I think that's a very cool idea. I haven't encountered it explicitly before, but I am reminded of two different video games that use time as a gimmick in interesting ways.
One is "The Talos Priciple", which is a puzzle game with a strong philosophical theme. In some of the later puzzles you need two characters to solve the puzzles, but you only have yourself. However, you do have a "record your actions" device. So you solve some of the puzzles, then play back your actions and interact with yourself to solve the puzzle. So past you helps current you solve a problem.
I forget the name of the other one, but it's essentially a shooter. You start each level swarmed by way too many enemies that you must shoot to kill. When you die, the level starts over with all of the same enemies. But the "ghost" of your last attempt is also there and repeats everything you just did. So now you have past you and current you trying to destroy all of the bad guys. If you die again, then another past you is there to help. This continues until you beat the level.
Posted April 9th