  We consider a version of the open-open game, indicating its connections with
universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is
universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable,
then the hyperspace exp(Y) with the Vietoris topology is I-favorable, and hence
universally Kuratowski-Ulam, (Theorems 6 and 9). Notions of uK-U and uK-U*
spaces are compared.
