  In this paper we consider two-person zero-sum risk-sensitive stochastic
dynamic games with Borel state and action spaces and bounded reward. The term
risk-sensitive refers to the fact that instead of the usual risk neutral
optimization criterion we consider the exponential certainty equivalent. The
discounted reward case on a finite and an infinite time horizon is considered,
as well as the ergodic reward case. Under continuity and compactness conditions
we prove that the value of the game exists and solves the Shapley equation and
we show the existence of optimal (non-stationary) strategies. In the ergodic
reward case we work with a local minorization property and a Lyapunov condition
and show that the value of the game solves the Poisson equation. Moreover, we
prove the existence of optimal stationary strategies. A simple example
highlights the influence of the risk-sensitivity parameter. Our results
generalize findings in Basu/Ghosh 2014 and answer an open question posed there.
