CONVERGENCE OF LARGE POPULATION GAMES TO MEAN FIELD GAMES WITH INTERACTION THROUGH THE CONTROLS

Mathieu Laurière, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review

Abstract

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by stochastic analysis methods, and which appear to be of independent interest. These propagation of chaos arguments allow us to derive moment and concentration bounds for the convergence of Nash equilibria.

Original languageEnglish (US)
Pages (from-to)3535-3574
Number of pages40
JournalSIAM Journal on Mathematical Analysis
Volume54
Issue number3
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • FBSDE
  • interaction through controls
  • large population games
  • maximum principle
  • mean field games
  • propagation of chaos

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