We consider two person zero-sum stochastic games. The recursive formula for
the values nu (lambda) (resp. nu (n)) of the discounted (resp. finitely re
peated) version can be written in terms of a single basic operator Phi(alph
a, f) where alpha is the weight on the present payoff and f the future payo
ff. We give sufficient conditions in terms of Phi(alpha, f) and its derivat
ive at 0 for lim v(n) and lim nu (lambda) to exist and to be equal.
We apply these results to obtain such convergence properties for absorbing
games with compact action spaces and incomplete information games.