"The biggest problem we encountered in both games was the "spoiler": The player who was not in a position to win, but was in a position to determine the winner."I guess you are not a fan of Diplomacy (http://en.wikipedia.org/wiki/Diplomacy_(game)), either.
Most, if not all, games of more than two players where players have some free choice eventually boil down to "you can't win it alone. You need help or a blooper from your enemy"
And that is true in sports, too. In any distance running, starting at 800m, athletes collectively make a choice whether to run a fast race or a slow race with a very fast finish. A fast sprinter will not win a fast race, so runners with lower top speed will try to make a fast race. Still, they won't want to be running in the front, they rather have another runner with lower top speed burn energy doing that.
This gets more evident the longer the distance and the larger the advantage of running in the slipstream of an opponent. Road races in cycling are perhaps the ultimate example. If "the peloton" doesn't want you to win, you have to be extremely good _and_ lucky to win.