Multi-activity Influence and Intervention

TL;DR

This paper develops a network model to analyze optimal interventions across multiple activities, considering social spillovers and interdependence, with results depending on spectral properties of social and activity matrices.

Contribution

It introduces a novel framework for understanding how intervention strategies depend on spectral properties of social and activity interdependence matrices.

Findings

Optimal intervention direction depends on spectral properties of social and interdependence matrices.

Principal components of the interdependence matrix guide resource allocation across activities.

Network effects influence resource distribution across agents based on strategic complementarity or substitutability.

Abstract

Using a general network model with multiple activities, we analyse a planner's welfare maximising interventions taking into account within-activity network spillovers and cross-activity interdependence. We show that the direction of the optimal intervention, under sufficiently large budgets, critically depends on the spectral properties of two matrices: the first matrix depicts the social connections among agents, while the second one quantifies the strategic interdependence among different activities. In particular, the first principal component of the interdependence matrix determines budget resource allocation across different activities, while the first (last) principal component of the network matrix shapes the resource allocation across different agents when network effects are strategic complements (substitutes). We explore some comparative statics analysis with respective to model primitives and discuss several applications and extensions.