English

$N$-player games and mean field games of moderate interactions

Optimization and Control 2021-12-20 v3

Abstract

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit as the number of players tends to infinity. Because it is of independent interest, we prove this result in full detail. We characterize the solutions of the limiting game via a verification argument.

Keywords

Cite

@article{arxiv.2104.03944,
  title  = {$N$-player games and mean field games of moderate interactions},
  author = {Franco Flandoli and Maddalena Ghio and Giulia Livieri},
  journal= {arXiv preprint arXiv:2104.03944},
  year   = {2021}
}