Computational Mathematics and Modeling

, Volume 27, Issue 3, pp 373–393 | Cite as

An Environment-Protection Hierarchical Differential Game Between Enterprise and State

  • E. V. Grigor’eva
  • E. N. Khailov

We consider an environment-protection hierarchical differential game between enterprise and state with the state acting as the leader. An algorithm for approximate solution of the game is proposed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yu. B. Germeier, Zero-Sum Games [in Russian], Nauka, Moscow (1971).Google Scholar
  2. 2.
    V. A. Gorlik and A. F. Kononenko, Game-Theoretical Decision Making Model in Environmental Economics Systems [in Russian], Radio i Svyaz’, Moscow (1982).Google Scholar
  3. 3.
    E. Dockner and S. Jorgensen, Differential Games in Economics and Management Science, Cambridge Univ. Press, Cambridge, MA (2006).Google Scholar
  4. 4.
    W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control [Russian translation], Mir, Moscow (1978).Google Scholar
  5. 5.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1983).Google Scholar
  6. 6.
    V. N. Afanas’ev, V. B. Kolmanovskii, and V. R. Nosov, Mathematical Theory of Control System Design [in Russian], Vysshaya Shkola, Moscow (1998).Google Scholar
  7. 7.
    N. N. Bautin and E. A. Leontovich, Methods and Techniques of Qualitative Investigation of Dynamical Systems on a Plane [in Russian], Nauka, Moscow (1990).Google Scholar
  8. 8.
    A. F. Filippov, Differential Equations with a Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).Google Scholar
  9. 9.
    A. V. Kryazhimskii and C. Watanabe, Optimization of Technological Growth, Gendaitosho, Japan (2004).Google Scholar
  10. 10.
    S. M. Aseev and A. V. Kryazhimvkii, “Pontryagin maximum principle and optimal economic growth,” Trudy Mat. Inst. im. V. A. Steklova, 257 (2007).Google Scholar
  11. 11.
    E. V. Grigorieva and E. N. Khailov, “Optimal control of a nonlinear model of economic growth,” in: Discrete and Continuous Dynamical Systems, Supplement Volume (2007), pp. 456–466.Google Scholar
  12. 12.
    S. M. Aseev, G. Hutschenreiter, and A. V. Kryazhimskii, A Dynamical Model of Optimal Allocation of Resources to R&D, Interim Report IR-02-016, IASA, Laxenburg.Google Scholar
  13. 13.
    F. P. Vasil’ev, Optimization Methods [in Russian], Faktorial Press, Moscow (2004).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • E. V. Grigor’eva
    • 1
  • E. N. Khailov
    • 2
  1. 1.Department of Mathematics and Computer SciencesTexas Women’s UniversityDentonUSA
  2. 2.Lomonosov Moscow State University, Faculty of Computation Mathematics and CyberneticsMoscowRussia

Personalised recommendations