High order variational numerical schemes with application to Nash-MFG vaccination games
Résumé
This paper introduces high-order explicit Runge-Kutta numerical schemes in metric spaces. We show that our approach reduces to the corresponding RungeKutta schemes if the ambient space is Hilbert. We apply these schemes to compute the Nash equilibrium in a mean field vaccination game. Numerical simulations show improvement in the speed of convergence towards the Nash equilibrium; the numerical scheme has high order (2-4) in time.