This paper provides a game-theoretical analysis of the use by athletes of performance-enhancing drugs. We focus on a two-player game where players are heterogeneous and performances are subject to uncertainty. While the standard setup assumes these drugs increase maximum performances, we assume that they also increase the probability that a given athlete competes at his best possible level. This second effect drives the doping strategies alone, suggesting that focusing on the first effect leads to incorrect conclusions. Doping strategies are strategic complements for the top dog, whereas they are strategic substitutes for the underdog. We show that the top dog always dopes more than the underdog, and that the top dog will often prefer a world with doping than without it. We also argue that anti-doping tests may increase doping for the underdog, and that targeting such tests to the top dog provides incentive to dope for the underdog.
