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Mathematics > Analysis of PDEs

arXiv:2108.10962 (math)
[Submitted on 24 Aug 2021 (v1), last revised 11 Apr 2022 (this version, v3)]

Title:Parameter sensitivity analysis for mean field games of production

Authors:P. Jameson Graber, Marcus Laurel
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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.
Subjects: Analysis of PDEs (math.AP); Optimization and Control (math.OC)
MSC classes: 35Q89
Cite as: arXiv:2108.10962 [math.AP]
  (or arXiv:2108.10962v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2108.10962

Submission history

From: Philip Jameson Graber [view email]
[v1] Tue, 24 Aug 2021 21:27:47 UTC (31 KB)
[v2] Thu, 26 Aug 2021 14:18:37 UTC (31 KB)
[v3] Mon, 11 Apr 2022 15:15:17 UTC (35 KB)
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