We 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 the payoff function is evaluated in accordance with the theory of strategic measures as developed by Dubins and Savage. It is shown that such a game has a value. Moreover, when a Borel structure is imposed on the problem with the law of motion restricted to the Borel \(\sigma\)-field being countably additive, the value of the game is the same whether calculated in terms of (measurable) countably additive strategies or finitely additive ones.