This page intentionally left blank Mechanism Design Mechanism design is an analytical framework for thinking clearly and carefully aboutexactlywhatagiveninstitutioncanachievewhentheinformationnecessary tomakedecisionsisdispersedandprivatelyheld.Thisbookprovidesanaccount oftheunderlyingmathematicsofmechanismdesignbasedonlinearprogramming. Threeadvantagescharacterizetheapproach.Thefirstissimplicity:argumentsbased onlinearprogrammingarebothelementaryandtransparent.Thesecondisunity: themachineryoflinearprogrammingprovidesawaytounifyresultsfromdisparate areasofmechanismdesign.Thethirdisreach:thetechniqueofferstheabilityto solveproblemsthatappeartobebeyondthereachoftraditionalmethods.Noclaim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the eco- nomictheoristwhoproposestounderstandeconomicphenomenathroughthelens ofmechanismdesign. RakeshV.VohraistheJohnL.andHelenKelloggProfessorofManagerialEco- nomicsandDecisionSciencesattheKelloggSchoolofManagement,Northwest- ernUniversity,whereheisalsoDirectoroftheCenterforMathematicalStudiesin EconomicsandManagementScience.HepreviouslytaughtattheFisherSchoolof Business,OhioStateUniversity,andistheauthorofAdvancedMathematicalEco- nomics(2005).ProfessorVohrahasalsocompletedamanuscriptontheprinciples of pricing with Lakshman Krishnamurthi, Professor of Marketing at the Kellogg School.ProfessorVohrareceivedhisdoctorateinmathematicsfromtheUniversity ofMaryland. EconometricSocietyMonographs Editors: RosaL.Matzkin,UniversityofCalifornia,LosAngeles GeorgeJ.Mailath,UniversityofPennsylvania TheEconometricSocietyisaninternationalsocietyfortheadvancementofeconomictheoryin relationto statistics and mathematics. The EconometricSociety Monographseries is designed to promote the publication of original research contributions of high quality in mathematical economicsandtheoreticalandappliedeconometrics. Othertitlesintheseries: G.S.Maddala,Limiteddependentandqualitativevariablesineconometrics,9780521241434, 9780521338257 GerardDebreu,Mathematicaleconomics:TwentypapersofGerardDebreu,9780521237369, 9780521335614 Jean-MichelGrandmont,Moneyandvalue:Areconsiderationofclassicalandneoclassical monetaryeconomics,9780521251419,9780521313643 FranklinM.Fisher,Disequilibriumfoundationsofequilibriumeconomics,9780521378567 AndreuMas-Colell,Thetheoryofgeneralequilibrium:Adifferentiableapproach, 9780521265140,9780521388702 TrumanF.Bewley,Editor,Advancesineconometrics–FifthWorldCongress(VolumeI), 9780521467261 TrumanF.Bewley,Editor,Advancesineconometrics–FifthWorldCongress(VolumeII), 9780521467254 Herve´Moulin,Axiomsofcooperativedecisionmaking,9780521360555,9780521424585 L.G.Godfrey,Misspecificationtestsineconometrics:TheLagrangemultiplierprincipleand otherapproaches,9780521424592 TonyLancaster,Theeconometricanalysisoftransitiondata,978052143789 AlvinE.RothandMarildaA.OlivieraSotomayor,Editors,Two-sidedmatching:Astudyin game-theoreticmodelingandanalysis,9780521437882 WolfgangHa¨rdle,Appliednonparametricregression,9780521429504 Jean-JacquesLaffont,Editor,Advancesineconomictheory–SixthWorldCongress(VolumeI), 9780521484596 Jean-JacquesLaffont,Editor,Advancesineconomictheory–SixthWorldCongress(VolumeII), 9780521484602 HalbertWhite,Estimation,inferenceandspecification,9780521252805,9780521574464 ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeI), 9780521444590,9780521566100 ChristopherSims,Editor,Advancesineconometrics–SixthWorldCongress(VolumeII), 9780521444606,9780521566094 RogerGuesnerie,Acontributiontothepuretheoryoftaxation,9780521629560 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeI),9780521589833 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeII),9780521589826 DavidM.KrepsandKennethF.Wallis,Editors,Advancesineconomicsandeconometrics– SeventhWorldCongress(VolumeIII),9780521580137,9780521589819 DonaldP.Jacobs,EhudKalai,andMortonI.Kamien,Editors,Frontiersofresearchineconomic theory:TheNancyL.SchwartzMemorialLectures,1983–1997,9780521632225, 9780521635387 A.ColinCameronandPravinK.Trivedi,Regressionanalysisofcountdata,9780521632010, 9780521635677 SteinarStrom,Editor,Econometricsandeconomictheoryinthe20thcentury:TheRagnarFrisch CentennialSymposium,9780521633239,9780521633659 Continuedonpagefollowingtheindex Mechanism Design A Linear Programming Approach Rakesh V. Vohra NorthwesternUniversity,Illinois cambridgeuniversitypress Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity CambridgeUniversityPress 32AvenueoftheAmericas,NewYork,NY10013-2473,USA www.cambridge.org Informationonthistitle:www.cambridge.org/9780521179461 (cid:2)c RakeshV.Vohra2011 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2011 PrintedintheUnitedStatesofAmerica AcatalogrecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloginginPublicationdata Vohra,RakeshV. Mechanismdesign:alinearprogrammingapproach/RakeshV.Vohra. p. cm.–(EconometricSocietymonographs;47) Includesbibliographicalreferencesandindex. ISBN978-1-107-00436-8(hardback)–ISBN978-0-521-17946-1(paperback) 1. Decision making – Linear programming. 2. Organizational behavior – Mathematical models. 3.Machinetheory. I.Title. HD30.23.V637 2011 658.4(cid:2)033–dc22 2011009042 ISBN978-1-107-00436-8Hardback ISBN978-0-521-17946-1Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLs for external or third-party Internet Web sites referred to in this publication and does not guaranteethatanycontentonsuchWebsitesis,orwillremain,accurateorappropriate. “Economists,unlikeLawyers,believeyouhavetopaypeopletotell thetruth.” MortonKamien “Ifyouweretoreciteevenasinglepageintheopenair,birdswould fallstunnedfromthesky.” CliveJames