How Much Information Do Markets Require?
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Below is an edited version of an essay that appeared on Truth on the Market.
One of the biggest names in economics, Daron Acemoglu, recently joined the mess that is Twitter. He wasted no time in throwing out big ideas for discussion and immediately getting tons of, let us say, spirited replies.
One of Acemoglu’s threads involved a discussion of F.A. Hayek’s famous essay “The Use of Knowledge in Society,” wherein Hayek questions central planners' ability to acquire and utilize such knowledge. Echoing many other commentators, Acemoglu asks: can supercomputers and artificial intelligence get around Hayek’s concerns?
Coming back to Hayek’s argument, there was another aspect of it that has always bothered me. What if computational power of central planners improved tremendously? Would Hayek then be happy with central planning?
While there are a few different layers to Hayek’s argument, at least one key aspect does not rest at all on computational power. Hayek argues that markets do not require users to have much information in order to make their decisions.
To use Hayek’s example, when the price of tin increases: "All that the users of tin need to know is that some of the tin they used to consume is now more profitably employed elsewhere." Knowing whether demand or supply shifted to cause the price increase would be redundant information for the tin user; the price provides all the information about market conditions that the user needs.
To Hayek, this informational role of prices is what makes markets unique (compared to central planning):
The most significant fact about this [market] system is the economy of knowledge with which it operates, or how little the individual participants need to know in order to take the right action.
Good computers, bad computers—it doesn’t matter. Markets just require less information from their individual participants. This was made precise in the 1970s and 1980s in a series of papers on the “informational efficiency” of competitive markets.
This post will give an explanation of what the formal results say. From there, we can go back to debating the relevance for Acemoglu’s argument and the future of central planning with AI.
From Hayek to Hurwicz
First, let’s run through an oversimplified history of economic thought. Hayek developed his argument about information and markets during the socialist-calculation debate between Hayek and Ludwig von Mises on one side and Oskar Lange and Abba Lerner on the other. Lange and Lerner argued that a planned socialist economy could replicate a market economy. Mises and Hayek argued that it could not, because the socialist planner would not have the relevant information.
In response to the socialist-calculation debate, Leonid Hurwicz—who studied with Hayek at the London School of Economics, overlapped with Mises in Geneva, and would ultimately be awarded the Nobel Memorial Prize in 2007—developed the formal language in the 1960s and 1970s that became what we now call “mechanism design.”
Specifically, Hurwicz developed an abstract way to measure how much information a system needed. What does it mean for a system to require little information? What is the “efficient” (i.e., minimal) amount of information? Two later papers (Mount and Reiter (1974) and Jordan (1982)) used Hurwicz’s framework to prove that competitive markets are informationally efficient.
Understanding the Meaning of Informational Efficiency
How much information do people need to achieve a competitive outcome? This is where Hurwicz’s theory comes in. He gave us a formal way to discuss more and less information: the size of the message space.
To understand the message space's size, consider an economy with six people: three buyers and three sellers. Some buyers—call them type B3—are willing to pay $3. Type B2 is willing to pay $2. Sellers of type S0 are willing to sell for $0. S1 for $1, and so on. Each buyer knows their valuation for the good, and each seller knows their cost.
Here’s the weird exercise. Along comes an oracle who knows everything. The oracle decides to figure out a competitive price that will clear the market, so he draws out the supply curve (in orange), and the demand curve (in blue) and picks an equilibrium point where they cross (in red).
So the oracle knows a price of $1.50 and a quantity of 2 is an equilibrium.
Now, we, the ignorant outsiders, come along and want to verify that the oracle is telling the truth and knows that it is an equilibrium. But we shouldn’t take the oracle's word for it.
How can the oracle convince us that this is an equilibrium? We don’t know anyone’s valuation.
The oracle puts forward a game to the six players. The oracle says:
The price is $1.50, meaning that if you buy 1, you pay $1.50; if you sell 1, you receive $1.50.
If you say you’re B3 (which means you value the good at $3), you must buy 1.
If you say you’re B2, you must buy 1.
If you say you’re B1, you must buy 0.
If you say you’re S0, you must sell 1.
