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.

翻译：基于观测到的个体特征进行处理的分配日益引起关注：例如定向营销、个性化信用报价及差异化定价。处理的个性化会激励个体通过调整其行为以获取更优的处理。策略性行为改变了协变量与潜在结果的联合分布。在无策略性行为的情况下，最优规则仅将处理分配给条件平均处理效应为正的个体。我们证明，在存在策略性行为时，最优规则可能涉及随机化——即使是对处理平均响应为正的个体，也以低于100%的概率分配处理。我们提出一种基于贝叶斯优化的序贯实验方法，该方法无需对个体策略性行为进行参数假设，即可收敛至最优处理规则。