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Master Equation for Cournot Mean Field Games of Controls with Absorption

Presenter
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.