In the conventional principal-agent problem, a principal delegates a task to an agent and formulates a contract to incentivize the agent's actions on behalf of the principal. However, this framework overlooks the information that is possibly available during the delegation process in some scenarios. To address this limitation, we propose a novel model that incorporates multiple intermediate states to capture such information revealed during the delegation. Furthermore, to evaluate the impact of the information embedded in these intermediate states, we introduce two distinct contracts: the pay-halfway contract, which provides payments based not only on final outcomes but also on intermediate states, and the terminate-halfway contract, which allows the principal to terminate the delegation process upon encountering undesirable intermediate states. This leads to the question of whether and how these contract types can leverage intermediate-state information? In particular, we ask: Can these contract types outperform standard contracts, and if so, when and to what extent? We answer the first question affirmatively and provide several important insights regarding the second, shedding light on the circumstances in which intermediate-state-aware contracts yield substantial advantages.

翻译：在传统的委托-代理问题中，委托人将任务委托给代理人，并制定契约以激励代理人代表委托人采取行动。然而，这一框架忽略了在某些场景下委托过程中可能可用的信息。为解决这一局限性，我们提出了一种新颖的模型，该模型引入了多个中间状态，以捕捉委托过程中揭示的此类信息。此外，为评估这些中间状态所嵌入信息的影响，我们引入了两种不同的契约：中途支付契约，它不仅基于最终结果提供报酬，还基于中间状态；以及中途终止契约，它允许委托人遇到不理想的中间状态时终止委托过程。这引出了一个问题：这些契约类型是否以及如何利用中间状态信息？具体而言，我们询问：这些契约类型能否优于标准契约，如果能，在何时以及何种程度上？我们对第一个问题给出了肯定回答，并就第二个问题提供了若干重要见解，揭示了中间状态感知契约能够带来显著优势的情形。