Mean Field Games: Numerical Methods

By Yves Achdou, I. Dolcetta. SIAM Journal on Numerical Analysis, 2010

416 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b4338835472330a3de7966b7b8fcd7db4a8e0d2d

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Citations in the corpus

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, methodology): “We also mention that numerical methods have been important in the development of mean field game theory; see especially Achdou and Cappuzzo-Dolcetta [3] and Achdou, et al. [2].”
Optimal stopping in mean field games, an obstacle problem approach (2017, background): “From the well posedness of the problem [5,22] to the difficult question of the master equation [7,22] through numerical questions [1,3] and developments like long time average [10] or learning in MFG [9], the original model has been the source of a huge number of mathematical questions.”
Continuous Time Finite State Mean Field Games (2012, methodology): “There is also a growing interest in numerical methods for these problems [ALT], [AD10].”
Linear-Quadratic Mean Field Games (2014, neutral): “[1], and Achdou and Capuzzo-Dolcetta [2].”
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 ”
Numerical method for FBSDEs of McKean–Vlasov type (2017, methodology): “We refer the interested reader to the following papers for various numerical methods, based upon finite differences or variational approaches, for mean field games: [1, 2, 4, 5, 28] and [3, 8, 29].”
Some remarks on mean field games (2018, methodology): “Numerical methods are being developed, let us cite [5, 6] for examples of this growing literature.”
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 [2, 3, 38], applications in economics”
Mean field games models of segregation (2016, methodology): “[4] it is proven that (37) has a solution in the case of a single population and periodic boundary conditions, (see Theorem 5).”
Mean Field Games Models—A Brief Survey (2013, methodology): “There is also a growing interest in numerical methods for these problems [2–4, 19, 25, 68].”