A Stochastic Decision Problem

  • H. S. Witsenhausen


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].




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