On monotonicity conditions for mean field games

Graber, P. Jameson; Mészáros, Alpár R.

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.

Citation

Graber, P. J., & Mészáros, A. R. (2023). On monotonicity conditions for mean field games. Journal of Functional Analysis, 285(9), Article 110095. https://doi.org/10.1016/j.jfa.2023.110095

• Journal Article Type: Article
• Acceptance Date: Jul 3, 2023
• Online Publication Date: Jul 13, 2023
• Publication Date: 2023-11
• Deposit Date: Aug 17, 2023
• Publicly Available Date: Aug 17, 2023
• Journal: Journal of Functional Analysis
• Print ISSN: 0022-1236
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 285
• Issue: 9
• Article Number: 110095
• DOI: https://doi.org/10.1016/j.jfa.2023.110095
• Keywords: Analysis
• Public URL: https://durham-repository.worktribe.com/output/1720346