In this model, shareholders can use auditors' reports to contract with a privately-informed manager. Imperfect audit technology allows the auditor and the manager to collude. Auditors are useful when they have good information and the manager's liability is high. Expected maximum deterrence is not desirable and production is suboptimal, even with unbounded punishments. Raising the manager's punishment raises the bribe he may offer the auditor, which raises the cost of preventing collusion. The authors also distinguish internal auditors (costless but collusive) from external ones (costly but not collusive) and show that the optimal contract may specify random external audits. Copyright 1993 by The Econometric Society.
Kofman et al. (Sat,) studied this question.