Metric gradient flows with state dependent functionals: the Nash-MFG equilibrium flows and their numerical schemes
Turinici, Gabriel (2017), Metric gradient flows with state dependent functionals: the Nash-MFG equilibrium flows and their numerical schemes, Nonlinear Analysis, 165, p. 163-181. 10.1016/j.na.2017.10.002
Type
Article accepté pour publication ou publiéExternal document link
https://hal.archives-ouvertes.fr/hal-01528480Date
2017Journal name
Nonlinear AnalysisVolume
165Publisher
Elsevier
Pages
163-181
Publication identifier
Metadata
Show full item recordAbstract (EN)
We investigate the convergence of a relaxed version of the best reply numerical schemes (also known as best response or fictitious play) used to find Nash-mean field games equilibriums. This leads us to consider evolution equations in metric spaces similar to gradient flows except that the functional to be differentiated depends on the current point; these are called equilibrium flows. We give two definitions of solutions and prove that as the time step tends to zero the interpolated (`a la de Giorgi) numerical curves converge to equilibrium flows. As a by-product we obtain a sufficient condition for the uniqueness of a mean field games equilibrium. We close with applications to congestion and vaccination mean field games.Subjects / Keywords
gradient flows; mean field games; vaccination gamesRelated items
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