We introduce and study a computational version of the principal-agent problem -- a classic problem in Economics that arises when a principal desires to contract an agent to carry out some task, but has incomplete information about the agent or their subsequent actions. The key challenge in this setting is for the principal to design a contract for the agent such that the agent's preferences are then aligned with those of the principal. We study this problem using a variation of Boolean games, where multiple players each choose valuations for Boolean variables under their control, seeking the satisfaction of a personal goal, given as a Boolean logic formula. In our setting, the principal can only observe some subset of these variables, and the principal chooses a contract which rewards players on the basis of the assignments they make for the variables that are observable to the principal. The principal's challenge is to design a contract so that, firstly, the principal's goal is achieved in some or all Nash equilibrium choices, and secondly, that the principal is able to verify that their goal is satisfied. In this paper, we formally define this problem and completely characterise the computational complexity of the most relevant decision problems associated with it.

翻译：我们引入并研究经济学中经典委托-代理问题的计算版本——该问题发生于委托人希望雇佣代理人执行某项任务，但对其代理人或其后续行为缺乏完全信息时。该场景的核心挑战在于，委托人需要为代理人设计一份合同，使得代理人的偏好与委托人保持一致。我们通过布尔博弈的变体研究该问题：在布尔博弈中，多个参与者各自为其控制的布尔变量选择赋值，寻求满足以布尔逻辑公式表示的个人目标。在我们的设定中，委托人仅能观测到部分变量，并根据代理人在可观测变量上的赋值选择奖励方案。委托人的挑战在于设计合同，使得：其一，委托人的目标在某种或全部纳什均衡选择中得以实现；其二，委托人能够验证其目标是否得到满足。本文正式定义了该问题，并完整刻画了其相关核心决策问题的计算复杂性。