Supplement to “ Savage in the Market ”

THIS SUPPLEMENT CONSISTS OF EIGHT SECTIONS. In Section S.1, we illustrate the use of SARSEU through a few simple theoretical exercises. In each case, the exercise is to present a well known alternative to risk-averse SEU and to show that data generated by these theories can violate SARSEU. In Section S.2, we show that, in the 2 × 2 case, SARSEU is equivalent to requirements (5) and (6) in the main paper. In Section S.3, we provide the details of the example of risk-averse probability sophisticated preferences that violate SARSEU. In Section S.4, we present the proof of Proposition 6, on the equivalence between SEU rationality and maxmin expected utility rationality. In Section S.5, we show that SEU and SDU are observationally equivalent under certain assumptions on the data. In Section S.6, we present the relationship between SARSEU and results obtained in the revealed preference literature on objective expected utility, where the probability over states is assumed to be observable and given as a primitive. The point is that the axiom to characterize objective expected utility has a similar syntax to SARSEU and that the differences between the two are instructive. In Section S.7, we present the proof of Theorem 22 in Appendix B of the paper. The theorem is a generalization of Section S.6 and the main result in the paper (Theorem 1) in the sense that we allow that there are some states whose probabilities are objective and known to us. In Section S.8, we study the relation between SARSEU and the axiomatization in Savage (1954). It is useful to see the role of SARSDU and SARSEU in ruling our violations of Savage’s axioms.