  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.
