## Journal of Applied Probability

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

### Two remarks on Blackwell's theorem

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 1 July 2008

**Permanent link to this document**

http://projecteuclid.org/euclid.jap/1214950370

**Digital Object Identifier**

doi:10.1239/jap/1214950370

**Mathematical Reviews number (MathSciNet)**

MR2426854

**Zentralblatt MATH identifier**

1141.62004

**Subjects**

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

**Keywords**

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

#### Citation

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