Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

• 成果类型: Article
• 署名作者: Basei, Matteo; Cao, Haoyang; Guo, Xin
• 署名单位: University of California System; University of California Berkeley; Electricite de France (EDF); Alan Turing Institute
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1131
• 发表日期: 2022
• 页码: 341-366
• 关键词: model; optimization; INVESTMENT; management; inventory; portfolio; policies; RISK

摘要

We consider a general class of nonzero-sum N-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to infinity, that is, a suitable mean-field game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an epsilon-NE approximation to the N-player game, with epsilon = O1/root N. As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player's optimal strategy, with sensitivity analysis of the model parameters.