Assessing performance tradeoffs in hierarchical organizations using a diffusive coupling model

TL;DR

This paper models hierarchical organizations as diffusive networks to analyze the tradeoff between fast coordination and effective information sharing across layers, providing insights into organizational efficiency.

Contribution

It introduces a diffusive coupling model for hierarchical networks and characterizes the tradeoff between coordination speed and information propagation using linear systems theory.

Findings

Faster coordination reduces information sharing from lower layers.

Analytical results reveal a fundamental tradeoff in hierarchical network performance.

Numerical simulations validate theoretical predictions.

Abstract

We study a continuous-time dynamical system of nodes diffusively coupled over a hierarchical network to examine the efficiency and performance tradeoffs that organizations, teams, and command and control units face while achieving coordination and sharing information across layers. Specifically, after defining a network structure that captures real-world features of hierarchical organizations, we use linear systems theory and perturbation theory to characterize the rate of convergence to a consensus state, and how effectively information can propagate through the network, depending on the breadth of the organization and the strength of inter-layer communication. Interestingly, our analytical insights highlight a fundamental performance tradeoff. Namely, networks that favor fast coordination will have decreased ability to share information that is generated in the lower layers of the organization and is to be passed up the hierarchy. Numerical results validate and extend our theoretical results.