MEAN-FIELD GAMES OF FINITE-FUEL CAPACITY EXPANSION WITH SINGULAR CONTROLS

• 成果类型: Article
• 署名作者: Campi, Luciano; De Angelis, Tiziano; Ghio, Maddalena; Livieri, Giulia
• 署名单位: University of Milan; University of Turin; Collegio Carlo Alberto; Scuola Normale Superiore di Pisa
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1771
• 发表日期: 2022
• 页码: 3674-3717
• 关键词: stochastic-control; free-boundary; probabilistic aspects; goodwill; connections; INVESTMENT; continuity; REGULARITY

摘要

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 e 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.