Network growth under opportunistic attachment

TL;DR

This paper introduces an opportunistic attachment model for network growth, where nodes consider features like PageRank scores of potential entry points, revealing complex dynamics and potential applications in economic theory.

Contribution

It presents a minimal, stylized model of entrepreneurial growth based on opportunistic attachment, linking network structure to economic opportunity and growth.

Findings

Model exhibits rich node dynamics and path dependence.

Opportunistic attachment leads to degenerate network structures.

Suggests a link between network topology and economic growth potential.

Abstract

Growing network models can potentially be a useful tool in the development of economic theory. This work introduces an "opportunistic attachment" mechanism where incoming nodes, in deciding where to join a network, consider features of the entry points available to them. For example, an entrepreneur looking to start a thriving business might consider the expected revenue of many hypothetical businesses. This mechanism is explored, in isolation, via a minimal model where PageRank serves to score the available opportunities. Despite its simplicity, this model gives rise to rich node dynamics, path-dependence, and an unexpected degenerate structure. We go on to argue that this model might be useful to theoretical development as a maximally stylised model of entrepreneurial growth. Central to the argument is an alternative set of microfoundations introduced in Leontief & Brody (1993) whereby the steady state of a random walk is a notion of economic equilibrium. To the extent this argument holds, our findings suggest that entrepreneurs face a shifting "opportunity space" where the number of potential business opportunities is effectively unbounded. Opportunistic attachment is thus a candidate mechanism for relating the structure of an economic system to its future growth.