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Two Remarks on Blackwell's Theorem

Part of: Decision theory Mathematical economics Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  14 July 2016

Ehud Lehrer  and
Eran Shmaya
Ehud Lehrer*
Affiliation:
Tel Aviv University and INSEAD
Eran Shmaya*
Affiliation:
Tel Aviv University
*
∗Postal address: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel.
∗Postal address: School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel.
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Abstract

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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.

Keywords

Blackwell's comparison of experimentswithdrawal optionBayesian decision problemminimax

MSC classification

Secondary: 46N10: Applications in optimization, convex analysis, mathematical programming, economics 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures 91B06: Decision theory 91B08: Individual preferences
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 580 - 586
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Blackwell, D. (1953). Equivalent comparisons of experiments. Ann. Math. Statist. 24, 265–272.Google Scholar
[2] Le Cam, L. (1996). Comparison of experiments—a short review. In Statistics, Probability and Game Theory (IMS Lecture Notes Monogr. Ser. 30), eds Ferguson, T. and Shapley, L., Institute of Mathematical Statistics, Hayward, CA, pp. 127–138.Google Scholar
[3] Torgersen, E. N. (1991). Comparison of Statistical Experiments. Cambridge University Press.Google Scholar
[4] Tversky, A. and Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science 211, 453–458.Google Scholar