The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 1 (2016), 402-424.
On values of repeated games with signals
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.
Ann. Appl. Probab., Volume 26, Number 1 (2016), 402-424.
Received: July 2014
Revised: December 2014
First available in Project Euclid: 5 January 2016
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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