A visiting Federal Reserve scholar attempts to explicate the difference between Hayek’s explanatory universe and the Arrow-Debreu explanatory universe using the conceptual language / conceptual straight jacket of . . . Arrow and Debreu:

Arrow and Debreu showed that allocations will be Pareto efficient even in economies in which time and uncertainty are explicitly represented. They showed that, in any economy, there is an irreducible minimum level of risk that somebody has to bear. In a competitive economy with well-functioning financial markets, this risk will be borne by those who are most risk tolerant and who therefore require the least compensation in terms of higher expected return for bearing the risk.  This is exactly as one would expect—risk-tolerant participants use financial markets to insure the risk averse. These aspects of equilibrium are discussed in standard texts on financial economics (such as LeRoy and Werner 2001).

However, demonstrating these results mathematically depends on assuming symmetric information — that is, assuming that everyone has unrestricted access to the same information. Such an assumption is less unrealistic than excluding uncertainty altogether, but it is still a strong restriction. The advent of game theory in recent decades has made it possible to relax the unattractive assumption of symmetric information. But Pareto efficiency often does not survive in settings that allow for asymmetric information.  Based on mathematical economic theory, then, it appears that the argument that private markets produce good economic outcomes is open to serious question ..

Nonmathematical economists such as Friedrich Hayek proposed an argument for the superiority of market systems that did not depend on Pareto efficiency. In fact, Hayek’s argument was the exact opposite of that of Arrow and Debreu. For him, it was the existence of asymmetric information that provided the strongest rationale in favor of market-based economic systems. Hayek emphasized that prices incorporate valuable information about desirability and scarcity, and the profit motive induces producers and consumers to respond to this information by economizing on expensive goods. He expressed the view that economies in which prices are not used to communicate information — planned economies, such as that of the Soviet Union — could not possibly induce suppliers to produce efficiently …

Note to Stephen LeRoy:  the notion of “information” as used in economics is a model builder’s makeshift — but failed — attempt to capture in “given bits” what in the real world are rival understandings of the world, with a place in unique, non-univocal individual networks of valuational relations.  These imaginary bits of “information” within an economist’s toy economy have an existence as univocal “givens” only within the reality of an economist’s math construct, and it is only this math construct and its elements which can be “given” to a single mind playing with the economic math construct.  These elements can never be found in the real world as given “information” univocal shared between real world human beings uniquely navigating the real world economy.

In the real world folks don’t have “given” information, they have rival ways of understanding the world, which are not univocal “bits” of objectively given “information”.  And these rival ways of understanding the world find there place within uniquely individual networks of valuational relations, which are never isomorphically shared between different individuals.  This is the marginalist real world economics of Carl Menger and Friedrich Hayek — essentially unknown to the math economists of today.

What Hayek in his work is talking about is “asymetrical” rivalrous understandings of the world, understandings which necessarily are both imperfect, non-univocal, and continually adapting to changing local conditions and relative prices.  None of this can be fully capture in a univocal mathematical construction — not the imperfect, non-univocal, rivalrous understandings and not the learning, correcting, and adapting process.

The central failure of the mathematical economists attempting the understand Hayek — and the market economy — is the signal failure to understand this central fact of economic science.