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

2021/09/18 by Ghosh, Mrinal K., Golui, Subrata, Pal, Chandan +1
#91A15 #91A25 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2109.08837

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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