Discord and Harmony in Networks

TL;DR

This paper analyzes how network structure and distribution of ideal points influence welfare in coordination games, revealing optimal interventions that either reduce local disagreement to maximize welfare or increase it to minimize welfare.

Contribution

It provides a complete characterization of optimal interventions in coordination games on networks using principal component decomposition of the adjacency matrix.

Findings

Welfare is most sensitive to interventions aligned with the last principal component.

Reducing local disagreement increases welfare, while increasing it decreases welfare.

Optimal interventions differ from traditional measures of discord like action variation.

Abstract

Consider a coordination game played on a network, where agents prefer taking actions closer to those of their neighbors and to their own ideal points in action space. We explore how the welfare outcomes of a coordination game depend on network structure and the distribution of ideal points throughout the network. To this end, we imagine a benevolent or adversarial planner who intervenes, at a cost, to change ideal points in order to maximize or minimize utilitarian welfare subject to a constraint. A complete characterization of optimal interventions is obtained by decomposing interventions into principal components of the network's adjacency matrix. Welfare is most sensitive to interventions proportional to the last principal component, which focus on local disagreement. A welfare-maximizing planner optimally works to reduce local disagreement, bringing the ideal points of neighbors closer together, whereas a malevolent adversary optimally drives neighbors' ideal points apart to decrease welfare. Such welfare-maximizing/minimizing interventions are very different from ones that would be done to change some traditional measures of discord, such as the cross-sectional variation of equilibrium actions. In fact, an adversary sowing disagreement to maximize her impact on welfare will minimize her impact on global variation in equilibrium actions, underscoring a tension between improving welfare and increasing global cohesion of equilibrium behavior.