Weak Solutions for First Order Mean Field Games with Local Coupling

By Pierre Cardaliaguet. 2013

155 citations recorded by the source corpus.

Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise e−Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/c608cba49ce8c02af45d6a6fcc9505fb837d5766

How researchers see this paper

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

In Applied Mathematics

In Finance

Citations in the corpus

Time-Dependent Mean-Field Games in the Subquadratic Case (2013, background): “In particular, a number of problems have been worked out in detail by various authors, including numerical methods [LST10], [ACD10], [ACCD12], applications in economics [LLG10a], [Gué09a] and environmental policy [LST10], finite state problems [GMS10], [GMS13], [FG13], explicit models [Gué09b], [NH1”
Time dependent mean-field games in the superquadratic case (2013, methodology): “These include numerical methods [2, 3, 36], applications in economics [32, 41] and environmental policy [36], finite state problems [17, 27, 28], explicit models [33, 45], obstacle-type problems [19], congestion [18, 25], extended mean-field games [24, 29], probabilistic methods [13, 14], long-time ”
Mean Field Games Models—A Brief Survey (2013, methodology): “In the case g ≥ 0, one can obtain the additional estimate By combining the estimates (17) and (18), Lions and Lasry in [70, 71] obtained existence of weak solutions for various mean-ﬁeld games; see also the forthcoming paper [83] and [22].”
A Stochastic Maximum Principle for General Mean-Field Systems (2016, background): “Recall now from [9] (see also [10]), a function f : P2(R) → R is said to be differentiable atμ0 ∈ P2(R) if there exists θ0 ∈ L2(F , Rd) with Pθ0 = μ0, such that its lift f is Fréchet differentiable at θ0.”
Mean field games via controlled martingale problems: Existence of Markovian equilibria (2014, methodology): “The successes of PDE methods include its amenability to numerics [1] and its ability to handle local mean field interactions [37, 22, 21, 10], in which the functions of (Xt, μt) involves the density dμt/dx(Xt), but these matters are not addressed in this paper.”
Optimal stopping in mean field games, an obstacle problem approach (2017, background): “This approach was presented in [19] and has been well studied since (see [3,6,8] for example).”
Mean-field stochastic differential equations and associated PDEs (2014, unknown): “Among the different notions of differentiability of a function f defined over P2(Rd), we adopt for our approach that introduced by Lions [17] in his lectures at Collège de France in Paris and revised in the notes by Cardaliaguet [6]; we refer the reader also, for instance, to Carmona and Delarue [9]”
Mean field games systems of first order (2014, methodology): “The existence and uniqueness of weak solutions for this first order system under general structure conditions was studied in Cardaliaguet [3] and in Graber [14].”