On cheating and whistleblowing

We study the role of whistleblowing in the following inspection game. Two agents who compete for a prize can either behave legally or illegally. After the competition, a controller investigates the agents' behavior. This inspection game has a unique Bayesian equilibrium in mixed strategies. We then add a whistleblowing 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. Whistleblowing 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.