  The infinite horizon risk-sensitive discounted-cost and ergodic-cost
nonzero-sum stochastic games for controlled Markov chains with countably many
states are analyzed. For the discounted-cost game, we prove the existence of
Nash equilibrium strategies in the class of Markov strategies under fairly
general conditions. Under an additional geometric ergodicity condition and a
small cost criterion, the existence of Nash equilibrium strategies in the class
of stationary Markov strategies is proved for the ergodic-cost game.
