TOTAL REWARD STOCHASTIC GAMES AND SENSITIVE AVERAGE REWARD STRATEGIES

In this paper, total reward stochastic games are surveyed. Total rewar d games are motivated as a refinement of average reward games. The tot al reward is defined as the limiting average of the partial sums of th e stream of payoffs. It is shown that total reward games with finite s tate space are strategically equivalent to a class of average reward g ames with an infinite countable state space. The role of stationary st rategies in total reward games is investigated in detail. Further, it is outlined that, for total reward games with average reward value 0 a nd where additionally both players possess average reward optimal stat ionary strategies, it holds that the total reward value exists.