The Economics of Scienti…c Misconduct

NicolaLacetera

CaseWesternReserveUniversityy

LorenzoZiruliaUniversityofBolognazCESPRI,BocconiUniversity

October18,2007

Abstract

Thetypesofscienti…cfraudsthatareobservedareunlikelytoberepresentativeoftheoverallamountofmalfeasanceinscience.Starscientistsaremorelikelytomisbehave,butlesslikelytobecaughtthanaveragescientists.Areductioninthecostsofcheckingforfraudsmayleadtoachangeinthetypeofresearchthatisperformed(e.g.moreorlessinnovative)ratherthantoareductionofmisconductepisodes.Contrarytoconventionalwisdom,anincreaseincompetitionbetweenscientistsmayreduce,andnotincrease,scienti…cmisconduct,asitstimulatesmoremonitoring.Amoreactiveroleofeditorsincheckingformisconductdoesnotalwaysprovideadditionaldeterrence.Theseclaimsderivefromagame-theoreticmodelofthepublicationprocess,whereauthorsareasymmetricallyinformedaboutthesuccessoftheirprojects,andcanfraudulentlymanipulatetheirresults.Inevaluatingapaper,theauthor’speershaveincentivestoperformathoroughscrutinysincetheyarecompetitorsoftheauthor,butalsohavedisincentivestodosoasusersorcomplementorsofthatparticularresearch.Themagnitudeandsignoftheutilitythatscientistsreceivefromapeer’ssuccesscruciallydeterminetheirincentivestodetectfraud,aswellasthedecisionofaresearchertocommitfraudinthe…rstplace.

WethankNickArgyres,NeerAsherie,EricBettinger,SylvainChassang,DavidCooper,RobinDubin,MaryannFeldman,PaulHeaton,DavidKaplan,FrancescoLissoni,GustavoManso,DanielePaserman,JimReb-itzer,TokeReichstein,HeatherRoyer,JustinSydnor,andJohnWalshfortheircomments.WearealsogratefultoMonicaBradfordandLindaMiller,oftheeditorialboardsofScienceandNaturerespectively,forsharingwithusdetailsontherefereeingandeditingprocessinscienti…cjournals.AdamStohsprovidedexemplaryresearchassistance.y

DepartmentofEconomics,WeatherheadSchoolofManagement,CaseWesternUniversity,Cleveland,OH,USA.Email:nxl51@case.edu.z

DepartmentofEconomics,UniversityofBologna,Italy.CenterofResearchonInnovationandInternational-ization(CESPRI),BocconiUniversity,Milano,Italy.Email:lorenzo.zirulia@unibocconi.it.

󰀄

Introduction

Inthe…rsthalfofthe1900s,theSwissbiochemistEmilAbderhaldenpublishedhundredsonarticleonwhathecalled\"defensiveenzymes\".Subsequently,numerousscientistsdevelopedseveraltestsbasedontheexistenceofdefensiveenzymes.Theseincludedpregnancytests,thediagnosisofsomeformsofcancer,andtestsforpsychiatricdisorders.ResearchersinNaziconcentrationcampsusedAbderhalden’stheoriesto\"prove\"thesuperiorityoftheAryanrace.LargeamountsofpublicandprivatemoniesweregrantedtoAbderhaldenandhiscollaborators.Afewresearchersinthe1920sbegantoquestionthevalidityandreplicabilityofAbderhalden’sexperiments,buthisworkwasrevealedtobelargelyfraudulentonlyin1998(DeichmannandMüller-Hill1998).Defensiveenzymes,simply,donotexist.

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In1988,thescienti…cjournalNatureagreedtopublishanarticleoftheimmunologistJacquesBenvenistewithpositiveevidenceofthee¤ectivenessofhomeopathy.Mostinvestigatorswereunabletoreplicatetheresults,andidenti…edseveralformsofnegligenceandmisconduct(Mad-dox1988,Park1997,Fisher1999).

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TheexperimentalworkofchildpsychologistBrunoBettelheimsuggestedthatamajorcauseofchildautismwasbadparenting,andinparticularthelackofa¤ectionofmotherstowardstheirchildren.These…ndingsa¤ectedgenerationsofpsychologists,parents,andchildren.However,afterBettelheim’sdeathin1990,mostoftheevidenceontherelationbetweenparentingandautismheproducedwasfoundtobenon-existentandalmostentirelyfabricated(Pollak1997).

