2023/07/13 by P. Jameson Graber, Alpár R. Mészáros · 17 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Computer science #Degenerate energy levels #Economic theories and models #Financial Risk and Volatility Modeling #Geometry #Mathematical analysis #Mathematical economics #Mathematics #Monotone polygon #Monotonic function #Nash equilibrium #Regularization (linguistics) #Stochastic processes and financial applications #Uniqueness
paper · doi:10.1016/j.jfa.2023.110095
published in Journal of Functional Analysis 285(9), 110095 (Elsevier BV)
openalex publication_date 2023/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.