The Annals of Applied Probability

On values of repeated games with signals

Hugo Gimbert, Jérôme Renault, Sylvain Sorin, Xavier Venel, and Wiesław Zielonka

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 1 (2016), 402-424.

Dates
Received: July 2014
Revised: December 2014
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1452003243

Digital Object Identifier
doi:10.1214/14-AAP1095

Mathematical Reviews number (MathSciNet)
MR3449322

Zentralblatt MATH identifier
1332.91023

Subjects
Primary: 91A20: Multistage and repeated games
Secondary: 91A05: 2-person games 91A15: Stochastic games 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Keywords
Multistage game repeated games with signals repeated games with symmetric information Borelian evaluation limsup value uniform value

Citation

Gimbert, Hugo; Renault, Jérôme; Sorin, Sylvain; Venel, Xavier; Zielonka, Wiesław. On values of repeated games with signals. Ann. Appl. Probab. 26 (2016), no. 1, 402--424. doi:10.1214/14-AAP1095. https://projecteuclid.org/euclid.aoap/1452003243


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