• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Mean field games with branching

Claisse, Julien; Ren, Zhenjie; Tan, Xiaolu (2023), Mean field games with branching, Annals of Applied Probability, p. 32

View/Open
163170520925145.pdf (449.3Kb)
Type
Article accepté pour publication ou publié
Date
2023
Journal name
Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Pages
32
Metadata
Show full item record
Author(s)
Claisse, Julien
CEntre 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 control

Related items

Showing items related by title and author.

  • Thumbnail
    Entropic optimal planning for path-dependent mean field games 
    Ren, Zhenjie; Tan, Xiaolu; Touzi, Nizar; Yang, Junjian (2022) Document de travail / Working paper
  • Thumbnail
    Ergodicity of the underdamped mean-field Langevin dynamics 
    Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian (2020) Document de travail / Working paper
  • Thumbnail
    Game on Random Environement, Mean-field Langevin System and Neural Networks 
    Conforti, Giovanni; Kazeykina, Anna; Ren, Zhenjie (2022) Article accepté pour publication ou publié
  • Thumbnail
    A pseudo-Markov property for controlled diffusion processes 
    Claisse, Julien; Talay, Denis; Tan, Xiaolu (2016) Article accepté pour publication ou publié
  • Thumbnail
    A pseudo-Markov property for controlled diffusion processes 
    Claisse, Julien; Talay, Denis; Tan, Xiaolu (2016) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo