Journal of Applied Probability

Two remarks on Blackwell's theorem

Ehud Lehrer and Eran Shmaya

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In a decision problem with uncertainty a decision maker receives partial information about the actual state via an information structure. After receiving a signal, he is allowed to withdraw and gets zero profit. We say that one structure is better than another when a withdrawal option exists if it may never happen that one structure guarantees a positive profit while the other structure guarantees only zero profit. This order between information structures is characterized in terms that are different from those used by Blackwell's comparison of experiments. We also treat the case of a malevolent nature that chooses a state in an adverse manner. It turns out that Blackwell's classical characterization also holds in this case.

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J. Appl. Probab. Volume 45, Number 2 (2008), 580-586.

First available in Project Euclid: 1 July 2008

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Primary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures 91B06: Decision theory [See also 62Cxx, 90B50, 91A35] 91B08: Individual preferences

Blackwell's comparison of experiments withdrawal option Bayesian decision problem minimax


Lehrer, Ehud; Shmaya, Eran. Two remarks on Blackwell's theorem. J. Appl. Probab. 45 (2008), no. 2, 580--586. doi:10.1239/jap/1214950370.

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