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

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7 Scopus citations

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.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Revised Selected Papers
EditorsIgor Bykadorov, Vitaly Strusevich, Tatiana Tchemisova
PublisherSpringer Nature
Pages178-191
Number of pages14
ISBN (Print)9783030333935
DOIs
StatePublished - 1 Jan 2019
Event18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019 - Ekaterinburg, Russian Federation
Duration: 8 Jul 201912 Jul 2019

Publication series

NameCommunications in Computer and Information Science
Volume1090 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
Country/TerritoryRussian Federation
CityEkaterinburg
Period8/07/1912/07/19

Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Keywords

  • Differential games with continuous updating
  • Hamilton-Jacobi-Bellman equation
  • Nash equilibrium
  • Nash equilibrium with continuous updating

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