From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again

Creators: Mu, Xiaosheng; Pomatto, Luciano; Strack, Philipp; Tamuz, Omer

Abstract

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences.

Additional Information

© 2021 The Econometric Society. Manuscript received 5 August, 2019; final version accepted 4 September, 2020; available online 11 September, 2020. We are grateful to the coeditor and three referees for their comments and suggestions. In addition, we would like to thank Kim Border, Laura Doval, Federico Echenique, Tobias Fritz, Drew Fudenberg, George Mailath, Massimo Marinacci, Margaret Meyer, Marco Ottaviani, and Peter Norman Sørensen for helpful discussions. Xiaosheng Mu acknowledges the hospitality of Columbia University and the Cowles Foundation at Yale University, which hosted him during parts of this research. Philipp Strack was supported by a Sloan research fellowship. Omer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan research fellowship, and a BSF award (#2018397).

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Published - ECTA17548.pdf

Accepted Version - 1906.02838.pdf

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