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Convergence to the mean field game limit: a case study. (English) Zbl 1437.91058
Summary: We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $$n$$-player equilibria converges to it as $$n\to\infty$$. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of $$n$$-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as “large $$n$$” equilibria.

##### MSC:
 91A16 Mean field games (aspects of game theory) 91A55 Games of timing 91A06 $$n$$-person games, $$n>2$$ 91A07 Games with infinitely many players 60G40 Stopping times; optimal stopping problems; gambling theory
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