Online Appendix

This online appendix accompanies the paper “Experiments on Decisions Under Uncertainty: A Theoretical Framework.” It provides an analysis of the consequences of restricting subjects’conjectures and a detailed model of data derived from aggregating observations. It also considers a variant of the model studied in the paper in which dimensions of signals are unordered. Last, it presents the formal proofs for the results in Section 4 of the paper. 1. Plausibility of Conjectures We start with the notion of conditionally independent and identically distributed (i.i.d.) signals. In a wide array of economic models, ranging from strategic voting to private value auctions, private signals are often assumed to be conditionally independent. Furthermore, in the statistics literature, the term Bayesian is frequently used to indicate conditional independence, the idea being that the sequence of signals s1, s2, . . . are samples from some distribution that depends on the state, or parameter, k. The statistician has some prior belief over the true parameter that governs the distribution of the sample, and she updates her belief given the observations (much like questions leading to maximum likelihood methods in econometrics, see, e.g., Greene, 1993). In analogy to our original definitions, we say that an updating rule σ : S∗ → ∆(K) is conditionally i.i.d. Bayesian if there exists a probability measure μ over K × S∞ such that, for every n, signals s1, s2, ... are conditionally i.i.d. given the state of nature k and for every Borel subset B of K, σ[s1, . . . , sn](B) = μ(B|s1, . . . , sn). ∗Managerial Economics and Decision Sciences (MEDS), Kellogg School of Management, Northwestern University, Evanston, IL 60208, USA. e-mail: [email protected] †Division of the Humanities and Social Sciences, Caltech, Pasadena, CA 91125, USA. e-mail: [email protected]