Long-time and large-population limits of displacement monotone linear-quadratic Nash systems
Year: 2026
Type: preprint
Abstract: For linear-quadratic $N$-dimensional Nash systems with mean-field-like scaling and strongly displacement monotone data, we prove uniform-in-time a priori derivative estimates exhibiting the expected scaling as $N \to \infty$ in order to pass the system to the limit. As a consequence, in a heterogeneous (i.e., non-symmetric) mean-field setting, we obtain both uniform-in-time convergence of the Nash system on any arbitrarily long horizon $[0,T]$ (as $N \to \infty$), and convergence of both the $N$-dimensional Nash system and the corresponding master equation to their respective ergodic counterparts (as $T \to \infty$).
Source: arXiv (Cornell University)
Author: Redaelli, Davide Francesco
Institution: University of Rome Tor Vergata
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7214630409