Failure to collude in the presence of asymmetric information

In this paper, we design the optimal contract when two agents can collude under asymmetric information. They have correlated types, produce complementary inputs and are protected by limited liability. Therefore, a joint manipulation of reports allows them to internalize informational and productive externalities. We show that by taking advantage of the transaction costs created by asymmetric information, even though they collude, the principal can achieve the outcome without collusion regardless of the sign and the degree of correlation. In particular, the principal can implement a non-monotonic quantity schedule in a collusion-proof way while this is impossible if collusion occurs under complete information.