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Constant payoff in stochastic games

Oliu-Barton, Miquel; Ziliotto, Bruno (2018), Constant payoff in stochastic games. https://basepub.dauphine.fr/handle/123456789/20711

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1811.04518.pdf (397.0Kb)
Type
Document de travail / Working paper
Date
2018
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
31
Metadata
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Author(s)
Oliu-Barton, Miquel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ziliotto, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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)
Subjects / Keywords
zero-sum stochastic games

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