Mean Field Games

By Yves Achdou, Pierre Cardaliaguet, François Delarue, Alessio Porretta, F. Santambrogio. Lecture notes in mathematics, 2020

215 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Management Science and Operations Research, Strategy and Management

View Paper: https://www.semanticscholar.org/paper/984ba42614e36cbd8c420115ea30dfda456b773c

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Citations in the corpus

Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game (2018, background): “Lions [25] and to [9, 19, 18, 17] for surveys on the theory and its applications.”
Zero-sum stochastic differential games of generalized McKean–Vlasov type (2018, background): “Lions [21] (see also [9]), and turns out to be equivalent to a more intrinsic notion (of derivative in the Wasserstein space) used by various authors in connection with optimal transport and gradient flows (see e.”
Weak quantitative propagation of chaos via differential calculus on the space of measures (2019, background): “[6] Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, and Pierre-Louis Lions.”
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (2014, methodology): “The second one gives another point of view, which seems to be quite useful for understanding the deep signification of the differential calculus on the space of probability measures introduced by Lions in [4].”
On differentiability in the Wasserstein space and well-posedness for Hamilton–Jacobi equations (2019, background): “A second task completed is to compare the extrinsic definitions of sub and super-differential of [9] with the intrinsic ones of [3].”
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games (2020, background): “[8] [25]) ♯(Sn) = ♯(S −1 n ) = LΩ, lim n→∞ ‖y − x ◦ Sn‖ = 0.”
Finite state mean field games with Wright–Fisher common noise (2019, methodology): “We refer to [7, 8, 10, 49] for foundations of the topics for mean field games set on Rd and to [2, 15, 6] for related issues for mean field games with a finite state space.”
Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift (2015, methodology): “The one used here has been introduced by Lions during its lecture at the Collège de France and can be found in Cardaliaguet’s note [Car10].”
Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity (2021, background): “The theory developed in [20, 31, 36, 40] shows that ∂μU(μ, ·) can be characterized by the property U(Lξ+η)− U(μ) = E [ 〈∂μU(μ, ξ), η〉 ] + o(‖η‖2), ∀ ξ, η, with Lξ = μ.”
Distribution dependent stochastic differential equations (2020, background): “Intrinsic derivative was first introduced in [1] in the configuration space over a Riemannian manifold, while the L-derivative appeared in the lecture notes [9] for the study of mean field games and is also called Lions derivative in references.”
Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation (2017, background): “[4], [6] or [2], where the latter two deal also with mean-field type optimal control.”