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Mechanism Design and the Free Market

Mises Daily: Monday, December 10, 2007 by

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Nobel Earlier this year three Americans won the Nobel Memorial Prize in Economics for laying the foundations of "mechanism design theory." The work of Leonid Hurwicz, Roger Myerson, and Eric Maskin was noted for its help in implementing efficient voting, trading, and regulatory schemes.

The official press release made it quite clear that although the Invisible Hand works well in the simplistic world of Adam Smith, it doesn't always succeed in our complex real world, with its private information, transaction costs, and externalities. According to the official statement, mechanism design theory is essential to "distinguish situations in which markets work well from those in which they do not." The press largely followed this lead; the Washington Post's headline read, "3 U.S. Economists Share Nobel for Work on Flawed Markets."

Such doubts about the market economy are unfounded. Like most of the important results in mainstream economics, the prize-winning work in mechanism design is very elegant mathematically, and offers many counterintuitive results — yet it has precious little bearing on the case for (or against) laissez-faire capitalism. Those who think otherwise are relying on a simplistic and naïve view of how the market and government actually operate. Before arguing this point, we should first review some basics.

Mechanism Design Theory

A mechanism is a specification of the strategies available to every agent in an economy, along with the outcome that occurs under every combination of strategies the agents might choose. The information available to an agent may be hidden from others, and an agent's actions may affect not only his own welfare but also that of other agents. Because of these two facts, the situation is far more complicated than the simple economic models of perfect competition. As Myerson puts it, "Mechanism theory shows that incentive constraints should be considered coequally with resource constraints in the formulation of the economic problem."PDF

Although much of mathematical economics remains mercifully confined to the ivory tower, the apparently abstract approach of mechanism design has actually been used to refine voting procedures in NCAA football rankings, to match organ donors with recipients, and to improve trading rules on stock exchanges. Because at least some of this impact has occurred in purely private settings, this is prima facie evidence that mechanism design theory is actually useful.

An Auction Example

In the classroom, the quickest way to convey the essence of mechanism design is to explain the different outcomes from various auction rules. To this end, imagine two auction bidders competing for a painting. Jim values the painting at $100, meaning he would consider himself better off if he acquired the painting for under $100, but wouldn't want to pay more. The second bidder, Sally, values the painting at $200.

Mainstream economists argue that a well-designed auction should ensure that Sally wins the painting. Because she values it more than Jim, she could make him an offer for it (of $150, say) and both parties would be happier. So if the auction rules permit Jim to walk away with the painting, it would constitute a Pareto-inefficient outcome; consequently mainstream economists wouldn't endorse such rules in the stipulated environment.

To see the importance of the rules of the game, suppose that the painting is auctioned off according to a first-price rule, where the person writing the highest (secret) bid wins the painting and pays his or her bid. In this case, Sally might incorrectly estimate that Jim values the painting at no more than $50, and so bid only $51. But since Jim in reality values the painting at much more than that, he might bid a higher amount and win. Because of strategic considerations, we see that a first-price auction may be inefficient when bidders don't know everyone else's valuation.

But this problem is avoided in a second-price auction in which the high bidder gets the painting, but only pays the bid of the second-highest bidder. It can be easily shown that bidding one's true valuation is a "weakly dominant strategy" in a second-price auction where each person has a private valuation of the object. Under this rule, Jim would never regret writing $100 on his slip of paper, nor would Sally ever regret writing $200 on hers. Even if Sally thought Jim valued the painting at $50, it would be foolish for her to write less than $200, because lowering her bid doesn't help her any, and it might allow Jim to win.

This simple auction example has illustrated the essence of mechanism design theory, in particular the important principle of incentive compatibility. Because of private information and selfish motivations, the institutional framework is very important — the "right" rules lead to "optimal" outcomes while bad rules lead to economic inefficiency.

Mechanism Design No Criticism of Private Property

For those who equate "the free market" with "atomistic individuals who reduce everything to money," it is obvious why the insights of mechanism design appear to impugn pure capitalism, and to justify enlightened government tinkering with spontaneous outcomes. Yet this view relies on a false caricature of the market economy, and a naïve faith in political action.

First, the market economy is not characterized by the "rational fools" ridiculed by Amartya Sen. To oppose government intervention in private property is not to don a top hat and send the crippled to be quartered and sold on the market for body organs. For example, people living in a purely free-market society could quite consistently give to charities, make "investments" with no rate of return such as the X-Prize, and even feed and house their children without charging them the market rate for boarders. Those who think these are "exceptions" to capitalism don't understand what capitalism is; in their view, nobody should ever spend money on a sports car because cheaper modes of transportation are available and hence more "profitable."

When we reflect that the free market is far more nuanced than the mainstream model of perfect competition, it becomes clear that the insights of mechanism design are comparable to, say, Henry Ford's innovations with the assembly line, or Peter Drucker's recommendations for better corporate management. Successful entrepreneurship upsets the status quo; this is the market in action, not evidence of "market failure." To the extent that mechanism design in the past shed light on inadequacies in auction rules and other organizational proceedings, it merely showed the ability of a free society to constantly improve.

In the second place, even if we concede that Pareto-inefficient outcomes can occur in a free market, as demonstrated in certain mathematical models, it doesn't follow that therefore the government ought to "fix it." To rush to this judgment assumes away all of the problems of government failure. In particular, this conclusion only holds if we assume that (a) the politicians are smart enough to set up the model correctly, with all of the relevant information to plug into the parameters, and then derive the "optimal" policy, and (b) the politicians are noble enough to ignore their campaign donors and actually implement this ideal policy. I am personally not convinced on either account.

