A theory of antitrust enforcement game

We analyze a situation where an antitrust authority delegates to an audit inspector the mission of gathering the sufficient information to condemn a cartel. The authority has two instruments at her disposal: rewarding the inspector with a proportion of the collected fine or providing him with information which enhances the probability of the success of the prosecution. More precisely, we explore the efficiency consequences of a contest between the audit inspector and the cartel. Both of them bid to win the contest by expending efforts. We show that the race issue depends positively on the financial incentives proposed to the inspector but the impact of an increase of the level of the fine, to be paid once an illegal agreement is detected, is ambiguous. Moreover, we show that the optimal combination of the two instruments consists in two regimes. When the marginal cost of providing the relevant information is relatively high, the antitrust authority equally shares the collected fine and does not provide the inspector with any information. Conversely, when this marginal cost is relatively small, the authority uses the two instruments. She has to provide him with the maximum level of information consistent with winning the contest with certainty