Tournament theory

Posted by Cheng Soon Ong on July 22, 2010

A rubber tapper in Malaysia gets paid based on the amount of latex that they can collect each morning. Therefore, if she produces double as much latex, she would earn double as much money. This is what standard economic theory dictates, because if marginal differences in productivity were not rewarded, then it would be a profit opportunity for someone else. However, Swiss hero Roger Federer doesn't earn twice as much money if he hits double the number of tennis balls. The problem is that it is kind of hard to measure Roger Federer's productivity in an absolute sense, and hence we reward him by comparing him with other people and paying the better player more. About 30 years ago, Lazear and Rosen wrote an influential economics paper about tournament theory, which is based on the idea of relative differences in productivity.

Since then, it has been used to describe various economic systems; sport and entertainment being the most common examples. In fact, it also can be used to argue why bosses are overpaid. "The salary of the vice president acts not so much as motivation for the vice president as it does as motivation for the assistant vice presidents." This also results in the long tail of income distribution; a few people at the top makes a lot, and many people at the bottom make very little. Recently, articles in the New York times and the Atlantic about abolishing tenure has attracted lots of comments for and against the idea of tenure for academia. Since it is hard to measure the productivity of a scientist in absolute terms, we reward them by playing them against each other when looking for new faculty and promoting the current winner.

For software, the story is similar with a small twist. For example, when you look at the revenue of top App Store apps you see the characteristic long tail. Also for machine learning software, there are a few packages that get most of the users. Admittedly, currently the benefits of being the best piece of machine learning software is a bit dubious. However, the author of a new package can choose to publish software in a new category. This different category (real or imagined) allows a fledgling programmer to have a chance at being the top of the heap. Sometimes it is an old research area with a new name, or instead of being the most accurate, the software promises to be the fastest, etc. I'm not sure what tournament theory has to say when there are multiple tournaments. Perhaps someone who knows game theory can comment?