This talk concerns with zero-sum stochastic games with the risk-sensitive average criterion. First, we establish the existence of the value and a saddle point under a mild condition， which is weaker than those in the existing literature. Next, different from the existing literature on the risk-sensitive average stochastic games, which only focuses on the existence of a saddle point, we additionally propose two efficient algorithms to approximate the value and saddle points, respectively. Finally, we illustrate our conclusions with an example.
