Causal Inference from Competing Treatments

TL;DR

This paper develops a game-theoretic framework for causal inference in settings with competing treatments, optimizing budget allocation to minimize estimation error and analyzing equilibrium behavior.

Contribution

It introduces a tractable approximation for causal effect estimation under competition, linking game theory and causal inference to find equilibrium strategies.

Findings

Existence of a pure Nash equilibrium in the proposed model

Approximate equilibrium aligns with minimizing estimation error

Framework applicable to various competitive treatment scenarios

Abstract

Many applications of RCTs involve the presence of multiple treatment administrators -- from field experiments to online advertising -- that compete for the subjects' attention. In the face of competition, estimating a causal effect becomes difficult, as the position at which a subject sees a treatment influences their response, and thus the treatment effect. In this paper, we build a game-theoretic model of agents who wish to estimate causal effects in the presence of competition, through a bidding system and a utility function that minimizes estimation error. Our main technical result establishes an approximation with a tractable objective that maximizes the sample value obtained through strategically allocating budget on subjects. This allows us to find an equilibrium in our model: we show that the tractable objective has a pure Nash equilibrium, and that any Nash equilibrium is an approximate equilibrium for our general objective that minimizes estimation error under broad conditions. Conceptually, our work successfully combines elements from causal inference and game theory to shed light on the equilibrium behavior of experimentation under competition.