Parameter Sensitivity Analysis for Mean Field Games of Production

摘要

( )We study a mean field game system introduced by Chan and Sircar (Appl Math Optim 71:533-569, 2015) to model production of an exhaustible resource. In particular, we study the sensitivity of the solution with respect to a parameter epsilon, which measures the degree to which producers are interchangeable. We prove that on some interval 0, epsilon(0), where epsilon(0) > 0, the solution is infinitely differentiable with respect to epsilon. The result is based on a set of new a priori estimates for forward-backward systems of linear partial differential equations.