We introduce a notion of substitutability for correspondences and establish a monotone comparative static result. More precisely, we introduce the notions of unified gross substitutes and nonreversingness and show that if Q : P ⇒ Q is a supply correspondence defined on a set of prices P which...

Economic agents often infer latent structures - such as preference types - from data, without exogenously specified priors. We model such agents as empirical Bayesians. They estimate both the prior over types and the meanings of types via maximum likelihood. We show this estimation is equivalent...

We study maximum-likelihood estimation and updating, subject to computational, cognitive, or behavioral constraints. We jointly characterize constrained estimates and updating within a framework reminiscent of a machine learning algorithm. Without frictions, the framework simplifies to standard...

Decision theory can be used to test the logic of decision making - one may ask whether a given set of decisions can be justified by a decision-theoretic model. Indeed, in principal-agent settings, such justifications may be required - a manager of an investment fund may be asked what beliefs she...