Zero-sum risk-sensitive stochastic games for continuous time Markov chains |
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Authors: | Mrinal K Ghosh K Suresh Kumar |
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Institution: | 1. Department of Mathematics, Indian Institute of Science, Bangalore, India;2. Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India |
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Abstract: | We study infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space. For the discounted-cost game, we prove the existence of value and saddle-point equilibrium in the class of Markov strategies under nominal conditions. For the ergodic-cost game, we prove the existence of values and saddle point equilibrium by studying the corresponding Hamilton-Jacobi-Isaacs equation under a certain Lyapunov condition. |
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Keywords: | Risk-sensitive cost infinite horizon discounted cost infinite horizon ergodic cost HJI equation value saddle point equilibrium |
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