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Some Recent Aspects of Differential Game Theory

Buckdahn, Rainer; Cardaliaguet, Pierre; Quincampoix, Marc (2011), Some Recent Aspects of Differential Game Theory, Dynamic Games and Applications, 1, 1, p. 74-114. http://dx.doi.org/10.1007/s13235-010-0005-0

Type
Article accepté pour publication ou publié
Date
2011
Journal name
Dynamic Games and Applications
Volume
1
Number
1
Publisher
Springer
Pages
74-114
Publication identifier
Metadata
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Author(s)
Buckdahn, Rainer
Cardaliaguet, Pierre
Quincampoix, Marc
Abstract (EN)
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.
Subjects / Keywords
Differential game; Viscosity solution; System of Hamilton–Jacobi equations; Mean-field games; State-constraints; Backward stochastic differential equations; Incomplete information
JEL
D83 - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
C7 - Game Theory and Bargaining Theory