Strategyproof Decision-Making in Panel Data Settings and Beyond

Abstract

We consider the problem of decision-making using panel data, in which a decision-maker gets noisy, repeated measurements of multiple units (or agents). We consider the setup used in synthetic control methods, 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. Unlike this classical setting, we permit the units generating the panel data to be strategic, i.e. units may modify their pre-intervention outcomes in order to receive a more desirable intervention. The principal's goal is to design a strategyproof intervention policy, i.e. a policy that assigns units their utility-maximizing interventions despite their potential strategizing. We first identify a necessary and sufficient condition under which a strategyproof intervention policy exists, and provide a strategyproof mechanism with a simple closed form when one does exist. Along the way, we prove impossibility results for strategic multiclass classification, a natural extension of the well-studied (binary) strategic classification problem to the multiclass setting, which may be of independent interest. When there are two interventions, we establish that there always exists a strategyproof mechanism, and provide an algorithm for learning such a mechanism. For three or more interventions, we provide an algorithm for learning a strategyproof mechanism if there exists a sufficiently large gap in the principal's rewards between 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.