In this paper we introduce a model 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：本文提出了一种模糊合同模型，该模型捕捉了许多现实场景中代理人参与存在一定程度不确定性的合同关系。我们的出发点是最著名的隐藏行动模型和经典合同概念，其中委托人承诺依据结果支付计划，以激励代理人采取高成本行动。模糊合同对此概念进行了泛化，允许委托人承诺一组两个或更多合同，而不指定将使用其中哪一个。在此类情况下，一个自然的行为假设是代理人采取最小化最大损失策略，即在最坏情况下（针对可能的合同集）最大化其期望效用。我们证明，委托人通常可以通过采用模糊合同来获得效用，但以牺牲代理人的效用为代价。我们给出了最优模糊合同的结构性质，表明最优模糊合同由简单合同组成。随后，我们利用这些性质设计了计算最优模糊合同的多项式时间算法。我们还给出了不可操纵合同类的刻画——即委托人无法通过采用模糊合同获得收益的合同类。我们证明，线性合同（区别于其他常见合同）是不可操纵的，这或许有助于解释其普遍性。最后，我们给出了模糊度差距的界限——即委托人通过模糊合同所能获得的效用与通过单一合同所能获得的效用之间的差距。