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 level-0 players adjust their actions in response to historical game play, whereas higher-level thinkers update their beliefs on opponents’ rule levels and best respond with different rule levels over time. As a consequence, players choose a dynamic rule level (i.e., sophisticated learning) from a varying rule hierarchy (i.e., adaptive learning). We apply our model to existing experimental data on three distinct games: the p-beauty contest, Cournot oligopoly, and private-value auction. We find that both types of learning are significant in p-beauty contest games, but only adaptive learning is significant in the Cournot oligopoly, and only sophisticated learning is significant in the private-value auction. We conclude that it is useful to have a unified framework that incorporates both types of learning to explain dynamic choice behavior across different settings. This paper was accepted by Manel Baucells, decision analysis.
Early initiation of highly active antiretroviral therapies for AIDS: Dynamic choice with endogenous and exogenous learning
