CHAPTER14:ALLOCATINGSCARCERESOURCESMultiagentSystemshttp://www.csc.liv - PDF document

CHAPTER14:ALLOCATINGSCARCERESOURCESMultiagentSystemshttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/Chapter14AnIntroductiontoMultiagentSystems2eOverviewAllocationofscarceresourcesamongstanumberofagentsiscentraltomultiagentsystems.Resourcemightbe:–aphysicalobject–therighttouseland–computationalresources(processor,memory,...)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/1 Chapter14AnIntroductiontoMultiagentSystems2eIftheresourceisn'tscarce,thereisnotroubleallocatingit.Ifthereisnocompetitionfortheresource,thenthereisnotroubleallocatingit.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/2Chapter14AnIntroductiontoMultiagentSystems2eInpractice,thismeanswewillbetalkingaboutauctions.Theseusedtoberare(andnotsolongago).However,auctionshavegrownmassivelywiththeWeb/Internet–FrictionlesscommerceNowfeasibletoauctionthingsthatweren'tpreviouslyprotable:–eBay–Adwordauctionshttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/3 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/4Chapter14AnIntroductiontoMultiagentSystems2eWhatisanauction?Concernedwithtradersandtheirallocationsof:–Unitsofanindivisiblegood;and–Money,whichisdivisible.Assumesomeinitialallocation.Exchangeisthefreealterationofallocationsofgoodsandmoneybetweentradershttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/5 Chapter14AnIntroductiontoMultiagentSystems2eLimitPriceEachtraderhasavalueorlimitpricethattheyplaceonthegood.Abuyerwhoexchangesmorethantheirlimitpriceforagoodmakesaloss.Asellerwhoexchangesagoodforlessthantheirlimitpricemakesaloss.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/6Chapter14AnIntroductiontoMultiagentSystems2eLimitpricesclearlyhaveaneffectonthebehavioroftraders.Thereareseveralmodels,embodyingdifferentassumptionsaboutthenatureofthegood.Threecommonlyusedmodels:–Privatevalue–Commonvalue–CorrelatedvalueThesearethemodelsyou'llndmostoftenadoptedintheliterature.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/7 Chapter14AnIntroductiontoMultiagentSystems2ePrivatevalueGoodhasanvaluetomethatisindependentofwhatitisworthtoyou.TextbookgivestheexampleofJohnLennon'slastdollarbill.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/8Chapter14AnIntroductiontoMultiagentSystems2eCommonvalueThegoodhasthesamevaluetoallofus,butwehavedifferingestimatesofwhatitis.Winner'scursehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/9 Chapter14AnIntroductiontoMultiagentSystems2eCorrelatedvalueOurvaluesarerelated.Themoreyouarepreparedtopay,themoreIshouldbepreparedtopay.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/10Chapter14AnIntroductiontoMultiagentSystems2eAmarketinstitutiondeneshowtheexchangetakesplace.–Deneswhatmessagescanbeexchanged.–Deneshowthenalallocationdependsonthemessages.Thechangeofallocationismarketclearing.Differencebetweenallocationsisnettrade.–Componentforeachtraderinthemarket.–Eachtraderwithanon-zerocomponenthasatradeortransactionprice.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/11 Chapter14AnIntroductiontoMultiagentSystems2e–Absolutevalueofthemoneycomponentdividedbythegoodcomponent.TraderswithpositivegoodcomponentarebuyersTraderswithnegativegoodcomponentaresellersOnewaytradersareeitherbuyersorsellersbutnotboth.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/12Chapter14AnIntroductiontoMultiagentSystems2eYes,butwhatisanauction?Anauctionisamarketinstitutioninwhichmessagesfromtradersincludesomepriceinformation—thisinformationmaybeanoffertobuyatagivenprice,inthecaseofabid,oranoffertosellatagivenprice,inthecaseofanask—andwhichgivesprioritytohigherbidsandlowerasks.Thisdenition,aswithallthisterminology,comesfromDanFriedman.