Control and Nash Games with Mean Field Effect

作     者：Alain BENSOUSSAN Jens FREHSE 

作者机构：International Center for Decision and Risk Analysis School of Management University of Texas-DallasFrance School of Business the Hong Kong Polytechnic University Graduate Department of Financial Engineering Ajou University Institute for Applied Mathematics University of Bonn 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2013年第34卷第2期

页      面：161-192页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the WCU World Class University program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (No. R31-20007) the Research Grants Council of HKSAR (No. PolyU 5001/11P) 

主　　题：Mean field Dynamic programming Nash games Equilibrium Calculus of variations 

摘      要：Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of *** general,the applications concern approximating an infinite number of players with common behavior by a representative *** agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of *** approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite *** this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential *** the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.