In a two-state follow-the-crowd mean field game, the authors show equilibrium non-uniqueness can be arbitrarily large when the background jump rate is below one half, and that the entropy solution is the selected limit for the finite-player game when the jump rate is zero.
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On non-uniqueness in mean field games
In a two-state follow-the-crowd mean field game, the authors show equilibrium non-uniqueness can be arbitrarily large when the background jump rate is below one half, and that the entropy solution is the selected limit for the finite-player game when the jump rate is zero.