Strategyproof Decision-Making in Panel Data Settings and Beyond

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.