Total Reward Stochastic Games and Sensitive Average Reward Strategies

In this paper, total reward stochastic games are surveyed. Total reward games are motivated as a refinement of average reward games. The total reward is defined as the limiting average of the partial sums of the stream of payoffs. It is shown that total reward games with finite state space are strategically equivalent to a class of average reward games with an infinite countable state space. The role of stationary strategies in total reward games is investigated in detail. Further, it is outlined that, for total reward games with average reward value 0 and where additionally both players possess average reward optimal stationary strategies, it holds that the total reward value exists.