Advertisement

Automation and Remote Control

, Volume 80, Issue 7, pp 1335–1346 | Cite as

Evolutionary Methods for Solving Dynamic Resource Allocation Problems

  • G. I. BeliavskyEmail author
  • N. V. DanilovaEmail author
  • G. A. OugolnitskyEmail author
Mathematical Game Theory and Applications

Abstract

This paper proposes a dynamic game-theoretic statement of the resource allocation problem in an organizational system. The application of evolutionary modeling algorithms for solving such problems is considered. Some illustrative examples are given.

Keywords

dynamic resource allocation problem differential games evolutionary modeling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

This work was supported by the Russian Science Foundation, project no. 17-19-01038.

References

  1. 1.
    Beliavsky, G.I., Lila, V.B., and Puchkov, E.V., The Algorithm and Software Implementation of Hybrid Learning for Artificial Neural Networks, Progr. Produkty Sist., 2012, no. 4, pp. 96–101.Google Scholar
  2. 2.
    Beliavsky, G.I., Danilova, N.V., and Ougolnitsky G.A., Evolutionary Modeling in the Problems of Sustainable Management of Active Systems, Mat. Teor. Igr Prilozh., 2016, vol. 8, no. 4, pp. 14–29.MathSciNetGoogle Scholar
  3. 3.
    Germeier, Yu.B. and Vatel’, I. A., Games with a Hierarchical Vector of Interests, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1974, no. 3, pp. 54–69.Google Scholar
  4. 4.
    Gladkov, L.A., Kureichik, V.V., and Kureichik, V.M., Geneticheskie algoritmy (Genetic Algorithms), Moscow: Fizmatlit, 2006.zbMATHGoogle Scholar
  5. 5.
    Gorbaneva, O.I., Game-Theoretic Resource Allocation Models in Hierarchical Quality Control Systems for River Water, Mat. Teor. Igr Prilozh., 2010, vol. 2, no. 1, pp. 27–46.zbMATHGoogle Scholar
  6. 6.
    Gorbaneva, O.I. and Ougolnitsky, G.A., Static Models of Coordination of Social and Private Interests in Resource Allocation, Autom. Remote Control, 2018, vol. 79, no. 7, pp. 1319–1341.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Emel’yanov, V.V., Kureichik, V.V., and Kureichik, V.M., Teoriya i praktika evolyutsionnogo modeliro-vaniya (Theory and Practice of Evolutionary Modeling), Moscow: Fizmatlit, 2003.Google Scholar
  8. 8.
    Kukushkin, N.S., On the Existence of Stable Outcomes in a Game-Theoretic Model of an Economy with Public Goods, Dokl. Akad. Nauk SSSR, 1991, vol. 320, no. 1, pp. 25–28.MathSciNetGoogle Scholar
  9. 9.
    Novikov, D., Theory of Control in Organizations, New York: Nova Science, 2013.Google Scholar
  10. 10.
    Pecherskii, S.L. and Yanovskaya, E.E., Kooperativnye igry: resheniya i aksiomy (Cooperative Games: Solutions and Axioms), St. Petersburg: Evrop. Univ., 2004.Google Scholar
  11. 11.
    Ugol’nitskii, G.A. and Usov, A.B, A Study ol Differential Models for Hierarchical Control Systems via Their Discretization, Autom. Remote Control, 2013, vol. 74, no. 2, pp. 252–263.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Bergstrom, T., Blume, O, and Varian, H., On the Private Provision ol Public Goods, J. Public Econom., 1986, no. 29, pp. 25–49.Google Scholar
  13. 13.
    Boadway, R., Pestiau, P., and Wildasin, D., Non-cooperative Behavior and Efficient Provision ol Public Goods, Public Finance, 1989, no. 44, pp. 1–7.Google Scholar
  14. 14.
    Boadway, R., Pestiau, P., and Wildasin, D., Tax-Transfer Policies and the Voluntary Provision ol Public Goods, J. Public Econom., 1989, no. 39, pp. 157–176.Google Scholar
  15. 15.
    Christodoulou, G., Sgouritza, A., and Tang, B., On the Efficiency olthe Proportional Allocation Mechanism for Divisible Resources, in Proc. 8th Int. Symp. on Algorithmic Game Theory (SAGT dy2015), Hoefer, M., Ed., New York: Springer, 2015, pp. 165–177.CrossRefGoogle Scholar
  16. 16.
    Cornes, R. and Hartley, R., Asymmetric Contests with General Technologies, Econom. Theory, 2005, vol. 26, no. 4, pp. 923–946.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Cornes, R. and Sato, T., Existence and Uniqueness ol Nash Equilibrium in Aggregative Games: An Expository Treatment, in Equilibrium Theory for Cournot Oligopolies and Related Games, von Mouche, P. and Quartieri, F., Eds., New York: Springer, 2016, pp. 47–61.CrossRefGoogle Scholar
  18. 18.
    Kahana, N. and Klunover, D., Private Provision ol a Public Good with a Time-Allocation Choice, Social Choice Welfare, 2016, no. 7, pp. 379–386.Google Scholar
  19. 19.
    Kukushkin, N.S., A Condition for Existence ol Nash Equilibrium in Games with Public and Private Objectives, Games Econom. Behav., 1994, no. 7, pp. 177–192.Google Scholar
  20. 20.
    van Long, N., A Survey of Dynamic Games in Economics, Singapore: World Scientific, 2010.CrossRefzbMATHGoogle Scholar
  21. 21.
    Petrosyan, L.A. and Zenkevich, N.A., Game Theory, Singapore: World Scientific, 2016.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Vorovich Institute of Mathematics, Mechanics and Computer SciencesSouthern Federal UniversityRostov-on-DonRussia

Personalised recommendations