Game Theory for Gymnastic Olympics
Website: http://www.nytimes.com/2008/08/06/sports/olympics/06scoring.html
The article describes how the point calculation system of gymnastics has evolved from receiving scores out of 10 points to a more complex system in which there is essentially no limit to the highest a gymnast can receive. The new score is based off of the level of difficulty of the gymnastic routines and how well the gymnast performs this routine. The level difficulty includes the difficulty of individual skills and tricks as well as connections between the tricks. The article describes the 2008 Olympic Champion, Nastia Liukin and her coach, and their responses to the new point system.
Nastia’s coach came up with an uneven bar routine that had a maximum of 7.7 points for its difficulty level (which does not include execution). This is consider a very high score for uneven bars. Game theory is applied to this. First the assumptions apply as everything the gymnasts care about are described by the payoffs, in that achieving a higher score, gives them a higher payoff. All of the gymnasts knows the rules of gymnastics and the tricks that are allowed in the competition. Furthermore, based on precious competitions, the gymnasts know what their competition is capable of doing. Lastly, all of the gymnasts desire to maximize their own scores, as seen by Nastia and her coach who came up with the routine. Assuming the execution for each gymnast is around the same, Nastia’s score for uneven bars should give a best response, and thus her routine should be a strictly dominant stategy.