Bayes and Hurwicz Without Bernoulli

Posted: 29 May 2020

See all articles by Simon Grant

Simon Grant

Rice University - Department of Economics

Patricia Rich

University of Bayreuth

Jack Douglas Stecher

University of Alberta - Department of Accounting, Operations & Information Systems

Date Written: May 1, 2020

Abstract

We provide a theory of decision under ambiguity that does not require expected utility maximization under risk. Instead, we require only that a decision maker be probabilistically sophisticated in evaluating a subcollection of acts. Three components determine the decision maker's ranking of acts: a prior, a map from ambiguous acts to equivalent risky lotteries, and a generalized notion of certainty equivalent. The prior is Bayesian, defined over the inverse image of acts for which the decision maker is probabilistically sophisticated. Ambiguity preferences are similar to Hurwicz, depending on an act's best- and worst-case interpretations. The generalized certainty equivalent may, but need not, come from a Bernoulli utility. The ability to combine appealing theories of risk and ambiguity at will has been sought after but missing from the literature, and our decomposition provides a promising way forward.

Keywords: uncertainty, risk, ambiguity, certainty equivalent

JEL Classification: D80, D81

Suggested Citation

Grant, Simon and Rich, Patricia and Stecher, Jack Douglas, Bayes and Hurwicz Without Bernoulli (May 1, 2020). Journal of Economic Theory, Forthcoming, DOI:10.1016/j.jet.2020.105027, Available at SSRN: https://ssrn.com/abstract=3590553

Simon Grant

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States

Patricia Rich (Contact Author)

University of Bayreuth ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

Jack Douglas Stecher

University of Alberta - Department of Accounting, Operations & Information Systems ( email )

Edmonton, Alberta T6G 2R6
Canada

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