Pontryagin’s Maximum Principle for Non-cooperative Differential Games with Continuous Updating

Ovanes Petrosian, Anna Tur, Jiangjing Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

1 Scopus citations

Abstract

The paper is devoted to the optimality conditions as determined by Pontryagin’s maximum principle for a non-cooperative differential game with continuous updating. Here it is assumed that at each time instant players have or use information about the game structure defined for the closed time interval with a fixed duration. The major difficulty in such a setting is how to define players’ behavior as the time evolves. Current time continuously evolves with an updating interval. As a solution for a non-cooperative game model, we adopt an open-loop Nash equilibrium within a setting of continuous updating. Theoretical results are demonstrated on an advertising game model, both initial and continuous updating versions are considered. A comparison of non-cooperative strategies and trajectories for both cases are presented.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research
Subtitle of host publication19th International Conference, MOTOR 2020, Revised Selected Papers
EditorsYury Kochetov, Igor Bykadorov, Tatiana Gruzdeva
PublisherSpringer Nature
Pages256-270
Number of pages15
ISBN (Print)9783030586560
DOIs
StatePublished - 2020
Event19th International Conference on Mathematical Optimization Theory and Operations Research,MOTOR 2020 - Novosibirsk, Russian Federation
Duration: 6 Jul 202010 Jul 2020

Publication series

NameCommunications in Computer and Information Science
Volume1275 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference19th International Conference on Mathematical Optimization Theory and Operations Research,MOTOR 2020
Country/TerritoryRussian Federation
CityNovosibirsk
Period6/07/2010/07/20

Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Keywords

  • Differential games with continuous updating
  • Hamiltonian
  • Open-loop Nash equilibrium
  • Pontryagin’s maximum principle

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