
Mean field games with branching
Claisse, Julien; Ren, Zhenjie; Tan, Xiaolu (2023), Mean field games with branching, Annals of Applied Probability, 33, 2, p. 834-875. 10.1214/22-AAP1835
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Article accepté pour publication ou publiéDate
2023Journal name
Annals of Applied ProbabilityVolume
33Number
2Publisher
Institute of Mathematical Statistics
Pages
834-875
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Claisse, JulienCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tan, Xiaolu
Department of Mathematics [CUHK]
Abstract (EN)
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout the game. However, in various applications, such as population dynamics or economic growth, the number of players can vary across time which may lead to different Nash equilibria. For this reason, we introduce a branching mechanism in the population of agents and obtain a variation on the mean field game problem. As a first step, we study a simple model using a PDE approach to illustrate the main differences 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.Subjects / Keywords
Mean field games; branching diffusion process; relaxed controlRelated items
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