Limit optimal trajectories in zero-sum stochastic games

Sorin, Sylvain; Vigeral, Guillaume

Sorin, Sylvain; Vigeral, Guillaume (2020), Limit optimal trajectories in zero-sum stochastic games, Dynamic Games and Applications, 10, 2, p. 555-572. 10.1007/s13235-019-00333-z

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01959326

Date

2020

Journal name

Dynamic Games and Applications

Volume

Number

Publisher

Springer

Pages

555-572

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