An example of multiple mean field limits in ergodic differential games

Pierre Cardaliaguet (1) , Catherine Rainer (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We present an example of symmetric ergodic N´players differential games, played in memory strategies on the position of the players, for which the limit set, as N Ñ`8, of Nash equilibrium payoffs is large, although the game has a single mean field game equilibrium. This example is in sharp contrast with a result by Lacker [23] for finite horizon problems.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Catherine Rainer. An example of multiple mean field limits in ergodic differential games. Nonlinear Differential Equations and Applications, 2020, 27 (3), pp.1-19. ⟨hal-02190812⟩