-level BCH model can reasonably capture changes in the sophistication of behavior over time. Compared with the adaptive learning model, introducing reasoning can significantly improve the interpretation of data. We further decompose the BCH model to investigate the effect of each modeling component and find that, in different games, players rely on different decision-making processes of learning and reasoning.