发表机构
ENSA – Université Ibn Zohr; Équipe Aide à la Décision（伊本·佐赫尔大学 ENSA; 决策辅助团队）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含三种机制切换的两人零和随机微分博弈，采用粘性解方法分析相关方程，推导值函数显式解，为刻画玩家最优策略提供系统方法。
AI 中文摘要
本文研究了具有三种不同机制的两人零和随机微分博弈，该博弈反映了系统内的机制切换动态。我们旨在通过粘性解方法推导该切换系统多种配置的显式解。特别地，我们分析了相关的哈密顿-雅可比-贝尔曼-艾萨克斯方程，考察不同机制间的相互作用如何影响值函数的结构。所提框架为刻画两名玩家的最优策略、在合适假设下获得值函数的显式表示提供了系统方法。我们还说明了在已知切换区域定性结构时如何推导值函数。
英文摘要
This paper investigates a two player zero-sum stochastic differential game characterized by three distinct regimes, reflecting the regime switching dynamics within the system. We aim to derive an explicit solution for a number of configurations of the switching system by means of the viscosity solutions approach. In particular, we analyze the associated Hamilton-Jacobi-Bellman-Isaacs equations and examine how the interactions between the different regimes affect the structure of the value function. The proposed framework provides a systematic approach to characterize the optimal strategies of the two players and to obtain explicit representations of the value function un der suitable assumptions. We also illustrate how to derive the value functions in case we know the qualitative structure of switching regions.
