Zeno's Fight Club

You're in a 20m long hallway. There is an exit. You must reach the exit to win but you can only cross half of the remaining distance at a time. There's also other players trying to get to the exit and you can fight them but you can only be hurt for half of your remaining life per hit. Can you reach the end? Can anyone be killed? Is there cake beyond the exit? It's all very philosophical.

See the game at https://zeno.swiftausteity.com/