Revealed Bayesian expected utility with limited data

This paper characterizes expected utility preferences with information acquisition and Bayesian updating using stochastic choice data on acts. This contrasts with research that uses state-dependent stochastic choices which is difficult to obtain outside of the laboratory. The characterization is in the spirit of the Wald-Pearce lemma and requires that there is no random deviation rule that improves ex-ante expected utility for all possible information structures consistent with the data. The result is extended to place bounds on an unknown prior and facilitate welfare comparisons in the presence of framing. These bounds are computable via linear programming. Moreover, we show that in special cases, the bounds can be found explicitly by solving a series of Bayesian persuasion games.