## The Annals of Applied Probability

### On values of repeated games with signals

#### 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
Revised: December 2014
First available in Project Euclid: 5 January 2016

https://projecteuclid.org/euclid.aoap/1452003243

Digital Object Identifier
doi:10.1214/14-AAP1095

Mathematical Reviews number (MathSciNet)
MR3449322

Zentralblatt MATH identifier
1332.91023

#### 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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