# A Stochastic Decision Problem

Chapter

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## Abstract

In a team decision problem there are *n* agents. Agent *i* observes random variable *Y* _{i} and, as a function of this observation, takes decision *u* _{i} from a given set *U* _{i} of possible decisions. Denoting the decision function by *γ* _{i}, the problem is to choose (*γ* _{1},...*γ* _{n}) so as to optimize the expectation of a criterion *C*(*u* _{1}, ..., *u* _{n}, *Z*), where Z is a random variable and the joint distribution of Z and the *Y* _{i} is given [1]. Note that by conditioning one can assume that Z is the *n*-tuple of all observations *Y* _{i}. Outside a few special cases, team problems are of high complexity [2].

## Keywords

Decision Problem Optimization Theory Joint Distribution High Complexity Independent Random Variable
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## References

- [1]J. Marschak and R. Radner,
*Economic Theory of Teams*, Yale University Press, New Haven, CT, 1972.zbMATHGoogle Scholar - [2]J.N. Tsitsiklis and M. Athans, “On the Complexity of Decentralized Decision Making and Detection Problems,”
*IEEE Trans. Automatic Control*, AC-30, pp. 440–446 (1985).MathSciNetCrossRefGoogle Scholar - [3]F.R.K. Chung, private communication (1983).Google Scholar
- [4]H.S. Witsenhausen, “Team Guessing with Lacunary Information,”
*Math. Operations Res*., 8, pp. 110–121 (1983).MathSciNetzbMATHCrossRefGoogle Scholar - [5]H.S. Witsenhausen, “The Cyclic Minimum Correlation Problem,”
*J. Optimization Theory Appl*., to appear.Google Scholar

## Copyright information

© Springer-Verlag New York Inc. 1987