Multi-agent contracting with countervailing incentives and limited liability

We consider a principal who deals with two privately informed agents protected by limited liability. Their technologies are such that the fixed costs decline with the marginal costs (the types), which are correlated. Because of these technological features, agents display countervailing incentives to misrepresent type. We show that, with high liability, the first-best outcome can be effected for any type if (1) the fixed cost is non-concave in type, under the contract that yields the smallest feasible loss to agents; (2) the fixed cost is not very concave in type, under the contract that yields the maximum sustainable loss to agents. We further show that, with low liability, the first-best outcome is still implemented for a non-degenerate range of types if the fixed cost is less concave in type than some given threshold, which tightens as the liability reduces. The optimal contract entails pooling otherwise..