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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01528480
Journal nameNonlinear Analysis
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Abstract (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 / Keywordsgradient flows; mean field games; vaccination games
Showing items related by title and author.
Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A(H1N1) Epidemic in France Laguzet, Laetitia; Turinici, Gabriel (2015) Article accepté pour publication ou publié