We propose a framework for decision-making in the presence of strategic agents with panel data, a standard setting in econometrics and statistics where one gets noisy, repeated measurements of multiple units. We consider a setup where there is a pre-intervention period, when the principal observes the outcomes of each unit, after which the principal uses these observations to assign a treatment to each unit. Our model can be thought of as a generalization of the synthetic controls and synthetic interventions frameworks, where units (or agents) may strategically manipulate pre-intervention outcomes to receive a more desirable intervention. We identify necessary and sufficient conditions under which a strategyproof mechanism that assigns interventions in the post-intervention period exists. Under a latent factor model assumption, we show that whenever a strategyproof mechanism exists, there is one with a simple closed form. In the setting where there is a single treatment and control (i.e., no other interventions), we establish that there is always a strategyproof mechanism, and provide an algorithm for learning such a mechanism. For the setting of multiple interventions, we provide an algorithm for learning a strategyproof mechanism, if there exists a sufficiently large gap in rewards between the different interventions. Finally, we empirically evaluate our model using real-world panel data collected from product sales over 18 months. We find that our methods compare favorably to baselines which do not take strategic interactions into consideration -- even in the presence of model misspecification. Along the way, we prove impossibility results for multi-class strategic classification, which may be of independent interest.

翻译：我们提出了一种在存在策略性代理且拥有面板数据时的决策框架，这是计量经济学和统计学中的标准设定，涉及对多个单位进行含噪重复测量。我们考虑以下设置：在干预前阶段，主理人观察每个单位的结果，随后利用这些观察结果为每个单位分配处理方案。我们的模型可视为合成控制与合成干预框架的泛化，其中单位（或代理）可能通过策略性地操纵干预前结果来获得更理想的干预。我们识别了在干预后阶段存在防策略机制的必要充分条件。在潜在因子模型假设下，我们证明：只要存在防策略机制，就存在一个具有简单闭式解的机制。对于单处理与单对照（即无其他干预）的设置，我们证实始终存在一个防策略机制，并给出了学习该机制的算法。针对多干预场景，若不同干预间的奖励存在足够大的差距，我们提供了学习防策略机制的算法。最后，我们使用18个月的产品销售真实面板数据对模型进行实证评估。结果表明，即使存在模型误设，我们的方法也显著优于未考虑策略交互的基线方法。此外，我们证明了多类别策略分类的不可行性结果，这本身可能具有独立研究价值。