Mean-field games of finite-fuel capacity expansion with singular controls

Campi, Luciano, de Angelis, Tiziano, Ghio, Maddalena and Livieri, Giulia ORCID: 0000-0002-3777-7329 (2022) Mean-field games of finite-fuel capacity expansion with singular controls. Annals of Applied Probability, 32 (5). pp. 3674-3717. ISSN 1050-5164

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Abstract

We study Nash equilibria for a sequence of symmetric N-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equilibria for the N-player games with approximation error ε going to zero as N tends to infinity. Our analysis relies entirely on probabilistic methods and extends the well-known connection between singular stochastic control and optimal stopping to a mean-field framework.

Item Type:	Article
Additional Information:	© Institute of Mathematical Statistics, 2022.
Divisions:	LSE
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Date Deposited:	25 Jun 2024 15:39
Last Modified:	20 Dec 2024 00:55
URI:	http://eprints.lse.ac.uk/id/eprint/123975

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