Limit Optimal Trajectories in Zero-Sum Stochastic Games

Sylvain Sorin and Guillaume Vigeral ()
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Guillaume Vigeral: Université Paris-Dauphine, PSL Research University

Dynamic Games and Applications, 2020, vol. 10, issue 2, No 11, 555-572

Abstract: Abstract We consider zero-sum stochastic games. For every discount factor $$\lambda $$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 $$t\in [0,1]$$t∈[0,1], under $$\varepsilon $$ε-optimal strategies. A limit optimal trajectory is defined as an accumulation point as ($$\lambda , \varepsilon )$$λ,ε) tend to 0. We study existence, uniqueness and characterization of these limit optimal trajectories for compact absorbing games.

Keywords: Zero-sum; Stochastic game; Absorbing game (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00333-z

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