Nash equilibrium strategies for non-zero-sum differential games of SDEs with time-varying coefficient and infinite Markov jumps

• Published in: Electronic Research Archive
• Main Authors: Yueying Liu, Mengping Sun, Zhen Wang, Xiangyun Lin, Cuihua Zhang
• Format: Article
• Language: English
• Published: AIMS Press 2025-04-01
• Subjects: stochastic differential equations; infinite markov jumps; non-zero-sum nash differential games; countable coupled generalized differential riccati equations; unified treatment
• Online Access: https://www.aimspress.com/article/doi/10.3934/era.2025112
• ISSN: 2688-1594

This paper mainly discusses the non-zero-sum Nash differential games for stochastic differential equations (SDEs) involving time-varying coefficient and infinite Markov jumps. First of all, a necessary and sufficient conditions for the existence of Nash equilibrium strategies is given, which turns the non-zero-sum Nash differential games into solving the equations that are composed of countable coupled generalized differential Riccati equations (CGDREs). As an application, a unified treatment is presented for $ H_{2} $, $ H_{\infty} $, and $ H_{2}/H_{\infty} $ control by the Nash game approach, which can reveal the relationship among these three problems. Furthermore, the theoretical results are used to solve a numerical example.