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Seminario di Equazioni Differenziali e Applicazioni: “One-dimensional, non-local, first-order, stationary mean-field games with congestion: a Fourier approach”

Mercoledì 3 Maggio 2017 alle ore 12:00 in Aula 2BC30, Levon Nurbekyan

ARGOMENTI: Seminari

Mercoledì 3 Maggio 2017 alle ore 12:00 in Aula 2BC30, Levon Nurbekyan (KAUST, Arabia Saudita) terrà un seminario dal titolo “One-dimensional, non-local, first-order, stationary mean-field games with congestion: a Fourier approach”.

Abstract
I will present a one-dimensional, non-local, first-order, stationary mean-field game (MFG) model with congestion. I will discuss how to reduce this model to a finite-dimensional optimization problem when the kernel in the non-local coupling is a trigonometric polynomial. Furthermore, I will show that this optimization problem admits a unique solution thus providing a unique smooth solution for the original problem. In the case of a general kernel in the non-local coupling, we will discuss a suitable approximation scheme. Additionally, I will present some explicit solutions, numerical solution methods, and possible extensions. My techniques are based on Fourier expansion methods.

Rif. Int. M. Bardi, C. Marchi, M. Cirant

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