Robust personal equilibrium effects in misspecified causal models

Abstract

Following the work of Spiegler (2016), we use directed acyclical graphs (DAGs) to model a decision maker (DM) who is boundedly rational in the sense of having a misspecified causal model. Spiegler (2016) shows that certain misspecifications can lead to personal equilibrium effects: the DM calculates conditional probabilities of the relevant state variables incorrectly, and the DM’s action influences her interpretation of the data in ways that exacerbate this issue. We show that these personal equilibrium effects are robust, i.e., they do not depend on the details of the underlying distribution. We provide an exact characterization of when robust personal equilibrium effects arise, which is formulated in terms of structural conditional independence assertions of the DM’s misspecified DAG. Examples demonstrate how sensitive robust PE effects are to the structural details of the subjective DAG that, in most cases, are the DM’s private information. We consider detecting robust personal equilibrium effects under partial knowledge of the DM’s misspecified causal model.