Agree with others re: you get to pick, but! we do (sort of) have a way for you to figure this out experimentally. (It wouldn't surprise me if someone has actually run this experiment in real life, I just don't have time to search right now. If anyone finds an existing real experiment please edit it in here.)
Create a game. Add lag so that choices are visible immediately but only take effect in game play after some duration. When there's no lag the game represents the current state of real life. When the lag only happens to one person, that represents the other person having precognition. When the lag happens to both people that represents both people having precognition. You can run this as, perhaps, a table top game with choices written down or represented by cards, or you can run it as a thought experiment in your head, and see how different parameters (how far in advance can you see, how can "future" choices be changed?) change the gameplay. (Perhaps precognition is fuzzy, you have to play as similar card as to what you indicated your plan was but not the exact same card...or one person is better at being un-precognible than the other so they have a wider range of choices...etc.)