  We prove that in a general zero-sum repeated game where the first player is
more informed than the second player and controls the evolution of information
on the state, the uniform value exists. This result extends previous results on
Markov decision processes with partial observation (Rosenberg, Solan, Vieille
2002), and repeated games with an informed controller (Renault 2012). Our
formal definition of a more informed player is more general than the inclusion
of signals, allowing therefore for imperfect monitoring of actions. We
construct an auxiliary stochastic game whose state space is the set of second
order beliefs of player 2 (beliefs about beliefs of player 1 on the true state
variable of the initial game) with perfect monitoring and we prove it has a
value by using a result of Renault 2012. A key element in this work is to prove
that player 1 can use strategies of the auxiliary game in the initial game in
our general framework, which allows to deduce that the value of the auxiliary
game is also the value of our initial repeated game by using classical
arguments.
