Having played and enjoyed bioshock infinite twice (hard and 1999) I have developed a theory about the ending of the game. I have a theory that the end of the game doesnt just speak to us about the endless realities within the game but is also trying to reach out into our living rooms and speak to us as gamers. There are massive spoilers ahead so read on at your descretion.
You will reach a point at the end where you will be outside a lighthouse looking at an endless sea of lighthouses. Every one of these represent a different dimension, everyone of them is a door to a different world, but the game is clear in stating that there are constants. This means that while in every world different things happen its still the same world. That is just like a video game. We all play differently and use different methods but were all playing the same game.
Rapture was not accidentaly thrown into this game. This is an obvious reference to bioshock but the reason it was there was to show you that you are about to go full circle. The end of one game (bioshock infinite) at the beggining of another (bioshock at the welcome center)
Elizabeth references both bioshock games when she says "there is always a lighthouse, there is always a man, there is always a city". She left the names out of that sentence to deliberately relate that she was not just speaking about their story but both games in general.
Bioshock infinite might be trying to tell us that the only way for the stories in games not to exist is not to play. If you recall booker is drowned before he can make a decision that starts either path. After the credits we see booker wake up in his apartment on the day he gave anna up. He seemingly remembers his ordeal as he calls out her name. This booker should not exist having been drowned after wounded knee but it could signify that someone somewhere has turned a game on.
Thanks for reading.