Duality between Knowledge Centralization and Market Completeness?

01 Aug 2004 11:55

This is a seriously underbaked thought, inspired by listening to Ed Durfee talk about his work on coordinating plans in multi-agent systems. (Prof. Durfee is in no way responsible for it.)

A key and persuasive part of the Austrian (von Mises/Hayek) critique of central planning is the knowledge problem --- that it is not possible to centralize all the knowledge which would be required to solve the social allocation problem, and that it would be computationally infeasible even if you could. (Hayek, in particular, would say that it's not possible even to articulate all the necessary knowledge, but this is a separate issue.) In other words, central planning could only be done by something like Laplace's Vast and Considerable Intellect. Markets, in this view, by coordinating individual actions, effectively calculate the solution (or a solution) without requiring centralization, exploiting computational parallelism and modularity.

But how many markets? To guarantee equilibrium, at least in the Arrow-Debreu framework, you need a complete set of contingent-contract markets. Economic actors, then, have to keep track of an extraordinarily large number of prices, and participate in an extraordinarily large number of markets. Now, it's no surprise that the neo-classical economic agent faces a computationally intractable problem (at least, it's not surprising to those of us brought up on Herbert Simon's writings), but what strikes me about this is that market participation is costly. Rather than have one agent, faced with an insoluble knowledge problem, we may have a huge number of agents, faced with unbearable transaction costs.

To put it a bit more formally, I wonder whether we can't establish, in some suitable class of models, a well-defined trade-off between knowledge centralization and the completeness of the system of markets, and hence between the difficulty of the central authority's allocation problem and the magnitude of the transaction costs paid by decentralized participants. It would be important, I imagine, to hold fixed the degree of optimization we're assuming the different institutional systems provide --- e.g., it could well be that an incomplete market system does better than an under-informed central planner.

Writing this out, I wonder if I haven't just reformulated Williamson's theory of institutional economics.