Economic Networks
An analytical hold on this perspective is achievable, not by trying to extend preference theory by ever higher order algebraic relaxations, but rather by rethinking the geometry of the space in which preferences are compiled and operated, and of the dynamics of this process.
Network theory has come a remarkably long way in recent years, from a staid and esoteric branch of pure mathematics with only oblique application (chemical enumeration, packing problems) to one of the hottest new fields of applied mathematics in the study of complexity.
If the economic system is a complex rule-system, then network theory is the most natural foundation for analysis of economic structure and dynamics. With network theory, we can hope to formalize analysis of the dynamics of complex economic structure in general and of consumption in particular.
A network, or graph, is a set of elements and a set of connections forming a system. Different classes of network are defined by the density and distribution of the connections between elements. At the limit of integral density, where every element is directly connected to every other, a network collapses into an integral space known more generally as the real field. Most micro- and macroeconomic theory implicitly assumes a real space.
There is much that can be said about the structural and dynamical implications of the state of complexity for the structural and dynamical properties of an economic system, and we shall examine some of these soon with respect to the relation between consumption and demand systems and production and supply networks, but network theory has also moved on significantly in the past few years, mostly due to the work of a scattering of non-linear mathematicians and solid-state physicists.
What is interesting about network theory for the analysis of economic systems is that it connects specific structural properties of networks with specific dynamical properties. Only complex adaptive systems are capable of ongoing evolution.
The problem with the sorts of network theory that mathematicians, physicists, and computational biologists have been developing is that, from the perspective of economic analysis, it all tends to be rather flat. For the most part, complexity is viewed as a global property of a system, which either is or is not present. But there is complexity and then there is complexity. Is the complexity of a chemical dissipative system the same sort of complexity as that found in a biological organism, and indeed, is this the same sort of complexity as found in an economic system.