MEAN FIELD GAMES WITH BRANCHING
成果类型：
Article
署名作者：
Claisse, Julien; Ren, Zhenjie; Tan, Xiaolu
署名单位：
Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/22-AAP1835
发表日期：
2023
页码：
834-875
关键词：
摘要：
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empir-ical distribution. In the classical setting, the number of players is large but fixed throughout the game. However, in various applications, such as popu-lation dynamics or economic growth, the number of players can vary across time and this may lead to different Nash equilibria. In order to account for this evolution, we introduce a branching mechanism in the population of agents and obtain a variant of the original mean field game problem. As a first step, we study a simple model using a PDE approach to illustrate the main differ-ences with the classical setting. We prove existence of a solution and show that it provides an approximate Nash-equilibrium for large population games. We also present a numerical example for a linear-quadratic model. Then we study the problem in a general setting by a probabilistic approach. It is based upon the relaxed formulation of stochastic control problems which allows us to obtain a general existence result.