We study the existence of different notions of values in two-person zero-sum repeatedgames where the state evolves and players receive signals. We provide some examplesshowing 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 apublic signal including the actions played. We prove also two other positive results withoutassumptions on the signaling structure: the existence of the sup-value and the existence ofthe uniform value in recursive games with non-negative payoffs.
Annals of Applied Probability, 2016