Guessing a Random Function and Repeated Games in Continuous Time

We study a game where one player selects a random function, and the other has to guess that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to continuous-time repeated games played with mixed strategies with delay, identify good responses of a player to any profile of her opponents, and show that the minmax value coincides with the minmax value in pure strategies of the one-shot game.