Contests With Doping

Doping, or the use of illegal performance-enhancing drugs, is an epidemic problem in sports ranging from the Olympics to high school athletics. This article presents a theoretical model of doping use in a contest environment. The authors show that, under fairly general conditions, the minimal frequency of random testing to prevent doping use increases in the number of contestants. The presence of even a small penalty, in addition to expulsion from the contest, makes random testing more effective, especially in large contests. For a given testing frequency, the minimal penalty to prevent doping can be nonmonotonic in the number of contestants.