i think this is kind of the inverse of how some emulators that add remote play deal with network lag... they will predict what control the opponent will give for the current frame and display it, but then when they actually receive the real opponent control some number of frames later, they will go back to that frame and re-calculate based on knowing the actual control input for that frame, and then catch up to the current frame. That way the game isn't waiting for remote inputs to refresh the screen, but can then reconcile once all information is known.