Nobel Designs
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Economics Strategy Nov 1, 2007

Nobel Designs

Understanding mechanism design

The 2007 Nobel in Economics raised smiles in the Managerial Economics and Decision Sciences (MEDS) department at Kellogg for two reasons. First, the prize honors a body of work, mechanism design, which has been and continues to be a cottage industry within the department. Second, it honors three individuals, Leo Hurwicz, Eric Maskin, and Roger Myerson, with ties to MEDS. Hurwicz is a particular friend of Stanley Reiter, a founder of the department. They have co-authored several papers as well as a book on mechanism design. Maskin is a co-author and former advisor of two current faculty members in MEDS (Sandeep Baliga and Péter Eső). And, of course, Roger Myerson was a faculty member for twenty-five years in the MEDS department.

The award raised hackles among the atheoretical unwashed because it elevates an abstract subject with roots in game theory. The New York Times felt compelled to report this in its October 20, 2007, issue. The article could be summarized thus: X says the award was undeserved, and Y said otherwise. Fair, balanced, and vacuous.

The laureates themselves have gamely tried in sound bites to describe their contribution and its importance. However, mechanism design does not lend itself to such a task. Its importance comes not from a collection of take-aways, to-do lists, or ten-point plans. Rather, it is an analytical framework for thinking clearly and carefully about the most fundamental of social problems: what exactly can a given institution achieve when the information necessary to make decisions is dispersed and privately held? The range of questions to which the approach can be applied is striking. To achieve a given reduction in carbon emissions, should one rely on taxes or a cap and trade system? Is it better to sell an IPO via auction or the traditional bookbuilding approach? Would juries produce more informed decisions under a unanimity rule or simple majority? Mechanism design helps us understand how the answers to these questions depend on the details of the underlying environment. In turn, this knowledge helps us understand which details matter and which do not. To paraphrase an old proverb, Hurwicz, Maskin, and Myerson gave us not fish for a day but fishing rods.

To get a sense of what mechanism design is, we begin with a story recounted by an earlier Nobelist, Ronald Coase, more than forty years ago. It involves a railroad with a coal-burning locomotive that runs near a stretch of land owned by a farmer.

The locomotive emits sparks that set fire to the farmer’s crops. Suppose running the train yields $1,000 worth of profit for the railroad but causes $2,000 worth of crop damage. Should the railroad be made to pay for the damage it causes?

The sparks by themselves do no damage. One might say the farmer caused the damage by placing her crops next to the railway line. It is the juxtaposition of sparks and crops that lead to the $2,000 worth of damage. Perhaps, then, the farmer is liable.

If you think this strange, suppose it costs the farmer $100 to ensure the safety of her crop. If we make the railroad liable for damage to the crop, what happens? The railroad stops running (assuming the absence of technology that would eliminate the sparks). Why spend $2,000 to get a return of $1,000? The farmer takes no precautions to secure her crop. As a society we are out $1,000, the profits the railroad would have made had it run. Now suppose we make the farmer liable. The train runs. The farmer pays the $100 to safeguard her crop rather than the $2,000 in crop damage. On balance, society is out only $100.

If we cared about avoiding damage in the most cost-effective way possible, we should make the farmer liable. Suppose, instead, the railroad has access to technology that would eliminate the sparks for a price of $50. In this case, since it is cheaper for the railroad to avoid the damage, it should be made liable. If cost effectiveness is our purpose, it puts us in a pickle because the assignment of liability depends on the details of the particular situation. Coase’s insight is that it matters not how liability is assigned as long as the parties are permitted to trade the liability amongst themselves.

