An example of multiple mean field limits in ergodic differential games.

Summary 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.