Nestedness in networks: A theoretical model and some applications

Abstract

We develop a dynamic network formation model that can explain the observed nestedness in real-world networks. Links are formed on the basis of agents' centrality and have an exponentially distributed lifetime. We use stochastic stability to identify the networks to which the network formation process converges and find that they are nested split graphs. We completely determine the topological properties of the stochastically stable networks and show that they match features exhibited by real-world networks. Using four different network data sets, we empirically test our model and show that it fits well the observed networks. 6 Mele (2010) and Liu et al. (2012) provide interesting dynamic network formation models where individuals decide with whom to form links by maximizing a utility function. However, contrary to our model, these papers do not characterize analytically the degree distribution and the resulting network statistics. 7 See Jackson and Zenou (2014), for a recent overview of this literature. 8 Bramoullé and Kranton (2007), Bramoullé et al. (2014), and Galeotti et al. (2010) are also important papers in this literature. The first paper focuses on strategic substitutabilities, while the second one provides a general framework for solving any game on networks with perfect information and linear best-reply functions. The last paper investigates the case when agents do not have perfect information about the network. Because of its tractability, in the present paper, we use the model of Ballester et al. (2006), who analyze a network game of local complementarities under perfect information.

Static and dynamic networks in interbank markets

“…In the following proposition (König et al, 2014a), we determine the asymptotic degree distribution of the nodes in the independent sets for n sufficiently large.…”

“…To describe the network formation process we follow König et al (2014a). Let time be measured at countable dates t = 1, 2, .…”

The Economic Consequences of Social Network Structure

“…One approach around this obstacle is, instead of modeling network effects at either the link level (and thus failing to incorporate interdependencies) or the full network level (and thus failing computability), to model things at a subnetwork level, which is then computable and also allows for rich sets of link interdependencies, as shown by Chandrasekhar andJackson (2013, 2015). Another approach is to model the network as an evolving process as in Price (1976); Barabasi and Albert (1999); Jackson and Rogers (2007a); Snijders (2001); ; Mele (2013); König, Tessone, and Zenou (2014), as such models allow for dependencies in that new links form at various points in time based on the currently existing network at the time of formation. For instance, network formation can be modeled as a sequential process where in each period a single randomly selected agent (or pair of agents) has the opportunity to form a link.…”

On the private provision of public goods on networks

“…In this case, our results are in line with similar observations in the literature on the economics of networks. Galeotti, Goyal, Jackson, Vega-Redondo, and Yariv [25] emphasize the importance of degree centrality as a measure of immediate influence and local knowledge of the network and König, Tessone, and Zenou [33] present a model of dynamic network formation where the degree and Bonacich centrality rankings coincide.…”