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

Rakesh Vohra

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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