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February 2016 On values of repeated games with signals
Hugo Gimbert, Jérôme Renault, Sylvain Sorin, Xavier Venel, Wiesław Zielonka
Ann. Appl. Probab. 26(1): 402-424 (February 2016). DOI: 10.1214/14-AAP1095


We study the existence of different notions of value in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in general. Then we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We also prove two other positive results without assumptions on the signaling structure: the existence of the $\sup$ value in any game and the existence of the uniform value in recursive games with nonnegative payoffs.


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Hugo Gimbert. Jérôme Renault. Sylvain Sorin. Xavier Venel. Wiesław Zielonka. "On values of repeated games with signals." Ann. Appl. Probab. 26 (1) 402 - 424, February 2016.


Received: 1 July 2014; Revised: 1 December 2014; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1332.91023
MathSciNet: MR3449322
Digital Object Identifier: 10.1214/14-AAP1095

Primary: 91A20
Secondary: 60G35, 91A05, 91A15

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 1 • February 2016
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