We study hidden-action principal-agent problems with multiple agents. These are problems in which a principal commits to an outcome-dependent payment scheme in order to incentivize some agents to take costly, unobservable actions that lead to favorable outcomes. Previous works on multi-agent problems study models where the principal observes a single outcome determined by the actions of all the agents. Such models considerably limit the contracting power of the principal, since payments can only depend on the joint result of all the agents' actions, and there is no way of paying each agent for their individual result. In this paper, we consider a model in which each agent determines their own individual outcome as an effect of their action only, the principal observes all the individual outcomes separately, and they perceive a reward that jointly depends on all these outcomes. This considerably enhances the principal's contracting capabilities, by allowing them to pay each agent on the basis of their individual result. We analyze the computational complexity of finding principal-optimal contracts, revolving around two newly-introduced properties of principal's rewards, which we call IR-supermodularity and DR-submodularity. Intuitively, the former captures settings with increasing returns, where the rewards grow faster as the agents' effort increases, while the latter models the case of diminishing returns, in which rewards grow slower instead. These two properties naturally model two common real-world phenomena, namely diseconomies and economies of scale. In this paper, we first address basic instances in which the principal knows everything about the agents, and, then, more general Bayesian instances where each agent has their own private type determining their features, such as action costs and how actions stochastically determine individual outcomes.

翻译：本文研究具有多个智能体的隐藏行动委托-代理问题。在此类问题中，委托人基于结果制定报酬方案以激励智能体采取有利但不可观测的高成本行动。以往关于多智能体问题的研究主要采用委托人观察由全体智能体行为共同决定的单一结果的模型。这种模型显著限制了委托人的缔约能力，因为报酬只能依赖于所有智能体行动的共同结果，而无法根据每个智能体的个体成果进行支付。本文提出一种新型模型：每个智能体仅通过自身行为决定独立个体结果，委托人可分别观测所有个体结果，并根据这些结果获得联合收益。该模型通过允许委托人基于个体成果支付报酬，显著增强了缔约能力。我们分析了求解委托人最优合同的计算复杂度，核心围绕委托人收益的两个新性质——IR-超模性与DR-子模性。直观而言，前者刻画收益递增环境（智能体努力增加时收益增速加快），后者建模收益递减情形（收益增速减缓）。这两个性质自然对应现实中的两类常见现象：规模不经济与规模经济。本文首先解决委托人完全掌握智能体信息的基准场景，进而拓展至更一般的贝叶斯场景——每个智能体拥有决定其特征（如行动成本及行动对个体结果的随机影响）的私有类型。