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On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating

  • Ildus Kuchkarov
  • Ovanes PetrosianEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

The subject of this paper is a linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new, there it is assumed that at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. As time goes on, information about the game structure updates. Under the information about the game structure we understand information about motion equations and payoff functions of players. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. The notion of Nash equilibrium as an optimality principle is defined and the explicit form of Nash equilibrium for the linear quadratic case is presented. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.

Keywords

Differential games with continuous updating Nash equilibrium Linear quadratic differential games 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySaint-PetersburgRussia
  2. 2.National Research University Higher School of EconomicsSaint-PetersburgRussia

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