标题： 生产场博弈的参数敏感性分析 显示英文标题

标题： Parameter sensitivity analysis for mean field games of production

摘要： 我们研究了Chan和Sircar（AMO，2015）引入的平均场博弈系统，用于模拟不可再生资源的生产。 特别是，我们研究了解对参数$\varepsilon$的敏感性，该参数衡量生产者之间可互换的程度。 我们证明了在某个区间$[0,\varepsilon_0]$内，其中$\varepsilon_0 > 0$，解相对于$\varepsilon$是无限可微的。 该结果基于对前向后向线性偏微分方程组的一组新的先验估计。 显示英文摘要

摘要： 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.