【行业研报】国际清算银行-完全去中心化系统中讲真话的一个不可能定理（英）-2023.8_市场营销策划.docx

AnImpossibi1ityTheoremonTruth-Te11inginFu11yDecentra1izedSystemsTheviewsexpressedarethoseoftheauthorsanddonotnecessari1yreectthoseoftheBIS.Wearegratefu1toBrunoBiais,Gabrie1eCamera,JonathanChiu,JohannesHoerner,ThorKoepp1,Jean-Char1esRochet,HyunSongShin,JensWitkowskiandconferenceandseminarparticipantsatthe2023TheoryandExperimentsinMonetaryEconomicsconferenceatGeorgeMasonUniversity,Tokenomics2023,the2023ASSAWinterMeetings,theFrankfurtSch1ofFinanceandManagement,theUniversityofBonn,andtheTou1ouseSchoo1ofEconomicsforhe1pfu1comments.tBankforInternationa1Sett1ements.Emai1:rodney.garrat1bis.org.*UniversityofBemandStudyCenterGerzensee.Emai1:Cyri1monnet1Inibe.chRodneyGarratt+Cyri1Monnet*August2023AbstractWeshowthattruthfu1reportingabouttherea1izationofapub1ic1yobservedeventcannotbeimp1ementedasauniqueequi1ibriuminacomp1ete1ydecentra1izedenvironment.Ourworkprovidesatheoretica1underpinningoftheneedfororac1esandthere1atedt4orac1cprob1em.”Keywords:decentra1izedsystems,smartcontracts,truth-te11ing,orac1eprob1emJE1C1assificationNumbers:C72,D72,D86,033Thetruth?What,sthat?Don'tyouknowthatthedayhascomewhenthetruthishatwecaretomakeit?-1ainCrichtonSmith,Considerthe1i1ies1IntroductionSmartcontractsarese1f-executingprogrammab1econtractsbetweentwoormoreparties.Smartcontractsdonotrequireavettingauthoritybecausetheir1egitimacyre1iesondecentra1ized1edgertechno1ogies.Howevertheimp1ementationofmanypotentia11yusefu1smartcontractapp1icationsdependsuponverifyingthatsomerea1-wor1deventhastakenp1ace(thinkinsurancecontracts).Thisisaprob1em.Giventheirfu11ydecentra1izednature,howdoesasmartcontractse1ectwhatthetruestateofthewor1dis?Moregenera11y,howdofu11ydecentra1izedsystemsfunctionwhentheiroperationdependsontheexistenceofasing1e,mutua11yaccepted,recordofthetruth,butthereisnosing1eauthoritythatcanprovidethisrecord?Thispaperconsidersasituationwheremu1tip1eindividua1sseektoenterintoagreementsbasedontheoutcomeofarea1-wor1devent,butthereisnotrustedparty(i.e.,contractib1esource)thatcanbeusedtodeterminepayoffs.Inthiscase,payoffsmustbebasedonsomeformofco11ectiveagreementonthetruestateofthewor1d.Byappea1ingtothreebasicproperties,anonymity,neutra1ity,andmonotonicity,wecanrestrictattentiontomajorityvoting.Inthisenvironment,agentsreportthetruththatismostbeneficia1forthem.Incentivestorewardconsensusdonotnecessari1ymakethingsbetter.Rather,they1eadtoasituationthatisakintoabeautycontesta1aKeynes(1936),inwhichagentsreportwhattheythinkthemajorityofotheragentswi11report.Withorwithoutreportingincentives,thereportofthetruestatethatresu1tsfrommajorityvotingdoesnotdependuponthetruestate.Ourmainana1ysisfocusesonsimu1taneousvoting.However,wea1sobrief1yexp1orethepossibi1ityofsequentia1p1ay,bya11owingindividua1stovoteinarandomorderanda11owingeachindhddua1toseethePreViOUSvotes.Inathree-agentmode1withsequentia1votingindividua1sunanimous1yagreeonwhatthestateofthewor1dis,butthismaynotbethetruestate.Theresu1tsuggeststhatsequentia1votingisnotaso1utiontothetruth-te11ingprob1em.Ourgenera1resu1t,whichapp1iestosimu1taneousvotinggames,isthattheon1ywaythatindividua1sarewi11ingtovoteaccordingtothetruestateisiftheyarecomp1ete1yindifferentastowhatthetruestateshou1dbe.Thatis,theirpayoffscannotdependontheiractionsortheirindividua1reports.Thisgenera1resu1tsuggeststhatabsentadditiona1motivation(e.g.,deonto1ogica1preferencestowardtruth-te11ing,seeBergstrometa1.(2019)that1inksindividua1payoffstothetruth,thereisnowaytoimp1ementcontractsthatpayoutbasedonanobservedstatewithoutatrustedsource.Ourana1ysishasaspectsincommonwithpeerpredictiongames(PPG);see,forexamp1eGaoeta1.(2016)andKongandSchoenbeck(2019)andthereferencestherein.Inthesesettings,thereistypica11yoneobjectthathasanunknowncharacteristicandsevera1agentscanexertefforttoobtainasigna1aboutthischaracteristic.Thesesigna1scanbecorre1ated(i.e,comefromthesamedistribution),butthereistypica11ynoknown“groundtruth.wThe1iteraturestudiespeerpredictionmechanismsthatareusedtomakesureagentsexerteffortandthattheycommunicatetheirsigna1struthfu11y.AnaspectthatmakesbothourgameandPPGsimi1aristhatinbothcasesagentshavetosendsigna1saboutwhattheyobserve.A1soneitherthepeerpredictionmechanismnorourscanre1yonthegroundtruth(evenifitexists)todiscip1ineagents.Thereare,however,importantdifferencesbetweenPPGsandourgame.Ourgameisoneofcommonknow1edge(everybodyknowsthetruestate,andeverybodyknowsthateverybodyknows,etc.),whi1ethereisnocommonknow1edgeinPPG.Thisisinpartbecausetheremaybenoobjectivegroundtruth,ratherthetruthmaybesubjective.Inaddition,inPPGs,agentsdonotknowthesigna1sofothers.Trida11y,ouragentsdonotneedtoexertefforttocoordinateonwhattheycommon1yandfree1yobserve.Ouragentshaveanex-antestakeinthe“truth,"whi1einPPGtheon1yrewardistheoneagentsobtainbyugettingitrightwre1ativetootheragents.Fina11y,inourgame,therewardisidiosyncraticanddependson“types”.Theimportanceoftheabi1itytowritecontractsbasedonobservedstateshas1ongbeenrecognizedintheeconomics1iterature.Radner(1968)forma1izedtherequirementforstateverificationinc1ass