A Bayesian Level-k Model in n-Person Games

In standard models of iterative thinking, players choose a fixed rule level from a fixed rule hierarchy. Nonequilibrium behavior emerges when players do not perform enough thinking steps. Existing approaches, however, are inherently static. This paper introduces a Bayesian level-k model, in which players perform Bayesian updating of their beliefs on opponents’ rule levels and best-respond with different rule levels over time. In this way, players exhibit sophisticated learning. We apply our model to experimental data on p-beauty contest and price matching games. We find that it is crucial to incorporate sophisticated learning to explain dynamic choice behavior.