Parameter Sensitivity Analysis for Mean Field Games of Production

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 ε , which measures the degree to which producers are interchangeable. We prove that on some interval [ 0 , ε 0 ] , where ε 0 > 0 , the solution is infinitely differentiable with respect to ε . The result is based on a set of new a priori estimates for forward-backward systems of linear partial differential equations.