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Convergence to the Mean Field Game Limit: A Case Study

Marcel Nutz, Jaime San Martin and Xiaowei Tan

Papers from arXiv.org

Abstract: 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.

New Economics Papers: this item is included in nep-exp and nep-gth
Date: 2018-06
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