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Long-time and large-population limits of displacement monotone linear-quadratic Nash systems

  • Davide Francesco Redaelli
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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 → ∞ 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 → ∞), and convergence of both the N-dimensional Nash system and the corresponding master equation to their respective ergodic counterparts (as T → ∞).

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Cite

BibTeXRIS
BibTeX
@misc{redaelli2026longtime,
  title = {{Long-time and large-population limits of displacement monotone linear-quadratic Nash systems}},
  author = {Davide Francesco Redaelli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31091},
  eprint = {2609.31091},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31091},
}
RIS
TY  - UNPB
TI  - Long-time and large-population limits of displacement monotone linear-quadratic Nash systems
AU  - Davide Francesco Redaelli
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31091
UR  - https://arxiv.org/abs/2609.31091
AB  - 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 → ∞ 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 → ∞), and convergence of both the N-dimensional Nash system and the corresponding master equation to their respective ergodic counterparts (as T → ∞).
ER  -