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On values of repeated games with signals

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Article
Author/s: 
Hugo Gimbert, Jérôme Renault, Sylvain Sorin, Xavier Venel, and Wiesław Zielonka
The Annals of Applied Probability
Issue number: 
Volume 26, Number 1
Year: 
2016
Journal pages: 
402-424
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 supsup value in any game and the existence of the uniform value in recursive games with nonnegative payoffs.
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