Dynamic Level-K and Cognitive Hierarchy Models of Repeated Normal-Form Games: A Note

This note investigates a set of dynamic versions of the level-k (LK) and cognitive hierarchy (CH) models in repeated normal-form games. Conventional LK and CH models assume a reasoning process that does not allow learning. This can be a restrictive assumption: When facing a repeated game, individuals tend to gather information from various sources. Even individuals with the lowest reasoning levels tend to improve their decisions over time. We propose dynamic level-k (DLK) and dynamic cognitive hierarchy (DCH) models to enable the interplay between within-period reasoning and between-period learning. In our models, players first update their beliefs about the choices made by their opponents across periods. Then, within each period, conditional on their reasoning levels, players stochastically best respond to the predicted play of their opponents. We select five publicly available datasets from four well-established papers to test the proposed models. Compared with other static and dynamic models, our models have better or similar performance both in terms of the in-sample fits and out-of-sample validations. Moreover, we provide a more detailed discussion linking each component of the models to the performance outcomes. The results underscore the importance of both learning and reasoning in understanding the experimental observations in repeated normal-form games.