Orateur
Description
Mean field games (MFGs) are a class of problems modeling Nash equilibria for a very large number of small agents in evolution, interacting through coupling terms depending on their distribution. We will describe in detail an MFG model consisting of two coupled second-order PDEs, equivalent to the optimality conditions for an optimal control problem of the Fokker-Planck equation. We will investigate a numerical method, called fictitious play, in which the agents play at each iteration a "best-response", corresponding to a predicted value of the coupling terms. We will show that this procedure is equivalent to the generalized conditional gradient method, which will allow us to establish convergence.
Joint work with Pierre Lavigne (Institut Louis Bachelier).
