English

Differential N-players game: Nash equilibria and Mather measures

Optimization and Control 2023-04-04 v1 Analysis of PDEs

Abstract

We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash equilibrium in mixed strategies exists and it is a Mather measure for the Lagrangian system defined by the cost functional. In conclusion, we show that the mean field limit of the N-players game is described by the ergodic PDE's system for a continuum of players.

Keywords

Cite

@article{arxiv.2302.10689,
  title  = {Differential N-players game: Nash equilibria and Mather measures},
  author = {Cristian Mendico},
  journal= {arXiv preprint arXiv:2302.10689},
  year   = {2023}
}