An operator approach to zero-sum repeated games

We consider two person zero-sum stochastic games. The recursive formula for the values nu (lambda) (resp. nu (n)) of the discounted (resp. finitely repeated) version can be written in terms of a single basic operator Phi(alpha, f) where alpha is the weight on the present payoff and f the future payoff. We give sufficient conditions in terms of Phi(alpha, f) and its derivative 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.