A 2-Person Game with Lack of Information on 1½ Sides

We consider a repeated 2-person 0-sum game with incomplete information about the pay-off matrix. Player I (maximizer) knows the real pay-off matrix but he is uncertain about the beliefs of his opponent. We show that in this case the Aumann-Maschler results on incomplete information on one side no longer hold. In particular such a game will not have a value in general, in spite of the fact that one player is fully informed about the state of nature.