Suppose the railroad is made liable. What matters is if the railroad can pay the farmer to shoulder the liability. Assume as before that the railroad cannot reduce the sparks emitted without shutting down the locomotive and that the farmer can avoid the crop damage at a cost of $100. Observe that the railroad is better off paying the farmer at least $100 (and no more than $1000) to move the crops. The farmer will also be better off. In effect, the railroad pays the farmer to assume the liability; a “win-win” situation. Thus, as long as we allow the parties concerned to trade their liabilities, the party with the least cost of avoiding the damage will shoulder the liability. In terms of economic efficiency, it matters not who is liable for what. It matters only that the liabilities be clearly defined, easily tradable, and enforced. It is true that the farmer and railroad care a great deal about who is held liable for what. If it is the railroad, then it must pay the farmer. If it is the farmer, then the railroad pays nothing. One may prefer, for reasons quite separate from economic efficiency, to hold one party liable rather than the other. But the outcome in terms of who does what remains the same.

Coase recognized that there are hassle costs associated with bargaining over the transfer of liabilities. Further, these costs might overwhelm the gains to be had from bargaining. Therefore, it is of fundamental importance that such costs be minimized. Nevertheless, mutually beneficial bargains fail to be struck even when hassle costs are nonexistent. Personality, ego, and history can conspire to prevent agreement. These are unsatisfying explanations for why mutually beneficial agreements are unmade because they are idiosyncratic and situation-specific. Mechanism design suggests another reason: the actual cost incurred by each party to avoid the damage is private information known only to themselves.

To see why, suppose the railroad incurs a cost $R of avoiding the damage while the farmer incurs a cost of $F to do the same. I have purposely chosen to use letters rather than concrete numbers to emphasize that only the railroad knows the actual value of $R and only the farmer knows the actual value of $F. If $F > $R, we (meaning society) would like the railroad to incur the cost of avoiding the damage. If $F < $R, we would like the farmer to incur the cost of avoiding the damage. In the event that $F=$R, we are indifferent between which one incurs the cost.

Now, let us quite arbitrarily make the railroad liable for the damage and trust that bargaining between railroad and farmer will result in the person with the lower cost of avoiding the damage undertaking the burden to avoid the damage. If $R > $F, the railroad should pay the farmer to take on the liability. Furthermore, it would want to pay as little as possible, ideally no more than $F. However, the railroad does not know the value of F. So how much should it offer? The lower the offer, the less likely it will be accepted. On the other hand, it is more profitable to the railroad if it is accepted. The farmer, however, has every incentive to bluff the railroad into thinking that $F is larger than it actually is so as to make a tidy profit. If the farmer is too aggressive in this regard, the railroad may walk away thinking that $R < $F. One can conceive of a variety of bargaining procedures that might mitigate these difficulties. Both could simultaneously reveal their actual costs and split the difference, or they could rely on some trusted third party as a mediator. Is there a bargaining protocol that will always lead to the party with the lower cost of avoiding the damage assuming the liability?

Mechanism design approaches this question using the tools of game theory. Any such protocol can be thought of as a game that encourages each party to reveal truthfully its cost of avoiding the damage so that the correct assignment of liability can be made. The encouragement to truthfully reveal this private information is bought with money. (Economists, unlike lawyers, believe you have to pay people to tell the truth.) The monetary rewards must be generated internally, i.e., there is no rich uncle waiting on the sidelines to come to the aid of either farmer or railroad. Thus, the question becomes a purely mathematical one: is there a game with these properties? Roger Myerson and his Kellogg colleague, Professor Mark Satterthwaite, proved that the answer to this question was a resounding, de Gaulle-like “NON.” There is no bargaining protocol or trusted mediator that is guaranteed in all circumstances to ensure that the party with the lower cost of avoiding the damage assumes the liability. None—no matter how imaginative, elaborate, or convoluted. Hence, there is always the possibility that no bargain will be struck even when it is in the mutual interest of both parties to come to terms.

Thus, Coase’s original observation that the assignment of liability is irrelevant since an incorrect assignment would be corrected by bargaining in the marketplace (provided hassle costs are small) is not true in the shadow of private information. Mechanism design also suggests how liability should be assigned. Specifically, to ensure that the liability is assigned to the party with the lowest cost for avoiding the damage, the right to avoid the liability should be auctioned off to the highest bidder. How is this possible?

