Thu. March 30 11.30 -13.30 M
Fri. March 31 14.30-17.30 E
Mon. April 3rd 8.30-11.30 L
Wed. April 5th 12.30-14.30 L
Fri. April 7th 8.30-11.30 G
Mon. April 10th 8.30 -11.30 Laboratory Gamma.
This course is a short introduction to mean-field game (MFG) models. The course starts with a discussion of optimal control, Hamilton-Jacobi equations and transport equations.
Next, we develop the concept of Nash equilibria and derive MFG models, which are systems of a Hamilton-Jacobi equation coupled with a transport or Fokker-Planck equation.
Subsequently, we examine models in which explicit calculations are possible and explore the connections between MFGs and calculus of variations problems. Subsequently, we discuss techniques to prove estimates for MFGs - these include methods for Hamilton-Jacobi equations, Fokker-Planck equations, and the nonlinear adjoint method.
Finally, we examine the continuation method to prove the existence of strong solutions and, time-permitting, the monotonicity method, for the construction of weak solutions.
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan Regularity theory for mean-field game systems. SpringerBriefs in Mathematics. 2016.