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Title: Mean-field games of optimal stopping : a relaxed solution approach
Authors: Bouveret, Géraldine
Dumitrescu, Roxana
Tankov, Peter
Keywords: Science
Issue Date: 2020
Source: Bouveret, G., Dumitrescu, R., & Tankov, P. (2020). Mean-field games of optimal stopping : a relaxed solution approach. SIAM Journal on Control and Optimization, 58(4), 1795–1821. doi:10.1137/18M1233480
Journal: SIAM Journal on Control and Optimization
Abstract: We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game. We place ourselves in the framework of relaxed optimal stopping, which amounts to looking for the optimal occupation measure of the stopper rather than the optimal stopping time. This framework allows us to prove the existence of a relaxed Nash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions. Further, we prove a rigorous relation between relaxed Nash equilibria and the notion of mixed solutions introduced in earlier works on the subject, and provide a criterion, under which the optimal strategies are pure strategies, that is, behave in a similar way to stopping times. Finally, we present a numerical method for computing the equilibrium in the case of potential games and show its convergence.
ISSN: 0363-0129
DOI: 10.1137/18M1233480
Rights: © 2020 Society for Industrial and Applied Mathematics (SIAM). All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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