Incomplete regulation, market competition and collusion

Regulators often do not regulate all firms competing in a given sector. Due to product substitutability, unregulated competitors have incentives to bribe regulated firms to have them overstate their costs and produce less, thereby softening competition. The best collusion-proof contract entails distortions both for inefficient and efficient regulated firms (distortion ‘at the top’). But a contract inducing active collusion may do better by allowing the regulator to ‘team up’ with the regulated firm to indirectly tax its competitor. The best such contract is characterized. It is such that the unregulated firm pays the regulated one to have it truthfully reveals its inefficiency. We finally compare those contracts