Differential N-players game: Nash equilibria and Mather measures
Affiliation:
1. Department of Mathematics, University of Rome Tor Vergata , Via della Ricerca Scientifica 1, 00133 Roma , Italy
Abstract
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 partial differential equation’s system for a continuum of players.
Funder
Istituto Nazionale di Alta Matematica, Italy
Department of Math- ematics, University of Roma Tor Vergata
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Control and Optimization,Control and Systems Engineering
Reference28 articles.
1. Nonlinear elliptic systems and mean-field games. NoDEA;Bardi;Nonlinear Differ. Equ. Appl.,2016
2. Mean Field Games and Mean Field Type Control Theory
3. Mean field control and mean field game models with several populations;Bensoussan;Minimax Theory Appl.,2018
4. Long-time behavior of first-order mean field games on euclidean space;Cannarsa;Dyn. Games Appl,2019
5. Weak kam approach to first-order mean field games with state constraints;Cannarsa;J. Dyn. Differ. Equ.,2021