Allocation of an indivisible resource: Optimal control and prices

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Abstract

Under study is a dynamical system of economics with discrete time whose states at each moment correspond to nonnegative integer points of a two-dimensional vector space. There are two types of products and two facilities each of which can change the state of the system by random integer vectors with different collections of probabilities. By a control we understand the choice at each moment of time of one available collection of probabilities. The goal of control is to minimize the probability of leaving the positive quadrant. The question is considered of the existence of some prices that agree with an optimal control.

Key words

optimal control prices Markov chain 

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References

  1. 1.
    R. Radner and M. Rothschild, “On the Allocation of Effort,” J. Economic Theory 10(3), 358–376 (1975).MATHCrossRefGoogle Scholar
  2. 2.
    R. Radner, “A Behavioral Model of Cost Reduction,” Bell J. Economics 6(1), 196–215 (1975).CrossRefMathSciNetGoogle Scholar
  3. 3.
    E. O. Rapoport, “About a Stochastic Model of Allocation of an Indivisible Resource,” in Proceedings of the Siberian Conference on Applied and Industrial Mathematics (Inst. Mat., Novosibirsk, 1997), pp. 197–206.Google Scholar
  4. 4.
    E.O. Rapoport, “Main Strategies for Allocation of an Indivisible Resource,” Diskret. Anal. Issled. Oper. Ser. 1, 4(1), 33–45 (1997).MathSciNetGoogle Scholar
  5. 5.
    E. O. Rapoport, “A Model for Allocation of an Indivisible Resource,” Diskret. Anal. Issled. Oper. Ser. 2, 12(1), 55–73 (2005).MathSciNetGoogle Scholar
  6. 6.
    J. G. Kemeny, A. W. Knapp, and L. J. Snell, Denumerable Markov Chains (Springer, New York, 1976; Nauka, Moscow, 1987).MATHGoogle Scholar
  7. 7.
    W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2 (John Wiley and Sons, New York, 1966; Mir, Moscow, 1984).Google Scholar
  8. 8.
    A. N. Shiryaev, Probability (Nauka, Moscow, 1980) [in Russian].MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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