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/13 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/14Chapter14AnIntroductiontoMultiagentSystems2eThezoologyofauctionsWecansplitauctionsintoanumberofdifferentcategories.Beinggoodcomputerscientists,wedrawupataxonomy.–Thisgivesusahandleonallthekindstheremightbe.–Itsuggestsparameterization.–Itcanhelpustothinkaboutimplementation.Thisparticularclassicationisabitzoological,butitisagoodplacetostart.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/15 Chapter14AnIntroductiontoMultiagentSystems2eSingleversusmulti-dimensionalSingledimensionalauctions–Theonlycontentofanofferarethepriceandquantityofsomespecictypeofgood.–“I'llbid$200forthose2chairs”Multidimensionalauctions–Offerscanrelatetomanydifferentaspectsofmanydifferentgoods.–“I'mpreparedtopay$200forthosetworedchairs,but$300ifyoucandeliverthemtomorrow.”http://www.csc.liv.ac.uk/˜mjw/pubs/imas/16Chapter14AnIntroductiontoMultiagentSystems2eSingleversusdouble-sidedSingle-sidedmarkets–Eitheronebuyerandmanysellers,oronesellerandmanybuyers.–Thelatteristhethingwenormallythinkofasanauction.Two-sidedmarkets–Manybuyersandmanysellers.Singlesidedmarketswithonesellerandmanybuyersare“sell-side”markets.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/17 Chapter14AnIntroductiontoMultiagentSystems2eSingle-sidedmarketswithonebuyerandmanysellersare“buy-side”.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/18Chapter14AnIntroductiontoMultiagentSystems2eOpen-cryversussealed-bidOpencry–TradersannouncetheirofferstoalltradersSealedbid–Onlytheauctioneerseestheoffers.Clearlyasabidderinanopen-cryauctionyouhavemoreinformation.Insomeauctionformsyoupayforpreferentialaccesstoinformation.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/19 Chapter14AnIntroductiontoMultiagentSystems2eSingle-unitversusmulti-unitHowmanyunitsofthesamegoodareweallowedtobidfor?Singleunit–Oneatatime.–Mightrepeatifmanyunitstobesold.Multi-unit–Bidbothpriceandquantity.“Unit”referstotheindivisibleunitthatweareselling.–Singleshversusboxofsh.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/20Chapter14AnIntroductiontoMultiagentSystems2eFirstpriceversuskthpriceDoesthewinnerpaythehighestpricebid,thesecondhighestprice,thekthhighestprice?http://www.csc.liv.ac.uk/˜mjw/pubs/imas/21 Chapter14AnIntroductiontoMultiagentSystems2eSingleitemversusmulti-itemNotsomuchquantityasheterogeneity.Singleitem–Justtheoneindivisiblethingthatisbeingauctioned.Multi-item–Bidforabundleofgoods.–“Tworedchairsandanorangecouch,orapurplebeanbag.”–Valuationsforbundlesarenotlinearcombinationsofthevaluesoftheconstituents.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/22Chapter14AnIntroductiontoMultiagentSystems2eStandardauctiontypesWewilllookatthefour“standard”auctions:–Englishauction–Dutchauction–First-pricesealedbidauction–VickreyauctionAlsotheso-calledJapaneseauction.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/23 Chapter14AnIntroductiontoMultiagentSystems2eEnglishauctionThisisthekindofauctioneveryoneknows.Typicalexampleissell-side.Buyerscalloutbids,bidsincreaseinprice.Insomeinstancestheauctioneermaycalloutpriceswithbuyersindicatingtheyagreetosuchaprice.Thesellermaysetareserveprice,thelowestacceptableprice.Auctionends:–ataxedtime(internetauctions);or–whenthereisnomorebiddingactivity.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/24Chapter14AnIntroductiontoMultiagentSystems2eThe“lastmanstanding”paystheirbid.