State Constrained Two Player Differential Games with Decoupled Dynamics

Piernicola Bettiol () and Jérémy Rouot ()
Additional contact information
Piernicola Bettiol: CNRS, UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique
Jérémy Rouot: CNRS, UMR 6205, Laboratoire de Mathématiques de Bretagne Atlantique

Dynamic Games and Applications, 2025, vol. 15, issue 2, No 12, 610-636

Abstract: Abstract We consider a two player zero-sum differential game with state constraints, in which the dynamics is decoupled: each player has to stay in a closed (nonempty) set. We prove that, under suitable assumptions, the lower and the upper values are locally Lipschitz continuous and we establish that they are solutions, in the viscosity sense, of the Hamilton–Jacobi–Isaacs equation, which involves an appropriate Hamiltonian, called inner Hamiltonian. We finally provide a comparison theorem. It follows that the differential game under consideration admits a value (which coincides with the lower and the upper values). A key step in our analysis is a new nonanticipative Filippov-type theorem, which is valid for general closed sets.

Keywords: Differential games; State constraints; Hamilton-Jacobi-Isaacs equation; Viscosity solutions (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13235-024-00589-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00589-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-024-00589-0

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().