On Cheating and Whistle-Blowing

We study the role of whistle-blowing in the following inspection game. Two agents who compete for a valuable prize can either behave legally or illegally. After the competition, a controller investigates the agents' behavior. This control game has a unique equilibrium in mixed strategies. We then add a whistle-blowing stage, where the controller asks the loser to blow the whistle. This extended game has a unique perfect Bayesian equilibrium in which only a cheating loser accuses the winner of cheating and the controller tests the winner if and only if the winner is accused of cheating. Whistle-blowing reduces the frequencies of cheating, is less costly in terms of test frequencies, and leads to a strict Pareto-improvement if punishments for cheating are sufficiently large.