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/25 Chapter14AnIntroductiontoMultiagentSystems2eClassiedinthetermsweusedabove:–Single-dimensional–Single-sided–Open-cry–Singleunit–First-price–SingleitemAround95%ofinternetauctionsareofthiskind.Classicuseissaleofantiquesandartwork.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/26Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/27 Chapter14AnIntroductiontoMultiagentSystems2eUnlikelytalesTheformerpresidentofParke-Benetreportsthatadealerattendingasaleofeighteenth-centuryFrenchfurniturehadarrangedtounbuttonhisovercoatwheneverhewishedtobid;buttoningtheovercoatagainwouldsignalthathehadceasedbidding.Thedealer,coatunbuttoned,wasinthemidstofbiddingforaLouisXVIsofawhenhesawsomeoneoutsidetowhomhewishedtospeakandsuddenlylefttheroom.Theauctioneercontinuedtobidforthedealerwho,whenhereturnedtotheroom,foundhehadbecometheownerofthesofaatanunexpectedlyhighprice.Anargumentthenfollowedastowhetheranunbuttonedcoatnotintheauctionroomisthesameasanunbuttonedcoatintheauctionroom.(Cassady,1969)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/28Chapter14AnIntroductiontoMultiagentSystems2eDutchauctionAlsocalleda“descendingclock”auction–Someauctionsuseaclocktodisplaytheprices.Startsatahighprice,andtheauctioneercallsoutdescendingprices.Onebidderclaimsthegoodbyindicatingthecurrentpriceisacceptable.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/29 Chapter14AnIntroductiontoMultiagentSystems2eTiesarebrokenbyrestartingthedescentfromaslightlyhigherpricethanthetieoccurredat.Thewinnerpaysthepriceatwhichthey“stoptheclock”.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/30Chapter14AnIntroductiontoMultiagentSystems2eClassiedinthetermsweusedabove:Single-dimensional;Single-sided;Open-cry;Singleunit;First-price;SingleitemHighvolume(sinceauctionproceedsswiftly).Oftenusedtosellperishablegoods:–FlowersintheNetherlands(eg.Aalsmeer)–FishinSpainandIsrael.–TobaccoinCanada.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/31 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/32Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/33 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/34Chapter14AnIntroductiontoMultiagentSystems2eTheGuardianstatesthattheAalsmeerauctiontrades19millionowersand2millionplants...everyday.April23rd2008(page18–19)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/35 Chapter14AnIntroductiontoMultiagentSystems2eFirst-pricesealedbidauctionInanEnglishauction,yougetinformationabouthowmuchagoodisworth.Otherpeople'sbidstellyouthingsaboutthemarket.Inasealedbidauction,noneofthathappens–atmostyouknowthewinningpriceaftertheauction.IntheFPSBauctionthehighestbidwinsasalwaysAsitsnamesuggests,thewinnerpaysthathighestprice(whichiswhattheybid).http://www.csc.liv.ac.uk/˜mjw/pubs/imas/36Chapter14AnIntroductiontoMultiagentSystems2eClassiedinthetermsweusedabove:–Single-dimensional–Single-sided–Sealed-bid–Singleunit–First-priceGovernmentsoftenusethismechanismtoselltreasurybonds.–UKstilldoes.–USrecentlychangedtoSPSB.Propertycanalsobesoldthisway(asinScotland).http://www.csc.liv.ac.uk/˜mjw/pubs/imas/37 Chapter14AnIntroductiontoMultiagentSystems2eTheAmsterdamauctionSincemedievaltime,propertyinthelowcountrieshastraditionallybeensoldusingthe“Amsterdam”auction.StartwithanEnglishauction.Whendowntothenaltwobidders,startaDutchauctionstage.DutchauctionstartsfromtwicethenalpriceoftheEnglishauction.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/38Chapter14AnIntroductiontoMultiagentSystems2eVickreyauctionsTheVickreyauctionisasealedbidauction.Thewinningbidisthehighestbid,butthewinningbidderpaystheamountofthesecondhighestbid.Thissoundsodd,butitisactuallyaverysmartdesign.Itisinthebidders'interesttobidtheirtruevalue.