Zero-sum Risk-Sensitive Stochastic Games

Abstract

In this paper we consider two-person zero-sum risk-sensitive stochastic dynamic games with Borel state and action spaces and bounded reward. The term risk-sensitive refers to the fact that instead of the usual risk neutral optimization criterion we consider the exponential certainty equivalent. The discounted reward case on a finite and an infinite time horizon is considered, as well as the ergodic reward case. Under continuity and compactness conditions we prove that the value of the game exists and solves the Shapley equation and we show the existence of optimal (non-stationary) strategies. In the ergodic reward case we work with a local minorization property and a Lyapunov condition and show that the value of the game solves the Poisson equation. Moreover, we prove the existence of optimal stationary strategies. A simple example highlights the influence of the risk-sensitivity parameter. Our results generalize findings in Basu/Ghosh 2014 and answer an open question posed there.

References in corpus (2)

• Partially Observable Risk-Sensitive Markov Decision Processes
• A Characterization of the optimal risk-Sensitive average cost in finite controlled Markov chains

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• Risk-Sensitive Reinforcement Learning: Near-Optimal Risk-Sample Tradeoff in Regret
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• Model and Reinforcement Learning for Markov Games with Risk Preferences
• Zero-sum risk-sensitive continuous-time stochastic games with unbounded payoff and transition rates and Borel spaces
• Zero-Sum Games for Continuous-time Markov Decision Processes with Risk-Sensitive Average Cost Criterion