On the Existence of Solutions for Stationary Mean-Field Games with Congestion
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ArticleAuthors
Evangelista, David
Gomes, Diogo A.

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2017-09-11Preprint Posting Date
2016-11-24Online Publication Date
2017-09-11Print Publication Date
2018-12Permanent link to this record
http://hdl.handle.net/10754/625765
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Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.Citation
Evangelista D, Gomes DA (2017) On the Existence of Solutions for Stationary Mean-Field Games with Congestion. Journal of Dynamics and Differential Equations. Available: http://dx.doi.org/10.1007/s10884-017-9615-1.Sponsors
D. Gomes and D. Evangelista were partially supported baseline and start-up funds from King Abdullah University of Science and Technology (KAUST).Publisher
Springer NaturearXiv
1611.08232Additional Links
http://link.springer.com/article/10.1007/s10884-017-9615-1ae974a485f413a2113503eed53cd6c53
10.1007/s10884-017-9615-1