–incentivecompatibleintheusualterminology.However,itisnotapanacea,astheNewZealandgovernmentfoundout.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/39 Chapter14AnIntroductiontoMultiagentSystems2eAgain,classiedasabove,itis:–Single-dimensional–Single-sided–Sealed-bid–Singleunit–Second-pricehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/40Chapter14AnIntroductiontoMultiagentSystems2eWhydoestheVickreyauctionwork?Supposeyoubidmorethanyourvaluation.–Youmaywinthegood.–Ifyoudo,youmayenduppayingmorethanyouthinkthegoodisworth.–Notsosmart.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/41 Chapter14AnIntroductiontoMultiagentSystems2eSupposeyoubidlessthanyourvaluation.–Youstandlesschanceofwinningthegood.–However,evenifyoudowinit,youwillenduppayingthesame.–Notsosmart.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/42Chapter14AnIntroductiontoMultiagentSystems2eSo:thereisnopointinbiddingaboveorbelowyourvaluation.Ofcourse,thisreallyassumestherearealargenumberofbidders(seetheNewZealandcase).http://www.csc.liv.ac.uk/˜mjw/pubs/imas/43 Chapter14AnIntroductiontoMultiagentSystems2eJapaneseshauctionTheauctionformusedtosellshinTokyoisdifferent:[The]distinctiveaspect[ofthisauctionform]isthatallbidsaremadebyprospectivebuyersatthesametime,orapproximatelythesametime,usingindividualhandsignsforeachmonetaryunit....Thebiddingstartsassoonastheauctioneergivesthesignal,andthehighestbidder,asdeterminedbytheauctioneer,isawardedthelot.ThisisthussimultaneousbiddingandratherlikeanFPSBauction.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/44Chapter14AnIntroductiontoMultiagentSystems2eTiesare“notuncommon[ly]”brokenbyplayingJanKenPon(or`paper,rock,scissors').http://www.csc.liv.ac.uk/˜mjw/pubs/imas/45 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/46Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/47 Chapter14AnIntroductiontoMultiagentSystems2ehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/48Chapter14AnIntroductiontoMultiagentSystems2eCombinatorialAuctionsAuctionsforbundlesofgoods.Agoodexampleofbundlesofgoodarespectrumlicences.Forthe1.7to1.72GHzbandforBrooklyntobeuseful,youneedalicenseforManhattan,Queens,StatenIsland.Mostvaluablearethelicensesforthesamebandwidth.Butadifferentbandwidthlicenceismorevaluablethannolicensehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/49 Chapter14AnIntroductiontoMultiagentSystems2e(TheFCCspectrumauctions,however,didnotuseacombinatorialauctionmechanism)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/50Chapter14AnIntroductiontoMultiagentSystems2eLetZ=fz1;:::;zmgbeasetofitemstobeauctioned.WegavetheusualsetofagentsAg=f1;:::;ng,andwecapturepreferencesofagentiwiththevaluationfunction:vi:2Z7!RmeaningthatforeverypossiblebundleofgoodsZZ,vi(Z)sayshowmuchZisworthtoi.Ifvi(;)=0,thenwesaythatthevaluationfunctionforiisnormalised.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/51 Chapter14AnIntroductiontoMultiagentSystems2eAnotherusefulideaisfreedisposal:Z1Z2impliesvi(Z1)vi(Z2)Inotherwords,anagentisneverworseoffhavingmorestuff.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/52Chapter14AnIntroductiontoMultiagentSystems2eWealreadymentionedtheideaofanallocation.FormallyanallocationisalistofsetsZ1;:::Zn,oneforeachagentAgiwiththestipulationthat:ZiZandforalli;j2Agsuchthati6=j,wehaveZi\Zj=;.Thusnogoodisallocatedtomorethanoneagent.ThesetofallallocationsofZtoagentsAgis:alloc(Z;Ag)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/53 Chapter14AnIntroductiontoMultiagentSystems2eIfwedesigntheauction,wegettosayhowtheallocationisdetermined.Howshouldthisbe?Onenaturalwayistomaximizesocialwelfare.