Parameter Sensitivity Analysis for Mean Field Games of Production

Abstract

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 $$\varepsilon $$ , which measures the degree to which producers are interchangeable. We prove that on some interval $$[0,\varepsilon _0]$$ , where $$\varepsilon _0 > 0$$ , the solution is infinitely differentiable with respect to $$\varepsilon $$ . The result is based on a set of new a priori estimates for forward-backward systems of linear partial differential equations.