Robust Network Targeting with Multiple Nash Equilibria

TL;DR

This paper develops a robust method for designing treatment policies in large strategic games with multiple equilibria, ensuring welfare maximization despite equilibrium uncertainties.

Contribution

It introduces a novel approach that remains agnostic to equilibrium selection mechanisms and provides a closed-form boundary for equilibrium outcomes.

Findings

The method effectively handles multiple equilibria in large-scale games.

It guarantees welfare performance with a derived regret bound.

Application to a microfinance dataset demonstrates practical utility.

Abstract

Many policy problems involve designing individualized treatment allocation rules to maximize the equilibrium social welfare of interacting agents. Focusing on large-scale simultaneous decision games with strategic complementarities, we develop a method to estimate an optimal treatment allocation rule that is robust to the presence of multiple equilibria. Our approach remains agnostic about changes in the equilibrium selection mechanism under counterfactual policies, and we provide a closed-form expression for the boundary of the set-identified equilibrium outcomes. To address the incompleteness that arises when an equilibrium selection mechanism is not specified, we use the maximin welfare criterion to select a policy, and implement this policy using a greedy algorithm. We establish a performance guarantee for our method by deriving a welfare regret bound, which accounts for sampling uncertainty and the use of the greedy algorithm. We demonstrate our method with an application to the microfinance dataset of Banerjee et al. (2013).