Zero-Sum Mean-Field Dynkin Games: Characterization and Convergence

• 成果类型: Article; Early Access
• 署名作者: Djehiche, Boualem; Dumitrescu, Roxana
• 署名单位: Royal Institute of Technology; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0080
• 发表日期: 2025
• 关键词: continuous-time; Stopping games; options; BSDEs

摘要

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish sufficient conditions under which such a game admits a value and a saddle point. Furthermore, we provide a characterization of the value of the game in terms of a specific class of doubly reflected backward stochastic differential equations of mean-field type, for which we derive an existence and uniqueness result. We then introduce a corresponding system of weakly interacting zero-sum Dynkin games and show its well-posedness. Finally, we provide a propagation of chaos result for the value of the zero-sum mean-field Dynkin game.