Suppose our auction works as follows. We have a price clock initially set at zero. We then raise the price. At each price we ask the bidders (railroad and farmer) whether they wish to buy the right to avoid liability at the current price. If both say “yes,” continue raising the price. Stop the instant one of them drops out and sell the right to the remaining active bidder at the terminal price. Observe that the farmer will stay active as long as the current price is below $F. The railroad will stay active as long as the current price is below $R. If the farmer drops out first, it must be because $F < $R, in which case the farmer assumes liability and the railroad pays the auctioneer $F. In short, the farmer, who had the lower cost of avoiding the damage, is saddled with the liability. If $R < $F, the reverse happens. The example of the railroad and the farmer involved the allocation of a liability. It could just as well as have involved the allocation of a property right. One is the obverse of the other.

What is the punch line of this brief excursion into mechanism design? When governments create new property rights or asset classes, to ensure they are allocated in an economically efficient manner, they should be auctioned off. It is exactly that reasoning that supports the allocation of spectrum rights by auction. It is exactly that reasoning that supports the allocation of permits to pollute by auction. It is exactly this reasoning that will eventually propel the FAA to use auctions to allocate arrival and departure slots at airports. John Maynard Keynes said it best: “I am sure that the power of vested interests is vastly exaggerated compared with the gradual encroachment of ideas.”

Mechanism design is a young scion of an unbroken line sprung from the belief that mathematics is a powerful engine of inquiry into the workings of commerce and government. One can trace the line back to the hand of Condorcet and the Enlightenment philosophers and probably beyond. I think they would have been proud of what has been wrought. It is a monument, to quote Horace,

“.....more lasting than bronze and far higher
than that royal pile of Pyramids,
which the gnawing rain and furious
north wind cannot destroy, nor the chain
of countless years and the flight of time.”

Center for Mathematical Studies in Economics and Management Science at Kellogg

For close to half a century the Kellogg School has been a strong believer in the power of mathematical analysis to yield insights into the workings of the private and public sector. That belief found substance in the establishment of the Center for Mathematical Studies in Economics and Management Science (CMS-EMS) about forty years ago. The founding director was Stanley Reiter, Morrison Professor of Economics and Mathematics. Reiter himself has made important contributions to mechanism design for which he was honored with, among other things, a Guggenheim award as well as membership in the American Academy of Arts and Sciences.

Since its inception the center has played an important role in turning Northwestern into one of the world’s largest and most important centers for the mathematical study of social phenomena. It has been a forum for the exchange and dissemination of ideas. Indeed, a number of the seminal papers on game theory, mechanism design, and auction theory were first presented at Center seminars and circulated as CMS-EMS technical reports. Myerson’s prize is the first to honor some of the work that arose from those activities but not the last. There are at least two more waiting in the wings.

That tradition of mathematics as an engine of inquiry continues today. The breadth of activity is astounding, including the design of auctions for the sale of carbon emission permits, the choice of constitutions, the analysis of communication, the study of open spectrum, the performance of prediction markets, the allocation of arrival slots at airports, the sale of online advertisements, the design of exchanges, and the study of reputation systems.

Further reading:

Coase, Ronald H. (1960). “The Problem of Social Cost,” Journal of Law and Economics, 3: 1-44.

Feddersen, Timothy J. and Wolfgang Pesendorfer (1998). “Convicting the Innocent: The Inferiority of Unanimous Jury Verdicts,” American Political Science Review, 92(1): 23-35. Kellogg Insight article: “Judging the Jury Vote.” April 2007

Jagannathan, Ravi and Ann E. Sherman (2006). “Why Do IPO Auctions Fail?” NBER Working Paper No. 12151. Kellogg Insight article: “Why Do IPO Auctions Fail?” May 2007.

Myerson, Roger B. and Mark A. Satterthwaite (1983): “Efficient Mechanisms for Bilateral Trading,” Journal of Economic Theory, 28(2): 265-281.

Featured Faculty

Faculty member in the Department of Managerial Economics & Decision Sciences until 2013

About the Writer
Rahesh Vohra is the John L. and Helen Kellogg Professor of Managerial Economics and Decision Sciences at the Kellogg School of Management
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