To each game form g an effectivity function (EFF) Eg is assigned. An EFF E is called formal (formal-minor) if E=Eg (respectively, E[less-than-or-equals, slant]Eg) for a game form g. (i) An EFF is formal iff it is superadditive and monotone. (ii) An EFF is formal-minor iff it is weakly...

We consider two-person zero-sum mean payoff undiscounted stochastic games and obtain sufficient conditions for the existence of a saddle point in uniformly optimal stationary strategies. Namely, these conditions enable us to bring the game, by applying potential transformations, to a canonical...