Skip to main content
SpringerLink
Log in

Strong Time-Consistent Subset of the Core in Cooperative Differential Games with Finite Time Horizon

  • Mathematical Game Theory and Applications
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Time consistency is one of the most important properties of solutions in cooperative differential games. This paper uses the core as a cooperative solution of the game. We design a strong time-consistent subset of the core. The design method of this subset is based on a special class of imputation distribution procedures (IDPs).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Vorob’ev, N.N., Teoriya igr dlya ekonomistov-kibernetikov (The Theory of Games for Economists-Cyberneticians), Moscow: Nauka, 1985.

    MATH  Google Scholar 

  2. Gromova, E.V. and Petrosyan, L.A., On an Approach to Constructing a Characteristic Function in Cooperative Differential Games, Autom. Remote Control, 2017, vol. 78, no. 9, pp. 1680–1692.

    Article  MathSciNet  Google Scholar 

  3. Gromova, E.V. and Petrosyan, L.A., Strong Time-Consistent Cooperative Solution for a Differential Game of Pollution Control, Upravlen. Bolsh. Sist., 2015, no. 55, pp. 140–159.

    MATH  Google Scholar 

  4. Petrosyan, L.A., Stability of the Solutions of Differential Games with Several Players, Vestn. Leningrad. Univ., 1977, no. 19, pp. 46–52.

    MathSciNet  Google Scholar 

  5. Petrosyan, L.A., Strong Time-Consistent Differential Optimality Principles, Vestn. Leningrad. Univ., 1993, no. 4, pp. 35–40.

    Google Scholar 

  6. Petrosyan, L.A. and Danilov, N.N., Stable Solutions in Nonantagonistic Differential Games with Transferable Payoffs, Vestn. Leningrad. Univ., 1979, no. 1, pp. 52–79.

    MATH  Google Scholar 

  7. Petrosian, O.L., Looking Forward Approach in Cooperative Differential Games with Infinite Horizon, Vestn. St. Peterb. Gos. Univ., Ser. 10, Prikl. Mat. Inform. Prots. Upravlen., 2016, no. 4, pp. 18–30.

    MathSciNet  MATH  Google Scholar 

  8. Pecherskii, S.L. and Yanovskaya, E.E., Kooperativnye igry: resheniya i aksiomy (Cooperative Games: Solutions and Axioms), St. Petersburg: Evrop. Univ., 2004.

    Google Scholar 

  9. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatlit, 1961.

    Google Scholar 

  10. Sedakov, A.A., On the Strong Time Consistency of the Core, Autom. Remote Control, 2018, vol. 79, no. 4, pp. 757–767.

    Article  MathSciNet  Google Scholar 

  11. Smirnova, E., Stable Cooperation in One Linear-Quadratic Differential Game, in Proc. Student Conf. “Control Processes and Stability” (CPS’13), St. Petersburg, 2013, pp. 666–672.

    Google Scholar 

  12. Basar, T. and Olsder, G., Dynamic Noncooperative Game Theory, London: Academic, 1995.

    MATH  Google Scholar 

  13. Bellman, R., Dynamic Programming, Princeton: Princeton Univ. Press, 1957.

    MATH  Google Scholar 

  14. Breton, M., Zaccour, G., and Zahaf, M., A Differential Game of Joint Implementation of Environmental Projects, Automatica, 2005, vol. 41, no. 10, pp. 1737–1749.

    Article  MathSciNet  MATH  Google Scholar 

  15. Dockner, E.J., Jorgensen, S., van Long, N., and Sorger, G., Differential Games in Economics and Management Science, New York: Cambridge Univ. Press, 2001.

    MATH  Google Scholar 

  16. Gromova, E., The Shapley Value as a Sustainable Cooperative Solution in Differential Games of 3 Players, in Recent Advances in Game Theory and Applications, Static and Dynamic Game Theory: Foundations and Applications, Chapter: IV, New York: Springer, 2016. DOI: 10.1007/978-3-319-43838-2_4

    Google Scholar 

  17. Gromova, E. and Petrosyan, O., Control of Informational Horizon for Cooperative Differential Game of Pollution Control, 2016 Int. Conf. on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference), 2016. DOI: 10.1109/STAB.2016.7541187

    Google Scholar 

  18. Haurie, A., A Note on Nonzero-Sum Differential Games with Bargaining Solutions, J. Optimiz. Theory Appl., 1976, vol. 18, no. 1, pp. 31–39.

    Article  MathSciNet  MATH  Google Scholar 

  19. Haurie, A. and Zaccour, G., Differential Game Models of Global Environmental Management, in Control Game-Theor. Model Environment, 1995, vol. 2, pp. 3–23.

    Article  MathSciNet  MATH  Google Scholar 

  20. Petrosian, O.L., Looking Forward Approach in Cooperative Differential Games, Int. Game Theory Rev., 2016. DOI: 10.1142/S0219198916400077

    Chapter  Google Scholar 

  21. Petrosian, O.L. and Barabanov, A.E., Looking Forward Approach in Cooperative Differential Games with Uncertain-Stochastic Dynamics, J. Optimiz. Theory Appl., 2016. DOI: 10.1007/s10957-016-1009-8

    Google Scholar 

  22. Petrosjan, L. and Zaccour, G., Time-consistent Shapley Value Allocation of Pollution Cost Reduction, J. Econom. Dynamics Control, 2003, vol. 27, no. 3, pp. 381–398.

    Article  MathSciNet  MATH  Google Scholar 

  23. Shapley, L.S., A Value for n-Person Games, in Contributions to the Theory of Games, vol. II, Kuhn, W. and Tucker, A.W., Eds., Princeton: Princeton Univ. Press, 1953, pp. 307–317.

    Google Scholar 

  24. Shapley, L.S., Cores of Convex Games, Int. J. Game Theory, 1971, vol. 1, no. 1, pp. 11–26.

    Article  MathSciNet  MATH  Google Scholar 

  25. Yeung, D.W.K., An Irrational-Behavior-Proofness Condition in Cooperative Differential Games, Int. J. Game Theory Rev., 2007, vol. 9, no. 1, pp. 256–273.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    O. L. Petrosian, E. V. Gromova & S. V. Pogozhev

Authors
  1. O. L. Petrosian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Gromova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. V. Pogozhev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. L. Petrosian.

Additional information

Original Russian Text © O.L. Petrosian, E.V. Gromova, S.V. Pogozhev, 2016, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2016, No. 4, pp. 79–106.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petrosian, O.L., Gromova, E.V. & Pogozhev, S.V. Strong Time-Consistent Subset of the Core in Cooperative Differential Games with Finite Time Horizon. Autom Remote Control 79, 1912–1928 (2018). https://doi.org/10.1134/S0005117918100144

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117918100144

Keywords

Search

Navigation