Statistical Treatment Rules under Social Interaction

TL;DR

This paper develops a framework for treatment assignment in social interaction settings, introducing a multinomial empirical success rule that is shown to be asymptotically optimal under a minimax regret criterion.

Contribution

It proposes a novel multinomial empirical success rule for treatment assignment under social interaction, extending Manski's rule, and proves its asymptotic optimality.

Findings

MES rule includes Manski's rule as a special case

Provides non-asymptotic bounds on expected utility

Proves asymptotic optimality of MES rule

Abstract

In this paper we study treatment assignment rules in the presence of social interaction. We construct an analytical framework under the anonymous interaction assumption, where the decision problem becomes choosing a treatment fraction. We propose a multinomial empirical success (MES) rule that includes the empirical success rule of Manski (2004) as a special case. We investigate the non-asymptotic bounds of the expected utility based on the MES rule. Finally, we prove that the MES rule achieves the asymptotic optimality with the minimax regret criterion.