Existence of a solution to an equation arising from the theory of Mean Field Games

By Wilfrid Gangbo, Andrzej Swiech. 2015

116 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/3005822a5694231652a8f2f4b20fe787dc5fb2eb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Modeling and Simulation

Citations in the corpus

The Master Equation and the Convergence Problem in Mean Field Games (2015, methodology): “Many works on mean field games (as in Buckdahn, Li, Peng and Rainer [16], Carmona and Delarue [19], Chassagneux, Crisan and Delarue [22], Gangbo and Swiech [28]) make use of an idea introduced by Lions in [52].”
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games (2020, background): “When the monotonicity condition fails and the noises are absent, only short time existence results of the scalar master equation were achieved in [24] for special Lagrangians, and later in [33] for more general ones.”
From the master equation to mean field game limit theory: a central limit theorem (2018, background): “To solve the master equation is no simple matter, though some preliminary well-posedness results may be found in [21, 14] in the case without common noise and [6, 9] in the case with common noise.”
Splitting methods and short time existence for the master equations in mean field games (2020, background): “This is the path followed in [17, 28] (when there is no diffusion at all: a “ a ” 0) and in [16] (when a ą 0 is constant and a “ 0).”
Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data (2019, background): “Gangbo-Swiech [43] showed the first order master equation (β1 = β = 0), derived from a deterministic linear quadratic mean field control problem, admits a local (in time) classical solution.”
On the convergence of closed-loop Nash equilibria to the mean field game limit (2018, background): “Furthermore, it is very challenging to produce a classical solution of the master equation, and this has been accomplished so far only in quite restricted settings [10, 20, 30].”
Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls (2018, background): “There are several works for first order master equations corresponding to the deterministic setting, see e.g. Cardaliaguet [7], Gangbo & Swiech [21, 22], and Bensoussan & Yam [4].”
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (2014, background): “In this framework, the existence of classical solutions has just been investigated for short time horizons by Gangbo and Swiech in the preprint [16].”
Long time behavior of the master equation in mean field game theory (2017, background): “We recall (see [21], [13], [7] and [6]) that the master equation is well-posed under the monotonicity condition on F and G and that the MFG system (1) plays the role of characteristics for this equation.”