Linear-Quadratic Non-Zero Sum Backward Stochastic Differential Game With Overlapping Information

• 成果类型: Article
• 署名作者: Wu, Shuang
• 署名单位: China University of Petroleum
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3159490
• 发表日期: 2023
• 页码: 1800-1806
• 关键词: Nash equilibrium; differential games; Stochastic processes; Differential equations; COSTS; Riccati equations; games; Backward stochastic differential equation; conditional mean-field stochastic differential equations; Nash equilibrium strategy; non-zero sum stochastic differential game; overlapping information

摘要

This article studies a linear quadratic non-zero sum stochastic differential game with overlapping information, where the state dynamics are described by a backward stochastic differential equation and the information obtained by two players has a common part but no inclusion relation. The open-loop Nash equilibrium strategy is given by some conditional mean-field stochastic differential equations. In addition, coupled Riccati equations are introduced to express the state feedback form of the Nash equilibrium strategy.