In this paper we initiate the study of ambiguous contracts, capturing many real-life scenarios where agents engage in contractual relations that leave some degree of uncertainty. Our starting point is the celebrated hidden-action model and the classic notion of a contract, where the principal commits to an outcome-contingent payment scheme for incentivizing an agent to take a costly action. An ambiguous contract generalizes this notion by allowing the principal to commit to a set of two or more contracts, without specifying which of these will be employed. A natural behavioral assumption in such cases is that the agent engages in a max-min strategy, maximizing her expected utility in the worst case over the set of possible contracts. We show that the principal can in general gain utility by employing an ambiguous contract, at the expense of the agent's utility. We provide structural properties of the optimal ambiguous contract, showing that an optimal ambiguous contract is composed of simple contracts. We then use these properties to devise poly-time algorithms for computing the optimal ambiguous contract. We also provide a characterization of non-manipulable classes of contracts - those where a principal cannot gain by employing an ambiguous contract. We show that linear contracts - unlike other common contracts - are non-manipulable, which might help explain their popularity. Finally, we provide bounds on the ambiguity gap - the gap between the utility the principal can achieve by employing ambiguous contracts and the utility the principal can achieve with a single contract

翻译：本文首次研究了模糊合同，这一概念捕捉了现实场景中代理人参与合同时存在不确定性情形。我们以经典的隐藏行动模型和传统合同概念为起点——即委托人承诺基于结果支付方案以激励代理人采取高成本行动。模糊合同将此概念推广至委托人可承诺包含两个或以上合同的集合，但未明确具体采用其中哪一个。在此类情形下，一个自然的行为学假设是代理人采取极大极小策略，即在可能合同集合的最坏情况下最大化其期望效用。研究表明，委托人通常可通过采用模糊合同获益，而代价是牺牲代理人的效用。我们给出了最优模糊合同的结构性质，证明其可由若干简单合同构成。基于这些性质，我们设计了计算最优模糊合同的多项式时间算法。此外，我们刻画了不可操纵的合同类别——即委托人无法通过采用模糊合同获益的情形。我们证明线性合同（不同于其他常见合同）具有不可操纵性，这或许有助于解释其普遍性。最后，我们给出了模糊性差距的界限——即委托人通过模糊合同与单一合同所能获得的效用差值。