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On the Selection of the Nash Equilibria in a Linear-Quadratic Differential Game of Pollution Control

  • Ekaterina GromovaEmail author
  • Yulia Lakhina
Chapter
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

The work is devoted to the problem of the selection of Nash equilibrium in non-cooperative differential games with an n-dimensional state variable. We consider the problem of the control harmful emissions. When solving the problem in the class of closed-loop strategies it turns out that Hamilton–Jacobi–Bellman equation may have multiple solutions. The application of an economic criterion and a classical method used in the theory of linear-quadratic regulators (LQR) to the selection of the admissible solutions from the set of obtained solutions was shown in the considered model.

Keywords

Differential games Linear-quadratic games Selection of Nash equilibrium Feedback strategies Multiple solutions LQR 

Notes

Acknowledgement

This work was supported by the grant 17-11-01093 of Russian Science Foundation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesEkaterinburgRussia

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