Network growth under opportunistic attachment

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.