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WhenhewontheOtto-Klung-WeberbankPrizeforPhysicsin2001atage31,JanHendrikSchön,arisingstarphysicistatBellLabs,waschurningonearticleeveryeightdays.Hisresearchonorganictransistorspromisedtoberevolutionaryandtohavemajorimpactsinseveralscienti…c…elds,includingthedevelopmentofnanotechnology.SomeobserversspeculatedthatSchön’sdiscoveriescouldspelltheendoftheentiresiliconchipindustry,sincetraditionalchipswouldbesubstitutedbyorganictransistors.Severalotherphysicists,however,beguntoquestionhisworkafter…ndinganomaliesinthedataonanumberofhispublishedarticles.EvidenceofSchön’sscienti…cmisconductwasfoundinatleastsixteenpapers.Wholedatasetswerereusedinanumberofdi¤erentexperiments,andsomegraphswerefoundtohavebeenproducedusingmathematicalfunctions.SeveraljournalswithdrewSchön’sarticles,BellLabs…redhim,andhewasdeprivedofhisdoctoratebytheUniversityofKonstanzin2004(GossLevi2002a,2002b,BellLabs2002,BBC2004).

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ThebiomedicalscientistWoo-SukHwangrosetofamein2004thankstoaseriesofbreak-throughsinthe…eldofstemcellresearch.Thenoveltyandrelevanceofhisalleged…ndingsledseveralscholarstoinvestigatefurtherintotheirsolidityandaccuracy.Hwang’sresultswerefoundtohavebeenfraudulentlyreported.Mostofthecelllinesobjectofhisresearchturnedouttohavebeenfaked,andpicturesofallegedlydi¤erentcellswerefoundtobephotosofthesamecell.Hwangadmittedtovariousliesandfrauds.1OnMay12,2006,hewasindictedonembezzlementandbioethicslawviolations(Kolata2005,Fi…eldandCookson2006).

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EricPoehlman,ascientistinthe…eldofhumanobesityandaging,wasaccusedofscienti…cmisconductandonMarch17,2005hepleadedguiltytothecharges,acknowledgingfalsifying17grantapplicationstotheNationalInstitutesofHealthandfabricatingdatain10ofhispapers.Hehadtheorizedthatmenopausemakeswomenlosemuscleandgainfat,andcauseshealthproblemsthathormonescouldhelp…x.Millionsofwomenwereprescribedhormonetherapybytheirdoctors,onlytolearnafterwardsthatitshealthbene…tswereneverprovedandtherewererisksinvolvedinstead.ThegovernmentprosecutorsstatedthatDr.Pohelmanhaddefraudedagenciesoutof$2.9million.InvestigationsonthescientistbeganafteronehiscollaboratorsrevealedthatPoehlmanwasfabricatingdatainhislaboratory.OnJune28,2006,Poehlmanwasorderedtoserveayearandadayinprisonforusingfalsi…eddatainfederalresearchgrants.Healsopaida$180,000…ne,andwasbarredforlifefromreceivingfederalresearchfunding.Itwasthe…rstcasewhereanacademicscientistwasgivenprisontimeforfalsifyingdataingrantsubmissions(Chang2004,O¢ceofResearchIntegrity2005,CBS2005,Kintisch2006).

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Ontheonehand,these\"vignettes\"o¤eragrimimageofthescienti…ccommunity,andindeedaveryworrisomeone.Knowledgeisakeyassetthatallowsindividualstoimprovetheirsocioeconomicstatus,companiestosucceedinthemarketplace,andcountriestogrowandprosper.Scienti…cresearchisamajorprocessthoughwhichknowledgeisgenerated.Suchdecisionsasbusinessstrategies,aswellasdecisionsaboutone’shealthorchildeducation,dependalsoonthe…ndingsfromscienti…cresearch,aspublishedinprofessionaljournalsanddivulgedthroughthemedia.Iffalseandfabricatedresultsaregeneratedandpublished,thenegativeconsequencesonsocialwelfarecanbemajor.Scienti…cfraudisthereforenotjustaninternalmatterforthescienti…ccommunity,butagreaterproblemthatsocialscientistneedtoaddress.

HealsoadmittedthathespentprivatedonationsforresearchtopaytheRussianma…aformammothtissues,tobeusedtocloneextinctspecies(Reuters2006).

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Ontheotherhand,ifscienti…cmalfeasancewaslimitedtoafewhigh-pro…lecasesandafew\"badapples\andthesewerepromptlydiscoveredthroughthestandardproceduresandself-correctingmechanismswithinthescienti…ccommunity,thentheconcernswouldbelargelyunjusti…ed.Butisthisthecase?Theexistingevidenceo¤ersalesscomfortingpicture.Reportsofdi¤erenttypesofmisconduct–suchasdatafabrication,falsi…cation,mining,andplagiarism–aboundinanyscienti…cdiscipline.FreelandJudson(2004)andPozziandDavid(2007)documentasteady‡owofnewcasesopenedandallegationscon…rmedattheUSO¢ceofResearchIntegrity(ORI)overthepastdecade.Swazeyetal.(1993)documentthatabout10%ofthescientistsrespondingtotheirsurveyshavewitnessedepisodesofscienti…cmisconduct.Martinsonetal.(2005)…ndthat,whileonlyfewscientistsadmithavingexplicitlyfabricatedor\"cookedup\"data,upto10-15%ofscientistsadmittedtohaveperformedsuchbehaviorsasomittingdatathatdidnotconformtotheirexantetheories,withoutanysolidlogicalbasisfortheirchoice.

