  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.
