Zero-Sum Games for Continuous-time Markov Decision Processes with Risk-Sensitive Average Cost Criterion

Mrinal K. Ghosh; Subrata Golui; Chandan Pal; Somnath Pradhan

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arXiv · 2109.08837

Zero-Sum Games for Continuous-time Markov Decision Processes with Risk-Sensitive Average Cost Criterion

Mrinal K. Ghosh·Subrata Golui·Chandan Pal·Somnath Pradhan

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Abstract

We consider zero-sum stochastic games for continuous time Markov decision processes with risk-sensitive average cost criterion. Here the transition and cost rates may be unbounded. We prove the existence of the value of the game and a saddle-point equilibrium in the class of all stationary strategies under a Lyapunov stability condition. This is accomplished by establishing the existence of a principal eigenpair for the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. This in turn is established by using the nonlinear version of Krein-Rutman theorem. We then obtain a characterization of the saddle-point equilibrium in terms of the corresponding HJI equation. Finally, we use a controlled population system to illustrate results.

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BibTeX RIS

Mrinal K. Ghosh, Subrata Golui, Chandan Pal, Somnath Pradhan. 2021-09-18. Zero-Sum Games for Continuous-time Markov Decision Processes with Risk-Sensitive Average Cost Criterion. https://arxiv.org/abs/2109.08837

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