The author considers infinitely repeated two-person zero-sum games of incomplete information in which the signals are the same for both players and consist of probability distributions on a given alphabet. He shows that such games have a value.
Forges, F. (1982). Infinitely repeated games of incomplete information: symmetric case with random signals. International Journal of Game Theory, 11(3-4), 203-213. https://doi.org/10.1007/BF01755730 (Original work published 1982)