The Wald Problem and the Relation of Sequential Sampling and Ex-Ante Information Costs

27 Pages Posted: 23 Jun 2017 Last revised: 21 Feb 2019

Date Written: February 18, 2019

Abstract

We consider the two state sequential sampling problem of Wald (1945). We show that any distribution of posteriors can be attained and that the ex-ante cost of attaining any probability distribution over posteriors equals the expected change of the log likelihood ratio. With many states, not all distributions can be attained but we provide a characterization of those that can be attained and show that the characterization of ex-ante cost generalizes naturally to those that can be attained.

Keywords: Sequential Sampling, Entropy Cost, Information Acquisition

JEL Classification: D83, C1

Suggested Citation

Morris, Stephen Edward and Strack, Philipp, The Wald Problem and the Relation of Sequential Sampling and Ex-Ante Information Costs (February 18, 2019). Available at SSRN: https://ssrn.com/abstract=2991567 or http://dx.doi.org/10.2139/ssrn.2991567

Stephen Edward Morris (Contact Author)

MIT ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

HOME PAGE: http://https://economics.mit.edu/faculty/semorris

Philipp Strack

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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