–Sumoftheutilitiesofalltheagents.Deneasocialwelfarefunction:sw(Z1;:::;Zn;v1;:::;vn)=nXi=1vi(Zi)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/54Chapter14AnIntroductiontoMultiagentSystems2eGiventhis,wecandeneacombinatorialauction.GivenasetofgoodsZandacollectionofvaluationfunctionsv1;:::;vn,oneforeachagenti2Ag,thegoalistondanallocationZ1;:::;Znthatmaximizessw,inotherwordsZ1;:::;Zn=argmax(Z1;:::;Zn)2alloc(Z;Ag)sw(Z1;:::;Zn;v1;:::;vn)Figuringthisoutiswinnerdetermination.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/55 Chapter14AnIntroductiontoMultiagentSystems2eHowdowedothis?Well,wecouldgeteveryagentitodeclaretheirvaluation^vi–Thehatdenotesthatthisiswhattheagentsays,notwhatitnecessarilyis.–Theagentmaylie!Thenwejustlookatallthepossibleallocationsandgureoutwhatthebestoneis.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/56Chapter14AnIntroductiontoMultiagentSystems2eOneproblemhereisrepresentation,valuationsareexponential:vi:2Z7!R–Anaiverepresentationisimpractical.–Inabandwidthauctionwith1122licenseswewouldhavetospecify21122valuesforeachbidder.Searchingthroughthemiscomputationallyintractable.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/57 Chapter14AnIntroductiontoMultiagentSystems2eBiddinglanguagesRatherthanexhaustiveevaluations,allowbidderstoconstructvaluationsfromthebitstheywanttomention.Atomicbids(Z;p)whereZZ.AbundleZ0satisesabid(Z;p)ifZZ0.Inotherwordsabundlesatisifesabidifitcontainsatleastthethingsinthebid.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/58Chapter14AnIntroductiontoMultiagentSystems2eAtomicbidsdenevaluationsv(Z0)=pifZ0satises(Z;p)0otherwiseAtomicbidsalonedon'tallowustoconstructveryinterestingvaluations.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/59 Chapter14AnIntroductiontoMultiagentSystems2eToconstructmorecomplexvaluations,atomicbidscanbecombinedintomorecomplexbids.OneapproachisXORbidsBi=(fa;bg;3)XOR(fc;dg;5)XORbecausewewillpayforatmostone.Wereadthebidtomean:Iwouldpay3forabundlethatcontainsaandbbutnotcandd.Iwillpay5forabundlethatcontainscanddbutnotaandb,andIwillpay5forabundlethatcontainsa,b,candd.Fromthiswecanconstructavaluation.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/60Chapter14AnIntroductiontoMultiagentSystems2eThus:v1(fag)=0v1(fbg)=0v1(fa;bg)=3v1(fc;dg)=5v1(fa;b;c;dg)=5http://www.csc.liv.ac.uk/˜mjw/pubs/imas/61 Chapter14AnIntroductiontoMultiagentSystems2eMoreformally,abidlikethis:=(Z1;p1)XOR:::XOR(Zk;pk)denesavaluationvlikeso:v(Z0)=0ifZ0doesn'tsatisfyany(Zi;pi)maxfpijZiZ0gotherwisehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/62Chapter14AnIntroductiontoMultiagentSystems2eXORbidsarefullyexpressive,thatistheycanexpressanyvaluationfunctionoverasetofgoods.Todothat,wemayneedanexponentiallylargenumberofatomicbids.However,thevaluationofabundlecanbecomputedinpolynomialtime.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/63 Chapter14AnIntroductiontoMultiagentSystems2eWinnerDeterminationThebasicproblemisintractable.Butthisisaworstcaseresult,soitmaybepossibletodevelopapproachesthatareoptimalandrunwellinmanycases.Canalsoforgetoptimalityandeither:–useheuristics;or–lookforapproximationalgorithms.Commonapproach:codetheproblemasanintegerlinearprogramanduseastandardsolver–oftenworksinpractice.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/64Chapter14AnIntroductiontoMultiagentSystems2eTheVCGMechanismIngeneralwedon'tknowwhetherthe^viaretruevaluations.Lifewouldbeeasieriftheywere!–Well,canwemakethemtruevaluations?Yes,inageneralizationoftheVickreyauction.