Continuous-Time Zero-Sum Games for Markov Decision Processes with Discounted Risk-Sensitive Cost Criterion

Subrata Golui (), Chandan Pal () and Subhamay Saha ()
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Subrata Golui: Indian Institute of Technology Guwahati
Chandan Pal: Indian Institute of Technology Guwahati
Subhamay Saha: Indian Institute of Technology Guwahati

Dynamic Games and Applications, 2022, vol. 12, issue 2, No 6, 485-512

Abstract: Abstract In this paper, we study two-person zero-sum stochastic games for controlled continuous time Markov decision processes with risk-sensitive discounted cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum stochastic game, we prove the existence of the value of the game and saddle-point equilibrium in the class of history dependent strategies under a Foster–Lyapunov condition. We achieve our results by studying the corresponding Hamilton–Jacobi–Isaacs equation.

Keywords: Zero-sum game; Risk-sensitive discounted cost criterion; HJI equation; Value of the game; Saddle point equilibrium (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13235-021-00391-2

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