Scienti…cmisconduct,therefore,appearsasapervasivephenomenon,asystemiccharacteris-ticofthescienti…ccommunityratherthenamatterofafewepisodesofmisbehavior.Especiallyinthenaturalsciences,scholarsareshowinggreatawarenessoftheproblem.Severalproposalstodetermalfeasanceinsciencehavebeenadvanced.Theseproposalsincludemakingreplicationeasierandmorerewarded,andsofteningcompetitionamongscientists,sinceharshrivalryforpriorityinpublicationisseenasconducivetodishonestpractices.2

Thecurrentunderstandingofthisphenomenon,however,isstillverylimited.Forexample,analysesarelargelybasedonreportsandaccountsaboutresearcherswhohavebeenfoundcommittingfrauds,3andespeciallyon\"highpro…le\"cases,suchassomeofthosedescribedabove.Asmuchastheseaccountsaresuggestive,theyo¤eronlyalimitedpictureoftheproblem.Morebroadly,thecurrentdebatelacksatheoreticalbackgroundoftheunderlyingincentivesofscientiststoundertakefraudulentbehaviorintheirresearch,andtheincentivesoftheirpeerstodetectthesebehaviors.Elaboratingsuchatheorywouldallowformorefoundedpredictionsofthekindsofresearchandofresearchersthataremorelikelytoengageinfraudulentbehavior,andoftheimpactofdi¤erentpolicyproposalstoreducemisconduct.Inthispaper,atheoryofscienti…cmalfeasanceisproposed.

Theresearchandpublicationprocessisanalyzedasadynamicgameofincompleteinfor-mationthatreproducesthemainfeaturesoftheoperatingofthescienti…ccommunity.4Inthe

SeeforexampleFreelandJudson2004,CouncilofScienceEditors2005,Fuller2006,andtheSpecialIssueofNatureonJanuary18,2007.Moreover,in2007theORIandtheEuropeanScienceFoundationhaveorganizedtheFirstWorldConferenceonResearchIntegrity.3

SeePozziandDavid(2007)forarecentdescriptiveaccountofmalfeasanceinscience,basedondiscoveredcases.Similaranalyses,basedondetectedcases,havebeenperformedwithreagrdtoothertypesofmisconduct,suchas…nancialfraud.SeeforexampleDycketal.(2007).4

Previousattemptstomodeltheresearchandpublicationprocess,withconsiderationformisconduct,includeWible1998andGlaeser2006.Thesestudiestreattheprocessasaone-persondecisionproblemratherthanamulti-agentgame.Glaeser’spaper,moreover,isexclusivelyfocussedontheanalysisofempiricalresearchin

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…rststageofthegame,ascientistdecideswhattypeofresearchtoundertake,i.e.,moreorlessradical.Theresearchissuccessfulwithsomeprobability.Thescientistthendecideswhethertosubmittheresultsoftheprojectforpublication.Iftheprojectfailed,thescientistcanstillsubmitapapertoajournal,butonlyaftercommittingsomefraudulentbehavior5–otherwise,reviewerswillimmediatelyspotthefailureoftheproject.Ifthepaperisacceptedandpublished,apotentialreaderofthearticledecideswhethertothoroughlycheckthepaper–inwhichcaseanyfraudisspotted–orjusttoreaditlightly.Theauthorofthepaperreceivesabene…tifthemanuscriptispublished.Ifhecommittedfraudandthefraudisdetected,incontrast,thescientisthasnegativeutility.Asforthereader,ontheonehandshemayenjoyanadvanceofscienceandmaybene…tfromaspeci…cresulthavingbeenfound.Thisresult,forexample,mightlegitimatethe…eldofresearchofthereader,andbecomplementarytoherownwork.Ontheotherhand,thereadermayalsoderivedisutilityfromthesuccessofathirdscientist’sresearch.Thesuccessofthescientistreducesherroomforcontributions.Shecanthereforebeacompetitor.

Themodelshows,…rst,thattheremaybeadivergencebetweentheprobabilitythatacertainkindoffraudiscommittedandtheprobabilitythatitisdiscovered.Inparticular,iftherewardfromradicalresearchishigh,theprobabilityofdetectingmisconductishigherforradicalresearch,althoughfraudsaremorecommoninincrementalresearch;similarly,itismorelikelythatfraudisdiscoveredintheworkofascientistwithalowerreputationthanintheworkofastar,eveniftheprobabilitytopublishafraudulentpaperishigherforastar.

