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A Mean Field Game of Optimal Stopping

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  • Marcel Nutz

Abstract

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the common noise that all agents are exposed to, whereas idiosyncratic randomness can be eliminated by an Exact Law of Large Numbers. Under a structural monotonicity assumption, we can identify equilibria with solutions of a simple equation involving the distribution function of the idiosyncratic noise. Solvable examples allow us to gain insight into the uniqueness of equilibria and the dynamics in the population.

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  • Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1605.09112
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    Cited by:

    1. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.

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