Individualized Treatment Allocation in Sequential Network Games

TL;DR

This paper presents a method for optimizing treatment assignments in sequential network games to maximize social welfare, using variational approximations and greedy algorithms, demonstrated through simulations and real data.

Contribution

It introduces a novel approach combining variational approximation and greedy optimization for treatment allocation in complex sequential decision games.

Findings

The method achieves significant welfare gains in simulations.

The approach provides a welfare regret bound for the approximation.

Empirical application shows practical effectiveness with Indian microfinance data.

Abstract

Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We implement our proposed method in simulation exercises and an empirical application using the Indian microfinance data (Banerjee et al., 2013), and show it delivers significant welfare gains.