Continuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterion

Abstract

This paper investigates the two-person zero-sum stochastic games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates are allowed to be unbounded from below and above. Under some mild conditions, we show the existence of the value of the game and an optimal randomized Markov saddle-point equilibrium in the class of all admissible feedback strategies. By studying the corresponding risk-sensitive finitehorizon optimal differential equations out of a class of possibly unbounded functions, to which the extended Feynman-Kac formula is also justified to hold, we obtain our required results.

Nonzero-Sum Risk-Sensitive Continuous-Time Stochastic Games with Ergodic Costs

“…For CTMDPs, zero-sum stochastic games with risk-sensitive costs for bounded cost and bounded transition rates have been studied in [14]. One can see [15,36], and the references therein for finite horizon risk-sensitive stochastic games for CTMDPs, where [15] deals with zero-sum game and [36] deals with nonzero-sum game. Recently risk sensitive continuous time Markov decision processes for ergodic cost criterion have been studied in [6,13,20,29,30].…”