** Hybrid seminar at McGill University or Zoom.**

We study zero-sum stochastic games for controlled discrete time Markov chains with risk-sensitive average cost criterion with countable/compact state space and Borel action spaces. The payoff function is nonnegative and possibly unbounded for a countable state space case and for a compact state space case, it is a real-valued and bounded function. For the countable state space case, under a certain Lyapunov-type stability assumption on the dynamics we establish the existence of the value and a saddle point equilibrium. For the compact state space case, we establish these results without any Lyapunov-type stability assumptions. Using the stochastic representation of the principal eigenfunction of the associated optimality equation, we completely characterize all possible saddle point strategies in the class of stationary Markov strategies.

Bio: My name is Subrata Golui and I am a postdoctoral fellow in the Department of Mathematics, Indian Institute of Technology, Bombay. I obtained PhD degree at Indian Institute of Technology Guwahati under the supervision of Dr. Chandan Pal on 5th July 2023. My thesis title is Risk-sensitive stochastic control and games. My research interests can be broadly classified into three areas: stochastic control theory, stochastic game theory, and queueing theory. Currently, I am working on the stochastic control theory. More specifically, I am studying the metastable behaviour exhibited by the Markov processes. I have 8 published articles and one more self-authored research work has been submitted for publication.