Open Access
February 2020 Convergence to the mean field game limit: A case study
Marcel Nutz, Jaime San Martin, Xiaowei Tan
Ann. Appl. Probab. 30(1): 259-286 (February 2020). DOI: 10.1214/19-AAP1501


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.


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Marcel Nutz. Jaime San Martin. Xiaowei Tan. "Convergence to the mean field game limit: A case study." Ann. Appl. Probab. 30 (1) 259 - 286, February 2020.


Received: 1 June 2018; Revised: 1 March 2019; Published: February 2020
First available in Project Euclid: 25 February 2020

zbMATH: 07200528
MathSciNet: MR4068311
Digital Object Identifier: 10.1214/19-AAP1501

Primary: 60G40 , 91A13 , 91A15 , 91A55

Keywords: $n$-player game , Equilibrium , mean field game , Optimal stopping

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 1 • February 2020
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