A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games

Bruno Ziliotto

Published 2015-01-26Version 1

We prove a Tauberian theorem for nonexpansive operators, and we apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game converges uniformly when lambda goes to 0 if and only if the value of the n-stage game converges uniformly when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and Sorin (1992) to the two-player-zero sum case.