The bad match; a total reward stochastic game (Q1088927)

For two-person zero-sum stochastic games we introduce a new criterion for evaluating streams of payoffs. When the players use this criterion we call such games total reward stochastic games. It is unknown whether total reward stochastic games, with the property that the average value is zero for each initial state, always have a value. We examine an example of such a total reward stochastic game in which one of the players can play \(\epsilon\)-optimal only by using history dependent strategies.