Duality between Knowledge Centralization and Market Completeness?01 Aug 2004 11:55
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.
- To read:
- Pieter Buzing , Adriaan ter Mors, Jeroen Valk and Cees Witteveen, "Coordinating Self-interested Planning Agents", Autonomous Agents and Multi-Agent Systems 12 (2006): 199--218 ["We consider planning problems where a number of non-cooperative agents have to work on a joint problem. Such problems consist in completing a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. Since the agents are non-cooperative, they insist on planning independently and do not want to revise their individual plans when the joint plan has to be assembled from the individual plans. We present a general formal framework to study some computational aspects of this non-cooperative coordination problem and we establish some complexity results to identify some of the factors that contribute to the complexity of this problem."]
- Jerry R. Green and Jean-Jacques Laffont, "Alternative limited communication systems: centralization versus interchange of information", pp. 255--270 of Uncertainty, Information, and Communication: Essays in Honor of Kenneth J. Arrow, vol. III, ed. Walter P. Heller, Ross M. Starr and David A. Starrett (Cambridge U.P., 1986) [Thus Mathematical Reviews (MR0927576): " The authors study organizational structure by means of team theory, using an example of a two-person organization which can be either centralized or decentralized, according as information exchange is asymmetrical or not. They find the centralized structure is better if one player has much better information and poor coordination is expensive."]
- Sarit Kraus, Strategic Negotiation in Multiagent Environments