Finitely additive and measurable stochastic games

The authors consider two-person zero-sum stochastic games with arbitrary state and action spaces, a finitely additive law of motion and limit superior payoff function. The players use finitely additive strategies and it is shown that such a game has a value, if the payoff function is evaluated in accordance with the theory of strategic measures as developed by Dubins and Savage. Moreover, when a Borel structure is imposed on the problem, together with an equi-continuity condition on the law of motion, the value of the game is the same whether calculated in terms of countably additive strategies or finitely additive ones.