Synopsis of Economic Networks: The New Challenges
2009 Frank Schweitzer, Didier Sornette, A. Vespignani, G. Fagiolo, F. Vega-Redondo, D. R. White. Economic Networks: The New Challenges. Science 24 July: 422-425. Special Issue on Complex Systems and Networks http://www.sciencemag.org/cgi/reprint/325/5939/422.pdf
(from the perspective of Doug White 17:28, 27 July 2009 (PDT))
In general, our article deals with the challenges of a new field, economic networks. Don Plott, a leading experimental economist, working on foundations of the theory of prices and markets, once told me that economics has no theory of network formation, and of how network formation affects the economy.
We discuss four aspects of this emergent field, one that merges network theory (ranging over the kinds of representations discussed in Carter's article in this special issue) with different economic processes:
1. How network structure interacts with network dynamics, given the details of different kinds of networks and the ways that different networks that overlay one another interact: e.g. interaction of agent behavior with the structural and feedback properties of the larger network in which that behavior takes place (which also affects how links are formed, modified, or dissolved)
2. How the more micro studies of agents and agent behavior in sociology and economics (or economic incentives, game theory dynamics, etc.) interact with the more macro statistical properties of the networks as studied in physics and computer science. Micro-macro interaction is one of the major topics in complexity theory, including tipping-points, for one example.
3. A third area of study, destabilization, is discussed with two examples where tipping points may occur:
3a) A first example is illustrated by Fig. 1, where too much environmental volatility or too much innovation (in this simulation) destabilizes network interactions or (as in Fig 1) lead to a phase transition, from a network topology that is efficient (i.e., not wasteful) in terms of optimum benefits to participants, to a network that is inefficient, even when agents continue to employ the same strategies (in this example, link with central actors).
3b) A second example of destabilization is given in the discussion of Fig.2, where high network density and strong dynamical interdependence may create clusters of self-amplifying feedback that may then spread to destablizing other clusters of highly connected nodes.
4. A fourth topic, stabilization theory (the opposite of destabilization) is one that has been simulated (e.g., by Scott Page in his recent book, “The Difference” or by UCI’s first Social Science dean, Jim March, in a now-famous paper on exploration through diversity and exploitation of expert knowledge in decision making) but little explored in empirical studies (an exception being our study of the innovative biotech industry, ref.  where I was second author). There is evidence that diversity and heterogeneity in networks, under some conditions, can lead to stabilization whereas uniformity in the composition of network actors or agents can lead to systemic risk.
5. The common theme of these kinds of feedback processes is complexity and complexity theory, which I have explored in several articles and my most recent book (2005) on Network Analysis and Ethnographic Problems. That book is not mentioned in our references but provides a key reference in a follow-up article of our group of authors to be published in the journal Advances in Complex Systems. The opening chapter deals with the micro-macro linkage in social networks, the structure-dynamics connection, emergence, leadership and innovation from the bottom-up, the dynamics of changes over time in network topology, and factors in the collapse in network sustainability.
Like Carter’s paper in this special issue, which deals with variations in how to represent networks as part of the researcher’s specific theoretical problem under study, our paper concludes with agenda for our specific focus of study (economic networks, now emerging as a specific field) as to data collection, time and space, how to specify the relevant measures of network structure, how to deal with heterogeneity in kinds of nodes (agents, actors, organizations, etc.) and edges (kinds of relations and their role in network dynamics), and attention to systemic feedbacks, including systemic risks in relation to failures at the individual or micro level, and potentials for understanding the problems of sustainable, metastable, or other types of stability in economic networks.
(As a side note, the example of a new way to specify a relevant measure of network structure is my paper with physicist Joerg Reichardt on the use of spin physics to solve the problem of how to reveal the complex role structure of world multicommodity patterns of trade. This kind of transdisciplinary collaboration has been common at the Santa Fe Institute and in the massively funded European Union complexity projects where I work, but these collaborations are omitted entirely in reference  which deals among other issues with the need for transdisciplinary work).
We predict in this paper that this field, economic networks, will emerge in the near future by attention to the problems of complexity analysis outlined in our exposition, and by collaborations from diverse disciplines, such as sociologists and economists, on the one hand, and physicists and computer scientists on the other.
P.S. There is one misprint in this article, on the bottom right of page 423. This had been corrected several times in manuscript preparation but managed to slip into the print edition. Where the text says "dollar trade in the world reaches" it should read "dollar trade in the world passes through" and "following existing links" should read "following existing links between other pairs of countries." The centrality measure here is that of Mark E. J. Newman A measure of betweenness centrality based on random walks, Social Networks 27, 39–54 (2005). It is cited in references  and  which are the relevant studies of the ITN (international trade network) under discussion.