Finitely additive and measurable stochastic games

Abstract

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 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 equicontinuity 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.