Targeted Intervention in Random Graphs

TL;DR

This paper explores how to design near-optimal intervention strategies in networks with unknown adjacency matrices drawn from random graph models, using spectral methods and sampling techniques.

Contribution

It introduces a spectral-based intervention approach for unknown random graphs and provides efficient methods to approximate the key eigenvector for practical implementation.

Findings

Single intervention proportional to the first eigenvector is near-optimal for large budgets.

Sampling methods can effectively approximate the first eigenvector when the distribution is unknown.

Spectral interventions outperform no-data strategies in synthetic and real-world networks.

Abstract

We consider a setting where individuals interact in a network, each choosing actions which optimize utility as a function of neighbors' actions. A central authority aiming to maximize social welfare at equilibrium can intervene by paying some cost to shift individual incentives, and the optimal intervention can be computed using the spectral decomposition of the graph, yet this is infeasible in practice if the adjacency matrix is unknown. In this paper, we study the question of designing intervention strategies for graphs where the adjacency matrix is unknown and is drawn from some distribution. For several commonly studied random graph models, we show that there is a single intervention, proportional to the first eigenvector of the expected adjacency matrix, which is near-optimal for almost all generated graphs when the budget is sufficiently large. We also provide several efficient sampling-based approaches for approximately recovering the first eigenvector when we do not know the distribution. On the whole, our analysis compares three categories of interventions: those which use no data about the network, those which use some data (such as distributional knowledge or queries to the graph), and those which are fully optimal. We evaluate these intervention strategies on synthetic and real-world network data, and our results suggest that analysis of random graph models can be useful for determining when certain heuristics may perform well in practice.