The Determinacy of Infinite Games with Eventual Perfect Monitoring, Proceedings of the American Mathematical Society
An infinite two-player zero-sum game with a Borel winning set, in which the opponent's actions are monitored eventually but not necessarily immediately after they are played, admits a value. The proof relies on a representation of the game as a stochastic game with perfect information, in which Nature operates as a delegate for the players and performs the randomizations for them.
Shmaya, Eran. 2011. The Determinacy of Infinite Games with Eventual Perfect Monitoring. Proceedings of the American Mathematical Society. 139: 3665-3678.