Hiring for An Uncertain Task: Joint Design of Information and Contracts

In this paper, we initiate the computational problem of jointly designing information and contracts. We consider three possible classes of contracts with decreasing flexibility and increasing simplicity: ambiguous contracts, menus of explicit contracts and explicit single contract. Ambiguous contracts allow the principal to conceal the applied payment schemes through a contract that depends on the unknown state of nature, while explicit contracts reveal the contract prior to the agent's decision. Our results show a trade-off between the simplicity of the contracts and the computational complexity of the joint design. Indeed, we show that an approximately-optimal mechanism with ambiguous contracts can be computed in polynomial time. However, they are convoluted mechanisms and not well-suited for some real-world scenarios. Conversely, explicit menus of contracts and single contracts are simpler mechanisms, but they cannot be computed efficiently. In particular, we show that computing the optimal mechanism with explicit menus of contracts and single contracts is APX-Hard. We also characterize the structure of optimal mechanisms. Interestingly, direct mechanisms are optimal for both the most flexible ambiguous contracts and the least flexible explicit single contract, but they are suboptimal for that with menus of contracts. Finally, motivated by our hardness results, we turn our attention to menus of linear contracts and single linear contracts. We show that both the problem of computing the optimal mechanism with an explicit menu of linear contracts and an explicit single linear contract admits an FPTAS.