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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.

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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