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.

翻译：本文首次提出了信息与合同联合设计的计算问题。我们考虑了三种灵活性递减、简洁性递增的合同类型：模糊合同、显式合同菜单及显式单一合同。模糊合同允许委托方通过依赖于未知自然状态的合同来隐藏所采用的支付方案，而显式合同则在代理方决策前公开合同条款。研究结果表明，合同的简洁性与联合设计的计算复杂度之间存在权衡关系。具体而言，我们证明具有模糊合同的近似最优机制可在多项式时间内计算得出，但这类机制结构复杂且不适用于某些现实场景。相反，显式合同菜单与单一合同是更简洁的机制，但无法被高效计算。特别地，我们证明了计算具有显式合同菜单及单一合同的最优机制属于APX难问题。同时，我们刻画了最优机制的结构特征。有趣的是，直接机制对于最灵活的模糊合同和最不灵活的显式单一合同都是最优的，但对于合同菜单机制则非最优。最后，基于计算困难性结果，我们将研究重点转向线性合同菜单与单一线性合同。研究表明，计算具有显式线性合同菜单的最优机制问题及显式单一线性合同的最优机制问题均存在完全多项式时间近似方案（FPTAS）。