Abstract
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, andleads to a strict Pareto-improvement if punishments for cheating are suffciently large.
Highlights
Our goal is to give the controller the possibility to make use of this private information. We model this by adding an additional stage to the control game, which we call whistle-blowing stage
The solution concept for the game we study is the Perfect Bayesian (Nash) Equilibrium (PBE)
We have analyzed the role of whistle-blowing in a game with two agents and a controller
Summary
If only one player plays the illegal strategy (“cheats”), he wins with certainty According to these assumptions, cheating is a dominant strategy. The controller faces the problem that the agents’ behavior is not publicly observable such that detecting cheating imposes costs. Even if it pays to control an agent’s behavior if there is a high probability that he cheats, it will not pay to control an agent if he is known to play legally. In the unique equilibrium of the control game, both agents randomize between cheating and not cheating.
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