Continuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterion. Issue 1 (3rd January 2022)

• Record Type: Journal Article
• Authors: Golui, Subrata; Pal, Chandan
• Is Part Of: Stochastic analysis and applications. Volume 40:Issue 1(2022)
• Page Start: 78
• Page End: 95
• Publication Date: 2022-01-03
• Subjects: Zero-sum game -- risk-sensitive finite-horizon cost criterion -- optimality equation -- value of the game -- saddle point equilibrium; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.1889381
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this paper, we study the two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum risk-sensitive stochastic game, we prove the existence of the value of the game and a Markov saddle-point equilibrium in the class of all history-dependent multi-strategies under the suitable conditions. We achieve our results by studying the corresponding risk-sensitive finite-horizon optimality equations.