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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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