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Mathematics > Analysis of PDEs

arXiv:2210.02281 (math)
[Submitted on 5 Oct 2022 (v1), last revised 20 Jul 2023 (this version, v2)]

Title:On monotonicity conditions for Mean Field Games

Authors:P. Jameson Graber, Alpár R. Mészáros
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Abstract:In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length of the time horizon, the regularity of the starting distribution of the agents, or the regularization effect of a non-degenerate idiosyncratic noise. Through a rich class of simple examples we show that these new conditions are not only in dichotomy with each other, but also with the two widely studied monotonicity conditions in the literature, the Lasry-Lions monotonicity and displacement monotonicity conditions.
Comments: to appear in J. Funct. Anal
Subjects: Analysis of PDEs (math.AP); Optimization and Control (math.OC)
Cite as: arXiv:2210.02281 [math.AP]
  (or arXiv:2210.02281v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2210.02281

Submission history

From: Alpár R. Mészáros [view email]
[v1] Wed, 5 Oct 2022 14:09:35 UTC (31 KB)
[v2] Thu, 20 Jul 2023 20:06:57 UTC (36 KB)
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