The Socialist Calculation Debate

The naïvete of mechanism design is epitomized in Myerson's superficially very evenhanded evaluation of the socialist calculation debate, where he concludes that socialism does well from an adverse-selection viewpoint, but poorly from a moral-hazard viewpoint (see pages 5 and 6 of this pdf). Ah, this nuanced conclusion seems far more robust — far more scientific — than the verbal dogmatism of Mises in the original debate!

Wait a second. Let's look at the alleged advantages of socialism a little more closely:

Under socialism, there is no problem getting the manager to reveal type honestly, because he is willing to report his type honestly when we just pay him a flat wage no matter what he reports. If we want to give him strict incentives to guide social decision-making about the project, the state could pay the manager ε(R — I) if the project succeeds, but make him pay εI if the project fails. For any ε>0, this payment plan would give the manager a positive incentive to recommend the project only when its expected social profit is positive….

This example is interesting for Tirole … because he is assuming that competition among investors in the financial market always lets the manager borrow at an interest rate such that investors get expected profit equal to zero given their information about the manager. With access to such competitive lenders, low-type managers would want to imitate high-type managers to get their favorable terms of credit. But under socialism, the monopolistic state lender can fully exploit the high-type manager, and then the low type would not want to borrow at all. So we find that socialism may actually have an advantage here, because socialism can flatten the manager's incentives to eliminate his temptation to lie about his chances of success.

As I say, Myerson is not one-sided in this treatment; after discussing the merits of socialism, he goes on in the next section to describe a model where

socialism looks rather less appealing from the perspective of this moral-hazard model, as it forces us to admit either inequality or coercion or productive inefficiency into our imagined socialist paradise. Indeed, our simple model does not do badly as a source of theoretical insights into the flaws of Soviet communism, and it formalizes some of Hayek's informal intuitive arguments: "To assume that it is possible to create conditions of full competition without making those who are responsible for the decisions pay for their mistakes seems to be pure illusion."

One can understand why modern mainstream economists pooh-pooh the supposedly dogmatic assertions of Mises and even Hayek, in contrast to the generalized models of mechanism design that allow for a full analysis of different economic institutions. Yet we must go back to the first block quote above, and ask whether Myerson's qualified defense of socialism really has anything to do with Mises's original critique. Once we understand exactly what Myerson is talking about, it's clear that he completely misses the Austrian claim. Of course, this alone doesn't mean the Austrians were right, but it does mean that the adverse-selection model that interested Tirole wouldn't have been too intriguing to Mises.

In the model to which Myerson alludes above, he is assuming that there are "high-type" and "low-type" managers. The managers can borrow a certain amount, I, in investment funds from the state and earn return R on a project if successful, or earn 0 if the project fails. The high-type manager is more likely to succeed, and the numbers are such that the state only wants the high-type managers to start these projects. The problem is that the type is known only to the managers themselves. Yet using the payment scheme explained by Myerson above, the high-type managers have the incentive to borrow funds and carry out the project, while the low-type managers don't. What's more, the state can cajole the high-type managers into stepping forward for a relative pittance, compared to the high incomes earned in private markets.

There are several problems with this analysis. For example, it assumes that the people who would squander state funds know that they're second-rate managers; yet surely the thousands of failed entrepreneurs in a capitalist economy show the weakness in that assumption. Another problem is that the analysis ignores the "Who guards the guardians?" issue; why should we trust the state rulers to employ Myerson's payment scheme, rather than some other politically motivated one?

These objections (some of which, I concede in fairness, spill over into the "moral hazard" discussion) are all incidental. In light of Mises's critique of socialism, the fundamental shortcoming of Tirole's adverse-selection model of socialist managers is that it takes for granted accurate profit and loss accounting. That is, Myerson simply assumes that there is some project with a return R and a cost I. Yet without a true market in capital goods, no one — not the state planners, nor the individual managers who may very well know their own aptitudes — can reduce the benefits and costs of an investment project down to two numbers.

The high-type manager might know, "If the state lends me 500 worker-hours, six tons of steel, 80,000 gallons of fuel, etc. etc. etc., then I can produce so many kilowatt-hours of electricity." Yet this knowledge alone doesn't indicate whether the project is worthwhile, whether it represents a proper use of scarce resources.

This point is crucial, so let me elaborate. Myerson's recommended compensation scheme only works if we can reduce all of the heterogeneous inputs and outputs to their market values. In terms of direct utility from this collection of goods, the high-type manager might actually prefer some small percentage of the inputs (e.g., 0.01% of the labor hours, steel, fuel, etc.) to the same percentage of the output (e.g., 0.01% of the electrical output). So the purist can't even say that Tirole and Myerson have put the capital-goods pricing problem to one side, and successfully dealt with the adverse-selection problem. Their "solution" itself relies on being able to motivate high-type managers with compensation packages that have positive market values, something that the manager would only recognize if there is a market for capital goods.

The Politically Incorrect Guide to Capitalism

Granted, the proponent of mathematical economics could say, "C'mon Murphy, every model has to make some simplifying assumptions. Yes, Tirole and then Myerson assumed away the issue of market prices for capital goods, in order to focus on the problem of managers who know their own types. On that score, socialism works." But is it really fair to say that Mises overstated his case — and I have heard game theorists say just that — because in a model where we assume away his concerns, then his objections fall apart?

Conclusion

Notwithstanding the official press release and subsequent media coverage, the goal of mechanism design is, generally speaking, to study how best to harness markets. As Hurwicz himself said in a famous passage, "[W]hat economists should be able to do is to figure out a system that works without shooting people." It's true that Hurwicz's definition of coercion is much narrower than the typical libertarian's, but, even so, Austrian economists should not dismiss this field simply because of a few misleading stories in the media. Mechanism design poses no threat to the free market.

The author would like to thank Tim Salmon for his help in the research for this article.