Asecondsetofresultsqualifyandevencontradictsomeoftheconventionalwisdomandproposedpoliciestodeterfraudinscience.First,weconsiderthee¤ectsofreducingthecostsofcheckingformisconductbyanauthor’speers.Weshowthat,ifareductionincheckingcostsdoesnotinduceachangeinthetypeofresearchanauthorundertakes(e.g.radicalversusincremental),thenthelikelihoodthatmisconductgoesundetecteddecreases.Incontrast,theprobabilityofundetectedfraudmayincreaseiftheauthorchangesthetypeofresearch.Second,weassesswhetherexcessivecompetitioninthescienti…carena,asfrequentlyclaimed,canbeamongthecausesoffraudulentbehavior.Inthiscase,weshowthatanincreaseincompetitionbetweenscientistsmayreducescienti…cmisconduct,insteadofincreasingit.Thisoccursbecausecompetitionalsoincreasesthebene…tsfromcheckingandthereforetheoverallintensityofscrutiny.

Athirdsetofresultsderivefromanextensionofthemodeltoconsideramoreactiverolebyajournal’seditorialboardsindeterringmisconduct.Ourmodelimpliesthatadditionalchecksbyjournals’editorialboardsbeforepublicationdodetermisconductinsomecircumstances,

Economics.MialonandMialon(2003)analyzethedecisionofascientistonhowinnovativetobe,withinanauthor-reviewergame.5

Weareassumingtherethereareno\"innocentmistakes\".Bettersaid,weassumethatitisalwayspossibletodiscernanhonestmistakefromafraud.

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especiallywhenthelikelihoodoftheseadditionalcheckstobeperformedisveryhigh.Inothercases,theseadditionalcontrolscaninsteadback…reandbeconducivetomoremisconduct.For,readersmaychecklessfrequentlyinresponse,andauthorsmaychangethetypeofresearchtheyperform,thuschangingtheequilibriumofthepublicationgame,includingthepropensitytocommitfrauds.

Theseresultsappearasconsistentwiththeanecdotalevidenceonscienti…cmalfeasanceinthat,forexample,accountsofmisconductoftenconcern(allegedly)pathbreakingresearchbyscientists\"ontherise\".Theresults,however,positnumerouscaveatsonthede…nitionofpoliciestodeterfraud.First,policyimplicationsonscienti…cmisconductshouldnotbasedondetectedfrauds,sincethe\"wrong\minoritariantypesofactualfraudandofscientistsmightbetargeted,throughpoliciesthatarenotappropriatefordeterringthemajorityof(undetected)frauds.Sec-ond,severalprovisionstypicallyassumedtoreducefraudulentbehaviormightactuallyback…reandleadtoahigher,insteadoflower,incidenceofmisconduct.Theseincludethereductionofreplicationcosts,thecontainmentofcompetitionamongresearchers,andtheinvolvementofmultiplelayersofdetectionbothbeforeandafterpublication.

Section1developsthepublicationgame,whichisthensolvedinSection2.InSection3,theimplicationsoftheresultsarederivedanddiscussed.Section4concludes.

1Thepublicationgame

Weintroduceagame-theoreticmodelofthepublicationprocess,wherescientistsperformre-searchwhoseresultstheycanalsofake,andtheysendpaperstojournals.Thesepapersareevaluatedbythescientists’peers.ThegameisrepresentedinextensiveforminFigure1.Adetaileddescriptionofthesetupfollows.Table6inAppendixAprovidesasummaryofthenotationadoptedinthemodel.

PlayersTherearefourplayers:theauthorofanarticle,(A),\"nature\"(N),aneditor-reviewer(E),andareaderofthearticle(R)ifthearticleispublished.Actions,timing,andinformationstructure

Thegamehas…vestages.Inthe…rststage,

theauthorAdecideswhethertoundertakea\"radical\"researchproject(actionrad),whichcanpotentiallyleadtomajornovelresults,ortoundertakeincrementalresearch(actionincr),whichmightleadtominorimprovementstotheexistingknowledge.

Inthesecondstage,nature(N)chooseswhethertheprojectissuccessful(succ)ornot(fail).Theprobabilitiesofsuccessofaradicalandofanincrementalprojectare,respectively,󰀃radand󰀃incr.Theoutcomeoftheprojectisobservedonlybytheauthor.

