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Dynamic Games and Applications

, Volume 1, Issue 1, pp 74–114 | Cite as

Some Recent Aspects of Differential Game Theory

  • R. Buckdahn
  • P. Cardaliaguet
  • M. Quincampoix
Article

Abstract

This survey paper presents some new advances in theoretical aspects of differential game theory. We particular focus on three topics: differential games with state constraints; backward stochastic differential equations approach to stochastic differential games; differential games with incomplete information. We also address some recent development in nonzero-sum differential games (analysis of systems of Hamilton–Jacobi equations by conservation laws methods; differential games with a large number of players, i.e., mean-field games) and long-time average of zero-sum differential games.

Keywords

Differential game Viscosity solution System of Hamilton–Jacobi equations Mean-field games State-constraints Backward stochastic differential equations Incomplete information 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques, UMR 6205Université de BrestBrestFrance
  2. 2.CeremadeUniversité Paris-DauphineParis Cedex 16France

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