A new olympic sport
Two runners start on opposite sides of a track, both facing counterclockwise. At the gun, they both start running. The winner is the one who catches up with the other from behind.
I don't know if this has ever been tried, but I am curious about what kind of strategy would be successful - could a sprinter catch up with a marathoner before he got tired? It could also degenerate into a very slow walk around the track, as sometimes happens in velodrome pursuit races, or like the chasing around a table scene that happens in movies.
Since the race could last anywhere from minutes to days, it probably wouldn't play well on tv. Perhaps a team version? Or, you could just start 50 runners spaced evenly around the track, and when anyone gets passed, they lose. That would make it more tv friendly. In velodrome pursuit, there is a time limit, but for me, what I'm really interested in is seeing people run until they really can't run anymore.