The Normality Assumption in Coordination Games with Flexible Information Acquisition

Many economic models assume that random variables follow normal (Gaussian) distributions. Yet, real-world variables may be non-normally distributed. How sensitive are these models' predictions to distribution misspecifications? This paper addresses the question in the context of linear-quadratic beauty contests played by rationally inattentive players. It breaks with the assumption that the (common prior) distribution of the fundamental be Gaussian and provides a characterization of the class of equilibria in continuous strategies. The characterization is used to show that small departures from normality can lead to distributions of the equilibrium average action that are qualitatively different from those of Gaussian models. Numerical results show that the rate at which an analyst's errors in determining the fundamental's distribution are amplified in her prediction is higher when the true prior is non-Gaussian than when it is an equally-misspecified Gaussian.