We prove here the existence of a value (of norm 1) on the spaces ′N A and even ′A N, the closure in the variation distance of the linear space spanned by all games f∘μ, where μ is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0,1] which...

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t<(k+1)\delta$, and therefore the average payoff of the $n$-stage play per unit of time is the sum of the payoffs in the first $n$ stages divided by $n\delta$, and the $\lambda$-discounted present value of a payoff $g$ in stage $k$ is $\lambda^{k\delta} g$. We define convergence, strong convergence, and exact convergence of the data of a family $(\Gamma_\delta)_{\delta>0}$ as the stage duration $\delta$ goes to $0$, and study the...</(k+1)\delta$,>