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

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

Research was supported by a grant from the Russian Science Foundation (Project No 18-71-00081).

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Author information

Authors and Affiliations

  1. St. Petersburg State University, Saint-Petersburg, 199034, Russia

    Ildus Kuchkarov & Ovanes Petrosian

  2. National Research University Higher School of Economics, Saint-Petersburg, 194100, Russia

    Ovanes Petrosian

Authors
  1. Ildus Kuchkarov
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  2. Ovanes Petrosian
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Corresponding author

Correspondence to Ovanes Petrosian .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Kuchkarov, I., Petrosian, O. (2019). On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_45

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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