Doping, the Inspection Game, and Bayesian Monitoring

Abstract

Doping tests create a signal of whether the athlete has acted fraudulently. If the signal is costly, but perfect, then the doping enforcer and the athlete play an "inspection game," which has no equilibrium in pure strategies. This paper presents a modification of that game: The "Bayesian monitoring" model rests on the assumption that signals are available without cost, but vulnerable to two types of errors. Both the inspection game and the new model assume that the enforcer is interested in fostering compliant behavior and making correct decisions. While the inspection game has only one mixed strategy equilibrium, three perfect Bayesian equilibria exist under Bayesian monitoring (one in pure strategies, two in mixed). These outcomes can be described with respect to their punishment styles: tyrannic, draconian, and lenient. The equilibrium probability of compliant behavior is lowest under a tyrannic regime, and highest under a lenient regime. Total deterrence of doping behavior is impossible. An increase of punishment does not increase the probability of compliant behavior.