Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Differential Games

  • Marc Quincampoix
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_123

Definition of the Subject

Differential games is a mathematical theory which is concernedwith problems of conflicts modelized as game problems in which thestate of the players depends on time in a continuous way. Thepositions of the players are the solution to differentialequations. Differential games can be described from two differentpoints of view, depending mainly on the field of application.Firstly, they can be considered as games where time is continuous.This aspect is often considered for applications in economics ormanagement sciences. Secondly, they also can be viewed as controlproblems with several controllers having different objectives. Inthis way, differential games are a part of control theory withconflicts between the players. The second aspect often concernsclassical applications of control theories: engineering sciences.

The importance of the subject was emphasized by J. von Neuman in1946 in his pioneer book “Theory of Games and EconomicBehaviour” [35]: We repeat most...

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Marc Quincampoix
    • 1
  1. 1.Université de Bretagne OccidentaleBrestFrance