When an inefficient competitor makes higher profit than its efficient rival

We consider a Cournot duopoly with strategic delegation, where quantities of firms are chosen by their managers. A firm can offer its manager one of the two incentive contracts: the profit incentive or the revenue incentive. We show that in this setting there are Nash equilibria in which an inefficient firm obtains higher profit than its efficient rival. This result continues to hold under a robust set of correlated equilibria.