–Vickrey/Clarke/GrovesMechanismMechanismisincentivecompatible:tellingthetruthisadominantstrategy.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/65 Chapter14AnIntroductiontoMultiagentSystems2eNeedsomemorenotation.Indifferentvaluationfunction:v0(Z)=0forallZ.swiisthesocialwelfarefunctionwithouti:swi(Z1;:::;Zn;v1;:::;vn)=Xj2Ag;j6=ivj(Zj)AndwecanthendenetheVCGmechanism.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/66Chapter14AnIntroductiontoMultiagentSystems2e1.Everyagentsimultaneouslydeclaresavaluation^vi.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/67 Chapter14AnIntroductiontoMultiagentSystems2e2.Themechanismcomputes:Z1;:::;Zn=argmax(Z1;:::;Zn)2alloc(Z;Ag)sw(Z1;:::;Zn;^v1;:::;^vi;:::;^vn)andtheallocationZ1;:::;Znischosen.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/68Chapter14AnIntroductiontoMultiagentSystems2e3.Themechanismalsocomputes,foreachagenti:Z01;:::;Z0n=argmax(Z1;:::;Zn)2alloc(Z;Ag)sw(Z1;:::;Zn;^v1;:::;v0;:::;^vn)theallocationthatmaximisessocialwelfarewerethatagenttohavedeclaredv0tobeitsvaluation.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/69 Chapter14AnIntroductiontoMultiagentSystems2e4.Everyagentipayspi,where:p=swi(Z01;:::;Z0n;^v1;:::;v0;:::;vn)swi(Z1;:::;Zn;^v1;:::;^vi;:::;vn)http://www.csc.liv.ac.uk/˜mjw/pubs/imas/70Chapter14AnIntroductiontoMultiagentSystems2eOnotherwords,eachagentpaysoutthecost,tootheragents,ofithavingparticipatedintheauction.ItisincentivecompatibleforexactlythesamereasonastheVickreyauctionwasbefore.Ifyoubidmorethanyourvaluationandwin,wellyouenduppayingbackwhatthegoodisworthtoeveryoneelse,whichismorethanitisworthtoyou.Ifyoushadeyourbid,youreduceyourchancetowin,butevenifyouwinyouarestillpayingwhateveryoneelsethinksitisworthsoyoudon'tsavemoneybyreducingyoruchancetowin.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/71 Chapter14AnIntroductiontoMultiagentSystems2eSowegetadominantstrategyforeachagentthatguaranteestomaximisesocialwelfare.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/72Chapter14AnIntroductiontoMultiagentSystems2eeBayhttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/73 Chapter14AnIntroductiontoMultiagentSystems2eeBayrunsavariationoftheEnglishauction.Vulnerabletosniping.Tocounterthis,eBayoffersaautomatedbiddingagent.–ReducestheauctiontoaFPSB.Manycompaniesoffersnipingservices.BTW,thereisaneasyxtosniping,buteBaychosenottouseit.–Activityrulehttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/74Chapter14AnIntroductiontoMultiagentSystems2eAdwordauctionshttp://www.csc.liv.ac.uk/˜mjw/pubs/imas/75 Chapter14AnIntroductiontoMultiagentSystems2eTodecidewhichadsgetshowninwhichpositionforwhichsearches,anadwordauctionisrun.Thisisruninrealtime.(Thoughclearlybidsareplacedbeforehand.)AuctionisavariationontheVickreyauction.85%ofGoogle'srevenue($4.1billion)in2005camefromtheseauctions.Veryactiveareaofresearch.–Notclearwhatthebestauctionmechanismisforthisapplication.–Notclearwhatthebestwaytobidis.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/76Chapter14AnIntroductiontoMultiagentSystems2eSummaryAllocatingscarceresourcescomesdowntoauctions.Welookedatarangeofdifferentsimpleauctionmechanisms.–Englishauction–Dutchauction–Firstpricesealedbid–VickreyauctionThewelookedatthepopulareldofcombinatorialauctions.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/77 Chapter14AnIntroductiontoMultiagentSystems2eWediscussedsomeoftheproblemsinimplementingcombinatorialauctions.AndwetalkedabouttheVickrey/Clarke/Grovesmechanism,ararerayofsunshineontheproblemsofmultiagentinteraction.http://www.csc.liv.ac.uk/˜mjw/pubs/imas/78