The Infinite Versus the Finite Game

Time works differently in football because the time on the ticker there does not equal the exact length of the game. Reproduction is something that seems to be designed to go on as long as it can and just keep the game going. But say in a more finite contest between two stags fighting for the right to mate with a female in the area, there is a winner and a loser. There's no way to win the game of reproduction.