Weak solutions for mean field games with a common noise
speaker: Pierre Cardaliaguet (Ceremade, Université Paris-Dauphine)abstract: In joint works with Panagiotis Souganidis (U. Chicago) we investigate mean field games (MFG) with a common noise but without idiosyncratic noise. In these problems one aims at describing Nash equilibria for an infinite population of small controllers subject to the same noise. There are two ways to describe these equilibria: the so-called MFG system, which---exactly as in standard optimal transport theory---couples a Hamilton-Jacobi equation with a continuity equation (however, here, both equations are random); or the so-called master equation, which is a deterministic partial differential equation in the space of measures. We explain how to build a unique weak solution to these equations and how to use these solutions for problems with finitely many controllers.
timetable:
Mon 24 Oct, 11:00 - 11:45, Aula Magna Bruno Pontecorvo
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