Track Cycling
https://marginalrevolution.com/marginalrevolution/2012/08/olympic-game-theory.html
Game Theory and Nash Equilibriums in Olympic Track Cycling. In the Individual sprint track cycling event two riders start head to head and the first person to complete three laps of the track wins. As in the case for most types of sprint races, one would assume that each competitor would try to go as fast as they can. However, in sprint cycling this is not the case. An interesting phenomenon occurs in this event where rather than sprinting the whole time each cyclist usually ends up trying to go slower than other for the majority race. Each rider for the first two laps tries to maintain a position behind the other. Since you can’t cycle backwards, the race almost becomes about who can bike slower without tipping over. It is only near the last lap of the race that the two cyclists start sprinting.
This counterintuitive strategy can be explained through a Nash equilibrium. The key factor that creates this seemingly paradoxical strategy is the role of air resistance. Air resisted is the force posing the rider motions. It forms from the rider pushing molecules of air in front of them and friction as the air moves past them. The cyclist in the front experiences more air resistance. The cyclist in the rear can draft being the front rider reducing the resistance. Therefor the cyclist in the rear doesn’t have to use as much energy. This creates incentive to be in the rear for most of the race because you can safe up energy and in the final bit use that extra energy to pass the rider in front. This incentive is the same for each player so they both end up trying to be behind the other. Once going slow the person in front doesn’t want to speed up because as you speed up air resistance increases giving even more advantage to the person in the back.
For the majority of the race the two cyclists are stuck in this equilibrium. However, at a certain point the person in the back has to try and pass. This creates an almost separate game. Before each player had essentially the same role and so the same strategy. Near the end of the race the role of front and back become very different since the objective now is to be first. The strategy for the riders becomes when to break this equilibrium and sprint to the finish. The person in the rear wants to time it in such a way that once they attempt to pass they don’t give the other cyclist enough time to draft behind them and eventually regain their leading position. They also don’t want to wait too long as it takes a bit of time to overtake. The leading cyclist can either initiate the sprint to try and catch the other rider by surprise and hope they don’t get passed, or they can wait for the person in the rear to make the first move and hope they mistimed it. This is a much more complex game, but the effect is that for mast races the sprint end up being initiated by either rider usually around the last lap.