Laplace principle for large population games with control interaction

Peng Luo, Ludovic Tangpi

Research output: Contribution to journalArticlepeer-review

Abstract

This work investigates continuous time 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. The control processes are assumed to be open-loop. We give regularity conditions guaranteeing that if the finite-player game admits a Nash equilibrium, then both the sequence of equilibria and the corresponding state processes satisfy a Sanov-type large deviation principle. The results require existence of a Lipschitz continuous solution of the master equation of the corresponding mean field game, and they carry over to cooperative (i.e. central planner) games. We study a linear-quadratic case of such games in details.

Original languageEnglish (US)
Article number104314
JournalStochastic Processes and their Applications
Volume171
DOIs
StatePublished - May 2024

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Concentration of measure
  • FBSDE
  • Interaction through controls
  • Large deviation principle
  • Large population games
  • McKean–Vlasov equations
  • Mean field games
  • PDEs on Wasserstein space

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