Treatment Allocation with Strategic Agents

There is increasing interest in allocating treatments based on observed individual characteristics: examples include targeted marketing, individualized credit offers, and heterogeneous pricing. Treatment personalization introduces incentives for individuals to modify their behavior to obtain a better treatment. Strategic behavior shifts the joint distribution of covariates and potential outcomes. The optimal rule without strategic behavior allocates treatments only to those with a positive conditional average treatment effect. With strategic behavior, we show that the optimal rule can involve randomization, allocating treatments with less than 100% probability even to those who respond positively on average to the treatment. We propose a sequential experiment based on Bayesian optimization that converges to the optimal treatment rule without parametric assumptions on individual strategic behavior. This paper was accepted by Vivek Farias, data science. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.01629 .