Osborne, Yohance AP;
Smears, Iain;
(2025)
Regularization of Stationary Second-Order Mean Field Game Partial Differential Inclusions.
SIAM Journal on Mathematical Analysis
, 57
(5)
pp. 5189-5215.
10.1137/24M1686401.
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Abstract
Mean field Game (MFG) Partial Differential Inclusions (PDI) are generalizations of the system of Partial Differential Equations (PDE) of Lasry and Lions to situations where players in the game may have possibly nonunique optimal controls, and the resulting Hamiltonian is not required to be differentiable. We study second-order MFG PDI with convex, Lipschitz continuous, but possibly nondifferentiable, Hamiltonians, and their approximation by systems of classical MFG PDE with regularized Hamiltonians. Under very broad conditions on the problem data, we show that, up to subsequences, the solutions of the regularized problems converge to solutions of the MFG PDI. In particular, we show the convergence of the value functions in the
| Type: | Article |
|---|---|
| Title: | Regularization of Stationary Second-Order Mean Field Game Partial Differential Inclusions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/24M1686401 |
| Publisher version: | https://doi.org/10.1137/24M1686401 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | mean field games, Hamilton–Jacobi–Bellman equations, nondifferentiable Hamiltonians, partial differential inclusions, regularization, convergence analysis |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10209995 |
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