Treatment Allocation with Strategic Agents

TL;DR

This paper investigates how to optimally allocate treatments when individuals can strategically modify their behavior, proposing a Bayesian Optimization method that accounts for strategic incentives without relying on parametric models.

Contribution

It introduces a novel treatment allocation framework considering strategic behavior and develops a sequential Bayesian Optimization approach to find optimal policies.

Findings

Optimal treatment rules can involve randomization under strategic behavior

The proposed method converges to the optimal rule without parametric assumptions

Strategic incentives significantly alter treatment allocation strategies

Abstract

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.