Inthethirdstage,theauthorAdecideswhethertosubmitapaperresultingfromtheresearch(subm),ornottosubmit(nosubm).Iftheprojectfailed,andtheauthorsubmitsthepaperas

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Aincrrad)-(1fail βincr)NsuccNsucc (β (βAsubmno submincr)-(1fail βradA-cincr; 0mAsubmno submno submrad)A-crad; 0mno submsubE)rej (1ncrrej)incr (1-cincr; 0-incr)Erejsubrej (1πi (1-crad; 0-rad (πad)πacc ()πracc-cincr; 0Rckcheckacc-cincr; 0acc ( (πradeck-πincrπ)-π)-crad; 0cherad)-crad; 0ckRckcheckno checheno chcheBincr-cincr;Wincr-gincr-cincr;Gincr-cRincrBincr-cincr;WincrBincr-cincr;Wincr-cRincrBrad-crad;Wrad-grad-crad;Grad-cRradBrad-crad;Wradno chno eckckBrad-crad;Wrad-cRradFigure1:Gametreeforthepublicationgame.Playersandpayo¤sarereportedinboldtypes.Actions

areinitalics.Thedottedellipsesrepresentinformationsets.Thenotationisdescribedbelow,andsummarizedinTable6inAppendixA.

itis,itwouldneverbepublished.Therefore,sendingthepaperisequivalenttonotsubmittingitatall.However,theauthorcandecidetofaketheresultsoftheresearchandsendapaperthusfaked.6

acceptsthepaperforpublication.Theeditor-reviewerEisthereforemodeledjustasaproba-Inthefourthstage,theeditor-reviewerE,withsomeprobability󰀆i2(0;1)(i=rad;incr)

bilitydistributionwithnoactiverole.Thischoiceisnottoorestrictiveforouraims.Journaleditorsandreviewersarenotexpectedtocheckformisconduct,forexampletheyarenotre-quiredtoasktheauthorsfortherawdata.Mostactionsaimedatcheckingforfraudsoccurafterthepublicationofastudy.Editorsmaycometoplayarolethen,buttypicallynotbeforepublication.7Inanextensionofthemodelbelow(Section3.3),wealsoconsiderthee¤ectof

Thesuccessorfailureoftheprojectdoesnotdependonthee¤ortspentbytheauthor,whichinfactisnotmodeledinthegame.Thisisclearlyalimitation,asonecouldarguethatbyexertinghighere¤ortandcare,ascientistreducesthechancesoffailure.Weareinterested,however,notasmuchinthedeterminantsofsuccessofaproject,asintheincentivesthatscientistshavetocommitfraud,andoftheirpeerstocheckforthesefrauds.Thedecisionofwhethertocommitfraudornotmaybeseenasnotrelatedtotheamountofe¤ortspentintheresearch.Inthisrespect,theexclusionofe¤ortfromthemodelisnottoorestrictive.7

Theinformationwegatheredonthistopicfromconversationswitheditorsatsomemajorscienti…cjournalsareconsistentwiththeseclaims.SeealsoLaFollette(1992)andHamermesh(2007).Notealsothatwearemerging

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havingmisconductchecksbeenperformedalsobyeditorsbeforepublication.

The…fthstageoccursonlyifthemanuscriptispublished.ThereaderRdecideswhethertocheckthepaperornot.Thecheckactionsummarizesdi¤erentbehaviors.Thereadermayrequesttherawdatatotheauthorandtrytorreplicatethestudy,orshemaytrytobuildasimilarexperiment.Thereadercanalsotrytobuildontheoriginalstudy,and,throughherownwork,shemay…nddiscrepanciesintheoriginalpaper.ThecasesdescribedintheIntroductionprovideexamplesonhowascientist’speersorevencollaboratorsscrutinizetheworkofaresearcher.Ifthecheckisperformed,cheating(ifoccurred)isdetectedwithcertainty.

Thereadercannottellwhethertheauthorhascommittedfraudunlesssheperformsathor-oughcheck.Onlytheprobabilitydistributionoversuccessversusfailure,andoverthebehavioroftheeditor-refereeE,iscommonknowledge.Thechoiceofthetypeofresearchisperfectlyobserved.Payo¤s

Performingresearchhasacostfortheauthor.Callthecostofperformingradical

researchcrad,andthecostofperformingincrementalresearchcincr.Performingresearchalsogeneratesabene…tforA,iftheresearchispublished:BradandBincr.Thisbene…tsummarizesreputationalgains,careeradvancements,andpossiblymonetaryrewards.

