Automation and Remote Control

, Volume 78, Issue 8, pp 1537–1544 | Cite as

Linear-quadratic discrete-time dynamic potential games

  • V. V. Mazalov
  • A. N. Rettieva
  • K. E. Avrachenkov
Mathematical Game Theory and Applications


Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rettieva, A.N., Discrete-Time Bioresource Management Problem with Asymmetric Players, Autom. Remote Control, 2014, vol. 75, no. 9, pp. 1665–1676.CrossRefGoogle Scholar
  2. 2.
    Basar, T. and Olsder, G.J., Dynamic Noncooperative Game Theory, New York: Academic, 1982.MATHGoogle Scholar
  3. 3.
    Dechert, W.D., Optimal Control Problems from Second Order Difference Equations, J. Econom. Theory, 1978, vol. 19, pp. 50–63.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dechert, W.D., Noncooperative Dynamic Games: A Control Theoretic Approach, Houston: Univ. of Houston, 1997.Google Scholar
  5. 5.
    Dragone, D., Lambertini, L., Leitmann, G., and Palestini, A., Hamilton Potential Functions for Differential Games, IFAC Proc. Volumes, 2009, vol. 42, no. 2, pp. 1–8.CrossRefMATHGoogle Scholar
  6. 6.
    Gonzalez-Sanchez, D. and Hernandez-Lerma, O., Dynamic Potential Games: The Discrete-Time Stochastic Case, Dynamic Games Appl., 2014, vol. 4, no. 3, pp. 309–328.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Gonzalez-Sanchez, D. and Hernandez-Lerma, O., Discrete-time Stochastic Control and Dynamic Potential Games: The Euler-Equation Approach, New York: Springer Science & Business Media, 2013.CrossRefMATHGoogle Scholar
  8. 8.
    Monderer, D. and Shapley, L.S., Potential Games, Games Econom. Behav., 1996, vol. 14, pp. 124–143.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Zazo, S., Macua, S.V., Sanchez-Fernandes, M., and Zazo, J., Dynamic Potential Games with Constraints: Fundamentals and Applications in Communications, IEEE Trans. Signal Proces., 2015, vol. 64, no. 14, pp. 3806–3821.MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • V. V. Mazalov
    • 1
  • A. N. Rettieva
    • 1
  • K. E. Avrachenkov
    • 2
  1. 1.Institute of Applied Mathematical ResearchKarelian Research Center of the Russian Academy of SciencesPetrozavodskRussia
  2. 2.INRIA Sophia-Antipolis MediterraneeSophia-AntipolisFrance

Personalised recommendations