Name
Abstract | ||
|---|---|---|
Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount limit to a unique solution up to constants. Then, we establish refined asymptotics for the limit. When those conditions do not hold, the limit problem may not have a unique solution and its solutions may not be smooth, as we illustrate in an elementary example. Finally, we investigate the stability of regular weak solutions and address the selection problem. Using ideas from Aubry-Mather theory, we establish a selection criterion for the limit. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.3934/nhm.2020019 | NETWORKS AND HETEROGENEOUS MEDIA |
Keywords | DocType | Volume |
Mean field games,Hamilton-Jacobi equation,selection problem,vanishing discount,asymptotic analysis | Journal | 15 |
Issue | ISSN | Citations |
4 | 1556-1801 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Diogo A. Gomes | 1 | 68 | 11.86 |
| Hiroyoshi Mitake | 2 | 2 | 1.57 |
| Terai Kengo | 3 | 0 | 0.34 |