So long as a ban is enforceable, large private athletic institutions—such as Major League Baseball and the National Collegiate Athletic Association—should not allow their athletes to take performance-enhancing drugs. The argument I present is game-theoretic: though each athlete prefers unilateral permission to dope over a universal ban, he also prefers a universal ban over universal permission to dope. That is because, while doping improves absolute measures of performance, it does not improve relative performance if many athletes dope. Large private athletic institutions should honour their athletes' preferences and should not enact any policy that gives only some athletes but not others permission to dope. Thus, they should ban doping. My paper examines and defends this game-theoretic argument. After explaining the argument, I compare it (favourably) to other arguments for the same conclusion. I then discuss whether the game-theoretic argument counterintuitively fails to justify banning some forms of doping (no), and whether it counterintuitively justifies banning things other than doping (also no). After arguing that a doping ban on game-theoretic grounds is neither wrongly paternalistic or nor wrongfully coercive, I end by discussing some limitations of the argument.