If you say you’re S1, you must sell 1.
If you say you’re S2, you must sell 0.
The oracle then asks everyone: do you accept the terms of this mechanism? Everyone says yes, because only the buyers who value it more than $1.50 buy and only the sellers with a cost less than $1.50 sell. By everyone agreeing, we (the ignorant outsiders) can verify that the oracle did, in fact, know people’s valuations.
Now, let’s count how much information the oracle needed to communicate. He needed to send a message that included the price and the trades for each type. Technically, he didn’t need to say S2 sells zero, because it is implied by the fact that the quantity bought must equal the quantity sold. In total, he needs to send six messages.
The formal exercise amounts to counting each message that needs to be sent. With a formally specified way of measuring how much information is required in competitive markets, we can now ask whether this is a lot.
If you don’t care about efficiency, you can always save on information and not say anything, don’t have anyone trade, and have a message space of size 0. That saves on information; just do nothing.
But in the context of the socialist-calculation debate, the argument was over how much information was needed to achieve “good” outcomes. Lange and Lerner argued that market socialism could be efficient, not that it would result in zero trade, so efficiency is the welfare benchmark we are aiming for.
If you restrict your attention to efficient outcomes, Mount and Reiter (1974) showed you cannot use less information than competitive markets. In a later paper, Jordan (1982) showed that there is no way to match the competitive mechanism in terms of information. The competitive mechanism is the unique mechanism with this dimension.
Now we have on formal answer our question, how much information do markets require? Not much.
Acemoglu reads Hayek as saying “central planning wouldn’t work because it would be impossible to collect and compute the right allocation of resources.” But the Jordan and Mount & Reiter papers don’t claim that computation is impossible for central planners. Take whatever computational abilities exist, from the first computer to the newest AI—competitive markets always require the least information possible. Supercomputers or AI do not, and cannot, change that relative comparison.
Beyond Computational Issues
In terms of information costs, the best a central planner could hope for is to mimic exactly the market mechanism. But then, of what use is the planner? She’s just one more actor who could divert the system toward her own interest. As Acemoglu points out, “if the planner could collect all of that information, she could do lots of bad things with it.”
The incentive problem is a separate problem, which is why Hayek tried to focus solely on information. Think about building a road. There is a concern that markets will not provide roads because people would be unwilling to pay for them without being coerced through taxes. You cannot simply ask people how much they are willing to pay for the road and charge them that price. People will lie and say they do not care about roads. No amount of computing power fixes incentives. Again, computing power is tangential to the question of markets versus planning. Superior computational power doesn’t help.
There’s a lot buried in Hayek and all of those ideas are important and worth considering. They are just further complications with which we should grapple. A handful of theory papers will never solve all of our questions about the nature of markets and central planning. Instead, the formal papers tell us, in a very stylized setting, what it would even mean to quantify the “amount of information.” And once we quantify it, we have an explicit way to ask: do markets use minimal information?
For several decades, we have known that the answer is yes. In recent work, Rafael Guthmann and I show that informational efficiency can extend to big platforms coordinating buyers and sellers—what we call market-makers.
The bigger problem with Acemoglu’s suggestion that computational abilities can solve Hayek’s challenge is that Hayek wasn’t merely thinking about computation and communication of information. Instead, Hayek was concerned about our ability to even articulate our desires. In the example above, the buyers know exactly how much they are willing to pay and sellers know exactly how much they are willing to sell for. But in the real world, people have tacit knowledge that they cannot communicate to third parties. This is especially true when we think about a dynamic world of innovation. How do you communicate to a central planner a new product?
The real issue is the market dynamics require entrepreneurs who are imagining new futures with new products like the iPhone. Major innovations will never be able to be articulated and communicated to a central planner. All of these readings of Hayek and the market’s ability to communicate information—from formal informational efficiency to tacit knowledge—are independent of computational capabilities.
In other news, Bob Murphy invited me on The Human Action Podcast to talk about Armen Alchian. Robert Lucas had died that morning, so we spent a while on Lucas, rational expectations, Minnesota economics, and more before going all in on Alchian. Readers of this humble newsletter should enjoy the conversation.