We study the role of regulatory inspections in a contract design problem in which a principal interacts separately with multiple agents. Each agent's hidden action includes a dimension that determines whether they undertake an extra costly step to adhere to safety protocols. The principal's objective is to use payments combined with a limited budget for random inspections to incentivize agents towards safety-compliant actions that maximize the principal's utility. We first focus on the single-agent setting with linear contracts and present an efficient algorithm that characterizes the optimal linear contract, which includes both payment and random inspection. We further investigate how the optimal contract changes as the inspection cost or the cost of adhering to safety protocols vary. Notably, we demonstrate that the agent's compensation increases if either of these costs escalates. However, while the probability of inspection decreases with rising inspection costs, it demonstrates nonmonotonic behavior as a function of the safety action costs. Lastly, we explore the multi-agent setting, where the principal's challenge is to determine the best distribution of inspection budgets among all agents. We propose an efficient approach based on dynamic programming to find an approximately optimal allocation of inspection budget across contracts. We also design a random sequential scheme to determine the inspector's assignments, ensuring each agent is inspected at most once and at the desired probability. Finally, we present a case study illustrating that a mere difference in the cost of inspection across various agents can drive the principal's decision to forego inspecting a significant fraction of them, concentrating its entire budget on those that are less costly to inspect.

翻译：我们研究了监管检查在合同设计问题中的作用，其中委托人与多个代理人分别互动。每个代理人的隐藏行为包含一个维度，该维度决定他们是否采取额外成本高昂的步骤来遵守安全协议。委托人的目标是通过支付与有限随机检查预算相结合，激励代理人采取符合安全要求的行为，以最大化委托人的效用。我们首先关注具有线性合同的单代理人场景，并提出一种高效算法来刻画最优线性合同，该合同包括支付和随机检查。我们进一步研究了当检查成本或遵守安全协议的成本变化时，最优合同如何调整。值得注意的是，我们证明如果这些成本中的任何一个增加，代理人的补偿也会提高。然而，尽管检查概率随检查成本上升而降低，但它作为安全行动成本的函数表现出非单调行为。最后，我们探讨了多代理人场景，其中委托人的挑战是确定所有代理人之间检查预算的最佳分配。我们提出了一种基于动态规划的高效方法，以找到近似最优的合同间检查预算分配。我们还设计了一种随机顺序方案来确定检查员的分配，确保每个代理人最多被检查一次，且达到期望的检查概率。最后，我们通过案例研究表明，不同代理人之间检查成本的微小差异，就可能导致委托人决定放弃检查其中很大一部分代理人，而将全部预算集中在那些检查成本较低的代理人身上。