2013/12/23 by Yurii Averboukh, Averboukh, Yurii
Economics, Econometrics and Finance · Mathematics · #35F21 #35F31 #49N70 #91A10 #91A23 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stochastic processes and financial applications #advanced mathematical theories #math.AP #math.OC #msc:35F21 #msc:35F31 #msc:49N70 #msc:91A10 #msc:91A23
paper · pdf · doi:10.48550/arxiv.1312.6627
27 pages
openalex publication_date 2013/12/23 · arxiv created 2014/04/18 · arxiv updated 2014/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The paper is devoted to the first-order mean field game system in the case when the distribution of players can contain atoms. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi equation. We prove the existence of the generalized (minimax) solution of the mean filed game system using the Nash equilibrium in the auxiliary differential game with infinitely many identical players. We show that the minimax solution of the original system provide the ε-Nash equilibrium in the differential game with finite number of players.