Continuous-time zero-sum games for markov decision processes with discounted risk-sensitive cost criterion on a general state space. Issue 2 (4th March 2023)

• Record Type: Journal Article
• Authors: Golui, Subrata; Pal, Chandan
• Is Part Of: Stochastic analysis and applications. Volume 41:Issue 2(2023)
• Page Start: 327
• Page End: 357
• Publication Date: 2023-03-04
• Subjects: Risk-sensitive discounted criterion -- history dependent strategy -- HJI equation -- value of the game -- saddle point equilibrium; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.2013889
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We consider zero-sum stochastic games for controlled continuous time Markov processes on a general state space with risk-sensitive discounted cost criteria. The transition and cost rates are possibly unbounded. Under a stability assumption, we prove the existence of a saddle-point equilibrium in the class of Markov strategies and give a characterization in terms of the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. Also, we illustrate our results and assumptions by an example.