The selection problem for some first-order stationary mean-field games
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant Number
OSR-CRG2017-3452Date
2020-09-01Preprint Posting Date
2019-08-18Online Publication Date
2020-09-01Print Publication Date
2020Embargo End Date
2021-09-01Submitted Date
2019-08-01Permanent link to this record
http://hdl.handle.net/10754/660687
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Show full item recordAbstract
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.Citation
A. Gomes, D., Mitake, H., & Terai, K. (2020). The selection problem for some first-order stationary Mean-field games. Networks & Heterogeneous Media, 15(4), 681–710. doi:10.3934/nhm.2020019Sponsors
D. Gomes was partially supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452. H. Mitake was partially supported by the JSPS grants: KAKENHI #19K03580, #19H00639, #17KK0093, #20H01816. K. Terai was supported by King Abdullah University of Science and Technology (KAUST) through the Visiting Student Research Program (VSRP) and by the JSPS grants: KAKENHI #20J10824.Journal
Networks & Heterogeneous MediaarXiv
1908.06485Additional Links
http://aimsciences.org//article/doi/10.3934/nhm.2020019ae974a485f413a2113503eed53cd6c53
10.3934/nhm.2020019