Zero-sum Stochastic Games: Limit Optimal Trajectories

We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of cumulated occupation measure up to time t $\in$ [0, 1], under $\epsilon$-optimal strategies. A limit optimal trajectory is defined as an accumulation point as the discount factor tends to 0. We study existence, uniqueness and characterization of these limit optimal trajectories for absorbing games.