  We study nonzero-sum stochastic games for continuous time Markov chains on a
denumerable state space with risk sensitive discounted and ergodic cost
criteria. For the discounted cost criterion we first show that the
corresponding system of coupled HJB equations has an appropriate solution. Then
under an additional additive structure on the transition rate matrix and payoff
functions, we establish the existence of a Nash equilibrium in Markov
strategies. For the ergodic cost criterion we assume a Lyapunov type stability
assumption and a small cost condition. Under these assumptions we show that the
corresponding system of coupled HJB equations admits a solution which leads to
the existence of Nash equilibrium in stationary strategies.

Optimization and Control