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Constant payoff in zero-sum stochastic games

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1811.04518.pdf (397.2Kb)
Date
2018
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01936572
Dewey
Analyse
Sujet
zero-sum stochastic games
URI
https://basepub.dauphine.fr/handle/123456789/18681
Collections
  • CEREMADE : Publications
Metadata
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Author
Oliu-Barton, Miquel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ziliotto, Bruno
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
31
Abstract (EN)
In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a random variable representing the state of nature. The total payoff is the discounted sum of the stage payoffs. Assume that the players are very patient and use optimal strategies. We then prove that, at any point in the game, players get essentially the same expected payoff: the payoff is constant. This solves a conjecture by Sorin, Venel and Vigeral (2010). The proof relies on the semi-algebraic approach for discounted stochastic games introduced by Bewley and Kohlberg (1976), on the theory of Markov chains with rare transitions, initiated by Friedlin and Wentzell (1984), and on some variational inequalities for value functions inspired by the recent work of Davini, Fathi, Iturriaga and Zavidovique (2016)

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