ThesuccessofA’sresearchgeneratesareturnofWi(i=rad,incr)forthereaderR.Thesereturnsmaybepositiveornegative.Rmayenjoyanadvanceofscience.Also,shemaybene…tfromacertainresultbeingpublished:thisresultmightcontributetolegitimatingthe…eldofresearchthereaderisalsoworkingon,andmaybecomplementarytoherworkand…ndings–thereader,too,isamemberofthescienti…ccommunity.RcanalsoderivedisutilityfromthesuccessofA’sresearch.RandAcanbecompetitors,sothatasuccessofAreducestheroomforcontributionsbyR.Thereaderalsobearssomecostsifsheplayscheck.CallthesecostscRradforradicalresearchandcRincrforincrementalresearch.Thesecostscanbeseenasafunctionofthetimeande¤ortspentinathoroughscrutiny.Theycanalsohaveotherdeterminants.Forexample,ayoungscholarquestioningtheworkofahigher-reputationpeermighthaveproblemsinhavingherownworkpublishedandinobtainingrecognitionsandpromotions.8

Ifcaughtcheating,Abearsadisutilitygi(i=rad,incr).Thiscostcanbeseenasaloss

twopotentiallydistinct…gures:theeditorandthereviewers.Editorsandreviewersmayhavepartiallydi¤erentattitudestowardapaper.Forexample,aneditormaybeverykeentopublishanallegedlygroundbreakingarticleinhisjournal.Thereviewer,instead,mightdecidetobetougheronpotentiallymoreinnovativeresearch,andshemayalsohaveanegativereturnfromacompetitormakingamajorleapina…eld.Numerousstudies,however,showthatinmostofthecaseseditorsfollowtheopinionsofthereferees,andtrytobuildconsensus(orreducediscrepancies)amongdi¤erentreferees(seeRothwellandMartyn2000).Interviewswitheditorsatafewleadingscienti…cjournalscon…rmedthisbehavior.Forthesereasons,mergingeditorsandrefereesdoesnotappearasanunacceptablesimpli…cation.8

In1986MargotO’Toole,apostdoctoralresearcheratMIT,questionedtheresultsinapaperoftheNobelPrizewinnerDavidBaltimore.Afterthisepisode,bothsupportersanddetractorsofO’Toole’sinitiativesdeemedhercareeras\"ruined\".She,infact,abandonedtheacademiccareersoonafter,eventhoughherclaimsturnedoutotbecorrect(Okie1988,LaFallette1992,FreelandJudson2004).

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ofreputation,orevenaslegalandmonetarycosts,asthecasesreportedintheIntroductiontestify.9Bycontrast,thereaderreceivesarewardifshedetectscheating.ForexamplethereadercanpublishpapersthatcontradictA’sresults,thusobtainingadditionalrecognition(Bo¤rey1988).CallthisrewardGi(i=rad,incr).

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2.1

Analysis

Theequilibriaineachsubgame

WesolveforthePerfectBayesianNashEquilibriaofthegame.Therearetwopropersubgames,eachstartingaftertheauthorAchooseswhethertoundertakeradicalorincrementalresearch.Thepayo¤softhetwosubgamesaredi¤erent,butthetwosubgamesareotherwiseidenticalintheirstructure.Weanalyzeonlyoneofthesesubgames,andomitthesubscriptsradandincrfornotationalsimplicity.WealsonameeachsubgameaftertheactionchosenbyA.So,forexample,theradgameisthesubgamefollowingthechoicebyAtoperformradicalresearch.Afterhavinganalyzedthesubgames,weconsiderthe…rstmovebyA–thedecisionofthetypeofresearch.

Sincesubmittingdominatesnotsubmittingwhentheprojectissuccessful,threetypesofequilibriamayexistineachsubgame:

1.Separatingequilibrium,inwhichAsubmitswhentheprojectissuccessful,anddoesnotsubmitotherwise.

2.Poolingequilibrium,whereAchoosessubm,regardlessofthesuccessorfailureoftheproject.

3.Semi-separatingequilibrium,whereArandomizesoversubmandnosubmifprojectisunsuccessful.

Anequilibriumineachsubgameisgivenbyafour-tuplecomposedbyi)theactionchosenbyAiftheprojectissuccessful;ii)theactionchosenbyAiftheprojectisafailure;iii)theactionchosenbyRandiv)theposteriorbeliefofRonthesuccessorfailureoftheproject.Webeginthecharacterizationoftheequilibriaineachsubgamewiththefollowinglemma:Lemma2.1.1ThereisnoseparatingequilibriumwhereAchooses\"subm\"iftheprojectissuccessful,andchooses\"nosubm\"iftheprojectisnotsuccessful.

Proof.Bycontradiction.AssumeAisseparatingandconsiderR’sresponse.Rupdatesherbeliefsonthesuccessoftheproject,andattributesprobability1tosuccess.Inthiscase,not

Insomecases,scientistscaughtcheating\"disappear\"fromthescienti…ccommunity(Odling-Smeeetal.2007).Stillinothercases,evidenceoffraudintheworkofascientistisfoundafterhisdeath,asithappenedforthechildpsychologistBrunoBettelheim.

