What were you thinking? Decision theory as coherence test

Abstract

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 used when valuing assets and a government may be asked whether a portfolio of rules and regulations is coherent. In this paper we ask which collections of uncertain‐act evaluations can be simultaneously justified under the maxmin expected utility criterion by a single set of probabilities. We draw connections to the fundamental theorem of finance (for the special case of a Bayesian agent) and revealed‐preference results.