This was part of Applications of Mean Field Games
Master Equation for Cournot Mean Field Games of Controls with Absorption
Jameson Graber, Baylor University
Thursday, November 18, 2021
Abstract: From the beginning, mean field games have been used to model economic production for a market with a large number of producers. The master equation is an infinite dimensional PDE that in principle allows us to solve the convergence problem for N-player equilibria as N goes to infinity. However, up until now, there are no results in the literature on the master equation that satisfy the assumptions needed for economic production. In the paper I will discuss, co-authored with Ronnie Sircar, we prove the existence and uniqueness of solutions to a master equation corresponding to a mean field Cournot game, with absorbing boundary conditions.