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Encyclopedia of Complexity and Systems Science pp 1948–1956Cite as

Differential Games

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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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Abbreviations

Dynamics:

This is the law which governs the evolution of thesystem: for differential games it is a differential equation.

Strategies:

This is the way a player chooses his control asa function of the state of the system and of the action of his opponents.

Information:

This is the set of parameters known by the player in order to build his strategy.

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Author information

Authors and Affiliations

  1. Université de Bretagne Occidentale, Brest, France

    Marc Quincampoix

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  1. Marc Quincampoix
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Quincampoix, M. (2009). Differential Games. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_123

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