Doping, or the use of illegal performance-enhancing drugs, is an epidemic problem in sports ranging from the Olympics to high school athletics. Sports organizations have been trying numerous approaches to discouraging these activities. This paper presents a theoretical model of doping in a winner-take-all contest environment to help investigate the efficiency of anti-doping enforcement policies. We show that, under fairly general conditions, the optimal frequency of random testing increases in the number of tournament participants. We also find that the presence of even a very small penalty, in addition to expulsion from the contest, makes random testing more effective, especially in large tournaments. Additionally, we find that for a given testing frequency, the optimal level of the penalty can be nonmonotonic in the number of players.
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