TAN Xiaolu

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Topics of productions
Affiliations
  • 2018 - 2021
    Chinese University of Hong Kong
  • 2012 - 2019
    Centre de recherches en mathématiques de la décision
  • 2013 - 2017
    Université Paris-Dauphine
  • 2010 - 2013
    Ecole Polytechnique
  • 2010 - 2013
    Détermination de Formes Et Identification
  • 2010 - 2013
    Centre de mathématiques appliquées
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2011
  • Mean field games with branching.

    Julien CLAISSE, Zhenjie REN, Xiaolu TAN
    2021
    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.
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