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A Stochastic Decision Problem

  • H. S. Witsenhausen

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    J. Marschak and R. Radner, Economic Theory of Teams, Yale University Press, New Haven, CT, 1972.MATHGoogle Scholar
  2. [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. [3]
    F.R.K. Chung, private communication (1983).Google Scholar
  4. [4]
    H.S. Witsenhausen, “Team Guessing with Lacunary Information,” Math. Operations Res., 8, pp. 110–121 (1983).MathSciNetMATHCrossRefGoogle Scholar
  5. [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

Authors and Affiliations

  • H. S. Witsenhausen
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA

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