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.