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Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

This paper is devoted to a new class of differential games with continuous updating. It is assumed that at each time instant, players have or use information about the game defined on a closed time interval. However, as the time evolves, information about the game updates, namely, there is a continuous shift of time interval, which determines the information available to players. Information about the game is the information about motion equations and payoff functions of players. For this class of games, the direct application of classical approaches to the determination of optimality principles such as Nash equilibrium is not possible. The subject of the current paper is the construction of solution concept similar to Nash equilibrium for this class of differential games and corresponding optimality conditions, in particular, modernized Hamilton-Jacobi-Bellman equations.

The reported study was funded by RFBR according to the research project No. 18-00-00727 (18-00-00725).

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Authors and Affiliations

  1. St. Petersburg State University, 7/9, Universitetskaya nab., Saint-Petersburg, 199034, Russia

    Ovanes Petrosian & Anna Tur

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

    Ovanes Petrosian

Authors
  1. Ovanes Petrosian
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  2. Anna Tur
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Correspondence to Anna Tur .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Petrosian, O., Tur, A. (2019). Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_14

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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