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Pré-Publication, Document De Travail Année : 2017

Metric gradient flows with state dependent functionals: the Nash-MFG equilibrium flows and their numerical schemes

Résumé

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.
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Dates et versions

hal-01528480 , version 1 (29-05-2017)
hal-01528480 , version 2 (07-10-2017)

Identifiants

  • HAL Id : hal-01528480 , version 1

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Gabriel Turinici. Metric gradient flows with state dependent functionals: the Nash-MFG equilibrium flows and their numerical schemes. 2017. ⟨hal-01528480v1⟩
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