Abstract
We consider zero-sum stochastic games. For every discount factor \(\lambda \), 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 \(t\in [0,1]\), under \(\varepsilon \)-optimal strategies. A limit optimal trajectory is defined as an accumulation point as (\(\lambda , \varepsilon )\) tend to 0. We study existence, uniqueness and characterization of these limit optimal trajectories for compact absorbing games.
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Some of the results of this paper were presented in “Atelier Franco-Chilien: Dynamiques, optimisation et apprentissage” Valparaiso, November 2010, and a preliminary version of this paper was given at the Game Theory Conference in Stony Brook, July 2012. This research was supported by Grant PGMO 0294-01 (France)
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Sorin, S., Vigeral, G. Limit Optimal Trajectories in Zero-Sum Stochastic Games. Dyn Games Appl 10, 555–572 (2020). https://doi.org/10.1007/s13235-019-00333-z
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DOI: https://doi.org/10.1007/s13235-019-00333-z