The value of two-person zero-sum repeated games with incomplete information and uncertain duration

Fix a zero-sum repeated game Γ with incomplete information on both sides. It is known that the value of the infinitely repeated game Γ _∞ need not exist (Aumann and Maschler 1995). It is proved that any number between the minmax and the maxmin of Γ _∞ is the value of a long finitely repeated game Γ _n where players' information about the uncertain number of repetitions n is asymmetric.