On the Existence of Solutions for Stationary Mean-Field Games with Congestion
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Preprint Posting Date2016-11-24
Online Publication Date2017-09-11
Print Publication Date2018-12
Permanent link to this recordhttp://hdl.handle.net/10754/625765
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AbstractMean-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.
CitationEvangelista 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.
SponsorsD. Gomes and D. Evangelista were partially supported baseline and start-up funds from King Abdullah University of Science and Technology (KAUST).