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checkingdominateschecking.However,anticipatingthis,Ahasanincentivetodeviatewhentheprojectturnsouttobeafailure,i.e.Awillsubmitalsowhentheprojectfails.

GivenLemma2.1.1,thefollowingpropositioncanbestated.Theproofofthisproposition,aswellastheproofsofalloftheotherresultsinthepaper,isinAppendixB.Proposition2.1Thesubgames\"rad\"and\"incr\"havethefollowingequilibria:1.Apoolingequilibrium(subm,subm;nocheck;󰀃)forGi󰀅Wi+

cRi

;i=rad;incr:1󰀂󰀃i

2.Asemi-separatingequilibrium(submwithprobabilitypi=1;submwithprobabilitypi

cRi󰀃i󰀃icRiBi)ifG>W+;=1󰀂;checkwithprobabilityr=;iii󰀃iGi󰀂Wi󰀂cRiBi+gi󰀃i+pi(1󰀂󰀃i)1󰀂󰀃i

i=rad;incr:Theparametersetsthatmakeeachequilibriumexistingaremutuallyexclusiveandconstituteapartitionofthewholeparameterspace.Figure2representsqualitativelytheregionswheredi¤erentequilibriaoccur.Proposition2.1hasastraightforwardcorollary:

Corollary2.1.1Inanyequilibriumofthepublicationgame,fraudoccurswithpositiveproba-bility.

Figure2:Parameterspaceforeachofthetwotypesofequilibriaineachpropersubgame(subscripts

havebeenomitted).

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2.2Detectedandundetectedmisconduct

Foreachofthetwosubgames,andforeachofthetwotypesofequilibria,wecancalculatetheprobabilitythatfraudulentpapersarewritten,arepublished,arepublishedwithoutbeingcaught,arepublishedandarecaught,andarecheckedwhen,instead,theyarenotfraudulent.Thefollowingpropositionsandtablesderivestraightforwardlyfromthepreviousresults.Proposition2.2Inapoolingequilibrium,theprobabilitythatafraudulentpaperiswrittenandsubmitted,Psubmi(i=rad;incr)is(1󰀂󰀃i).Theprobabilitythatafraudulentpaperissubmittedandpublished,P(subm;acc)iis󰀆i(1󰀂󰀃i);andisequaltotheprobabilitythatafraudulentpaperissubmitted,published,andnotcaught,P(subm;acc;nc)i:Theprobabilitythatafraudulentpaperissubmitted,published,andcaught,P(subm;acc;c)iiszero,andsoistheprobabilitythatanon-fraudulentpaper,ifpublished,goesunderacheckbythereader.

Proposition2.3Inasemi-separatingequilibriumtheprobabilitythatafraudulentpaperiswrittenandsubmitted,Psubmi(i=rad;incr)is(1󰀂󰀃i)pi=

fraudulentpaperissubmittedandpublished,P(subm;acc)iis󰀆i(1󰀂󰀃i)pi=bilitythatafraudulentpaperissubmitted,published,andcaught,checkis

󰀅i󰀃iBiBi+gi:

󰀃cRiGi󰀂Wi󰀂cRi.

Theprobabilitythata

Finally,theprobabilitythatanon-fraudulentpaperissubmitted,published,andgoesundera

Theprobabilitythatafraudulentpaperissubmitted,published,andnotcaught,

󰀅i󰀃icRigiGi󰀂Wi󰀂ciBi+gi:

󰀅i󰀃icRiGi󰀂Wi󰀂cRi:Theproba-󰀅i󰀃icRiBi

P(subm;acc;c)iisGi󰀂Wi󰀂cRiBi+gi:

P(subm;acc;nc)i;is󰀆i(1󰀂󰀃i)pi(1󰀂ri)=onP(subm;acc;nc)i:

Wehavethefollowingcomparativestatics

@P(subm;acc;nc)i@P(subm;acc;nc)i@P(subm;acc;nc)i@P(subm;acc;nc)i@P(subm;acc;nc)i

;;;;@󰀅i@󰀃i@gi@cRi@Wi@P(subm;acc;nc)i@P(subm;acc;nc)i;@Gi@Bi

>0;

<0:

poolingeq.semi-separatingeq.󰀅rad󰀃radcRradgrad

Grad󰀂Wrad󰀂cRradBrad+grad󰀅incr󰀃incrcRincrgincr

Gincr󰀂Wincr󰀂cRincrBincr+gincr

Typeofresearch:radincr

󰀆rad(1󰀂󰀃rad)󰀆incr(1󰀂󰀃incr)

