Parameter sensitivity analysis for mean field games of production

TL;DR

This paper analyzes how the solutions of a mean field game model for resource production change as the degree of producer interchangeability varies, establishing smoothness of solutions with respect to this parameter.

Contribution

It proves the infinite differentiability of the mean field game solution concerning the interchangeability parameter within a certain range, using new a priori estimates.

Findings

Solution is infinitely differentiable in parameter on [0, ε₀]

Established new a priori estimates for PDE systems

Provides insights into sensitivity of resource production models

Abstract

We study a mean field game system introduced by Chan and Sircar (AMO, 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.