Differential N-players game: Nash equilibria and Mather measures

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.

References in corpus (5)

• Convergence of the solutions of the discounted equation
• Weak KAM theorem on non compact manifolds
• Convergence of the solutions of the discounted equation: the discrete case
• Long Time Behavior of First Order Mean Field Games on Euclidean Space
• Weak KAM approach to first-order Mean Field Games with state constraints