Some recent aspects of differential game theory. (English) Zbl 1214.91013
Summary: 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.
MSC:
| 91A23 | Differential games (aspects of game theory) |
| 91A15 | Stochastic games, stochastic differential games |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
Keywords:
differential game; viscosity solution; system of Hamilton-Jacobi equations; mean-field games; state-constraints; backward stochastic differential equations; incomplete informationReferences:
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