Limit Optimal Trajectories in Zero-Sum Stochastic Games

We consider zero-sum stochastic games. For every discount factor λ , a time normalization allows to represent the discounted game as being played during the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of cumulated occupation measure on the state space up to time t ∈ [ 0 , 1 ] , under ε -optimal strategies. A limit optimal trajectory is defined as an accumulation point as ( λ , ε ) tend to 0. We study existence, uniqueness and characterization of these limit optimal trajectories for compact absorbing games.