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].
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References
J. Marschak and R. Radner, Economic Theory of Teams, Yale University Press, New Haven, CT, 1972.
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).
F.R.K. Chung, private communication (1983).
H.S. Witsenhausen, “Team Guessing with Lacunary Information,” Math. Operations Res., 8, pp. 110–121 (1983).
H.S. Witsenhausen, “The Cyclic Minimum Correlation Problem,” J. Optimization Theory Appl., to appear.
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© 1987 Springer-Verlag New York Inc.
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Witsenhausen, H.S. (1987). A Stochastic Decision Problem. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_10
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DOI: https://doi.org/10.1007/978-1-4612-4808-8_10
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