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.
Funding Statement
T. De Angelis gratefully acknowledges support from EPSRC via grant EP/R021201/1; M. Ghio and G. Livieri acknowledge the financial support of UniCredit Bank R&D group through the Dynamical and Information Research Institute at the Scuola Normale Superiore.
Acknowledgments
We thank the Associate Editor and two referees for useful comments that improved the quality of the paper.
Citation
Luciano Campi. Tiziano De Angelis. Maddalena Ghio. Giulia Livieri. "Mean-field games of finite-fuel capacity expansion with singular controls." Ann. Appl. Probab. 32 (5) 3674 - 3717, October 2022. https://doi.org/10.1214/21-AAP1771
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