I'm not convinced by 1. You know your universe already exists. Why would there be another identical universe with a you who wants to travel across dimensions to give you a sandwich? Did he receive his own sandwich from another you from yet a third dimension and now needs to pass the favour on? If you don't feel like giving yourself a sandwich, why would he?
It may be that at the moment you chose to go back to the past, a new universe with a new past is created and anything you do to alter the past doesn't affect your original universe.
My paragraph about explains why...
thaluikhain said:
Though, most sci-fi does this really badly. They might have time travel as a gimmick, but they'll avoid dealing with it to any great degree.
It's very difficult to create a time-travel story that is completely watertight and also investigates the potential issue with time travel in a believable way.
The issue with 2 is when does it blink out of existence? In 2014 or 2016? It might be better to say that such a universe could never have existed in the first place (If we think that everything that happens in the universe is determined by its starting conditions). Imagine that we know you received a sandwich from your future self. Instead of simply deciding not to go back in time you decide to flip a coin to see if you will go back or not. Since we know you did, the result of that coin flip must come up heads. Suppose that now you decide to flip two coins and only go back if both of them are heads. Again they must both be heads. Add as many coins as you want the result should still be the same, however as you start to get to infinitely small possibilities the chances of it being a clone/robot/other strangeness I mentioned becomes more and more likely relatively to the possibility getting the right number of heads. I imagine writing a story where time travel becomes as cheap as flying abroad and everyone can do it. In this reality the chances of such an Earth existing without paradox quickly becomes much more unlikely than some devastating calamity wipes out the human population.
Number 3 is of course the most likely.