Articlegreen2019

On mean field games with common noise and McKean-Vlasov SPDEs

Vassili Nikitich Kolokoltsov · Marianna Stepanovna Troeva

48 citations0/0 files storedStochastic Analysis and Applications

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Game Theory and Applications Stochastic processes and statistical mechanics

Abstract

We formulate the MFG limit for N interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any (regular enough) solution provides an 1/N-Nash-equilibrium profile for the initial N-player game. We use the method of stochastic characteristics to provide the link with the basic models of MFG with a major player. We develop two auxiliary theories of independent interest: sensitivity and regularity analysis for McKean-Vlasov SPDEs and the 1/N-convergence rate for the propagation of chaos property of interacting diffusions.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 48 citations exist upstream.

References

2006Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle 1998Stochastic Flows and Stochastic Differential Equations 2007Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria 2006Jeux à champ moyen. I – Le cas stationnaire 2013Mean Field Games and Mean Field Type Control Theory 2010Mean Field Games and Applications 2018Probabilistic Theory of Mean Field Games with Applications II 2013Probabilistic Analysis of Mean-Field Games

Cited by

2022McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations 2021A General Stochastic Maximum Principle for Mean-Field Controls with Regime Switching 2017Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation 2019A stochastic maximum principle for switching diffusions using conditional mean-fields with applications to control problems 2022Superposition and mimicking theorems for conditional McKean–Vlasov equations

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.