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Limit optimal trajectories in zero-sum stochastic games

Sorin, Sylvain; Vigeral, Guillaume (2019), Limit optimal trajectories in zero-sum stochastic games, Dynamic Games and Applications, p. 1-18. 10.1007/s13235-019-00333-z

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01959326
Date
2019
Journal name
Dynamic Games and Applications
Publisher
Springer
Pages
1-18
Publication identifier
Metadata
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Author(s)
Sorin, Sylvain
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Vigeral, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Zero-sum; Stochastic game; Absorbing game