Let's say a tournament decides to have special consolation prizes for players who finish in the 20th, 30th, 40th, and 50th positions. It does this to give incentive to players to keep playing all rounds even if they don't have a chance of finishing in the top 10, who would get the normal prizes.
Now suppose player X playing the last round calculates that if he now resigns, he finishes exactly 20th, so he resigns. However, his opponent Y calculates that if he resigns now, he finishes 30th. Both players have incentive to resign. So as soon as X resigns, Y resigns as well.
So what is the result of the game?