Mean Field Games *** this position has been filled ***

• Location: Università Degli Studi di Roma - La Sapienza
• Advisor: I. Capuzzo Dolcetta
• Secondment: Inria Saclay Ile de France

• Application deadline: March 2011.
• Contact: I. Capuzzo Dolcetta

Mathematical models in the framework of control and differential games theory provide fundamental qualitative, computational and simulations tools in different branches of engineering, economy and, more recently, social sciences. When these models incorporate decision features (optimization of some performance index, Nash or Pareto equilibria, ...) one has to face problems concerning the qualitative and numerical analysis of nonlinear elliptic and/or parabolic partial differential equations (or systems of) of Hamilton-Jacobi-Isaacs type. This is a very recent research topic where few results have been obtained. The methodology of viscosity solutions has proved to be an effective tool in this respect. Extremely interesting advances, both from the modelling and theoretical point of view, in this active research field are provided by the theory of Mean Field Games recently developed by J.-M Lasry and P.-L. Lions. We plan to develop methods for the approximation and the computation of the solutions of the system of Hamilton-Jacobi-Isaacs partial differential equations arising in the context of Mean Field Games theory. The first results of research in this very promising direction habe been recently obtained by Achdou-Capuzzo Dolcetta.