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Quantitative Convergence for Displacement Monotone Mean Field Games with Controlled Volatility

Author

Listed:
  • Joe Jackson

    (Department of Mathematics, The University of Chicago, Chicago, Illinois 60637)

  • Ludovic Tangpi

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

Abstract
We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Laurière and the second author, using the maximum principle to recast the convergence problem as a question of “forward-backward propagation of chaos” (i.e., (conditional) propagation of chaos for systems of particles evolving forward and backward in time). Our main results show that displacement monotonicity can be used to obtain this propagation of chaos, which leads to quantitative convergence results for open-loop Nash equilibria for a class of mean field games. Our results seem to be the first (quantitative or qualitative) that apply to games in which the common noise is controlled. The proofs are relatively simple and rely on a well-known technique for proving wellposedness of forward-backward stochastic differential equations, which is combined with displacement monotonicity in a novel way. To demonstrate the flexibility of the approach, we also use the same arguments to obtain convergence results for a class of infinite horizon discounted mean field games.

Suggested Citation

  • Joe Jackson & Ludovic Tangpi, 2024. "Quantitative Convergence for Displacement Monotone Mean Field Games with Controlled Volatility," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2527-2564, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2527-2564
    DOI: 10.1287/moor.2023.0106
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