When Adam Smith wrote about the working of the invisible hand, how it led self-interested individuals to act in a way that furthered the efficient allocation of resources, he had in mind an economy that was already decentralized and complex. In this economy, each individual was a small part and had little knowledge of the whole. These individuals pursued their own narrow interests with little thought for the rest of the complex process that constituted the life of the economy. That order could come from the uncoordinated decisions of these agents is still an amazing insight.

The theory of competitive general equilibrium that culminated in the the Arrow–Debreu–McKenzie (ADM) model is a beautiful formalization of Smith's insight. It remains the best rationalization we have of the viability of the market system. It also provides an analytical model that is still the workhorse of many areas of economics. But in spite of its subtlety and power, the ADM model hardly does justice to the richness of Smith's vision. The decision-making framework represented by the ADM model, which we take to be the paradigm of perfect competition, reduces the whole economy to a single auction market. Although the ADM model can be interpreted as a theory of general equilibrium in a complete economy, it does not take seriously the distinction between partial and general equilibrium. It allows for any number of commodities, even an infinite number, and this is often interpreted as meaning that there is a large number of markets.