Existence for stationary mean-field games with congestion and quadratic Hamiltonians

  • Diogo A. Gomes
  • Hiroyoshi MitakeEmail author


Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.


Mean-field games Quadratic Hamiltonians Congestion 

Mathematics Subject Classification

35J47 35A01 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.CSMSE DivisionKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  2. 2.KAUST SRI Uncertainty Quantification Center in Computational Science and EngineeringThuwalSaudi Arabia
  3. 3.Institute for Sustainable Sciences and DevelopmentHiroshima UniversityHigashi-HiroshimaJapan

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