Table1:Probabilitythatafraudulentpaperissubmitted,published,andnotcaught

poolingeq.Typeofresearch:

radincr

00

semi-separatingeq.󰀅rad󰀃radcRradBradGrad󰀂Wrad󰀂cRradBrad+grad󰀅incr󰀃incrcRincrBincrGincr󰀂Wincr󰀂cRincrBincr+gincrTable2:Probabilitythatafraudulentpaperissubmitted,published,andcaught

11

poolingeq.Typeofresearch:

radincr

00

semi-separatingeq.󰀅rad󰀃radBradBrad+grad󰀅incr󰀃incrBincrBincr+gincrTable3:Probabilitythatanon-fraudulentpaperissubmitted,published,andchecked

2.3Thechoiceofthetypeofresearchandtheequilibriumofthewholegame

Bybackwardinduction,theauthorAchoosesthetypeofresearchtoperform,inordertomaximizehisexpectedpayo¤.Anequilibriuminthewholegameis…ve-tuplecomposedby:i)thechoiceofthetypeofresearchbyA(radorincr);ii)theactionchosenbyAiftheprojectissuccessful;iii)theactionchosenbyAiftheprojectisafailure(subornosubm);iv)theactionchosenbyR(checkornocheck);andv)theposteriorbeliefbyRonthesuccessorfailureoftheproject.Proposition2.4belowisdividedinfourpoints(1,2,3and4),eachofwhichhastwosubcases(aandb).ThefourpointsfollowProposition2.1aboveandshowtheconditionsunderwhichapoolingorsemi-separatingequilibriumforeachpropersubgamewilloccur,giventhetypeofresearch.Foreachpoint,thesubpointsaandbshowtheconditionsunderwhichAwillchooseradicalorincrementalresearch.Theproofofthispropositionfollowsimmediatelyfromthepreviousresults.Proposition2.41.IfGrad󰀅Wrad+

cRincrcRrad

andGincr󰀅Wincr+:

1󰀂󰀃rad1󰀂󰀃incr

(a)If󰀆radBrad󰀂crad>󰀆incrBincr󰀂cincr;thentheequilibriumofthegameis(rad;subm,

subm;nocheck;󰀃rad);

(b)If󰀆incrBincr󰀂cincr󰀆󰀆radBrad󰀂cradthentheequilibriumofthegameis(incr;subm,

subm;nocheck;󰀃incr):

2.IfGrad󰀅Wrad+

cRradcRincr

andGincr>Wincr+:

1󰀂󰀃rad1󰀂󰀃incr

(a)If󰀆radBrad󰀂crad>󰀆incr󰀃incrBincr󰀂cincrthentheequilibriumofthegameis(rad;

subm,subm;nocheck;󰀃rad);

(b)If󰀆incr󰀃incrBincr󰀂cincr󰀆󰀆radBrad󰀂cradthentheequilibriumofthegameis(incr;

submwithprobabilitypincr=1;submwithprobabilitypincr=;checkwithprobabilityrincr=

3.IfGrad>Wrad+

󰀃incrBincr;Bincr+gincr󰀃incr+pincr(1󰀂󰀃incr)).

󰀃incrcRincr1󰀂󰀃incrGincr󰀂Wincr󰀂cRincr

cRradcRincr

andGincr󰀅Wincr+:

1󰀂󰀃rad1󰀂󰀃incr

12

(a)If󰀆rad󰀃radBrad󰀂crad>󰀆incrBincr󰀂cincr;thentheequilibriumofthegameis(rad;

submwithprobabilityprad=1;submwithprobabilityprad=checkwithprobabilityrrad=

󰀃radBradBrad+grad;󰀃rad+prad(1󰀂󰀃rad));

󰀃radcRrad1󰀂󰀃radGrad󰀂Wrad󰀂cRrad;

(b)If󰀆incrBincr󰀂cincr󰀆󰀆rad󰀃radBrad󰀂crad;thentheequilibriumofthegameis(incr;

subm,subm;nocheck,nocheck;󰀃incr).

4.IfGrad>Wrad+

cRincrcRrad

andGincr>Wincr+:

1󰀂󰀃rad1󰀂󰀃incr

󰀃radcRrad1󰀂󰀃radGrad󰀂Wrad󰀂cRrad;

(a)If󰀆rad󰀃radBrad󰀂crad>󰀆incr󰀃incrBincr󰀂cincr;thentheequilibriumofthegameis

(rad;submwithprobabilityprad=1;submwithprobabilityprad=checkwithprobabilityrrad=

󰀃radBradBrad+grad;󰀃rad+prad(1󰀂󰀃rad));

(b)If󰀆incr󰀃incrBincr󰀂cincr󰀆󰀆rad󰀃radBrad󰀂crad;thentheequilibriumofthegameis

(incr;submwithprobabilitypincr=1;submwithprobabilitypincr=

󰀃incrBincr

;Bincr+gincr󰀃incr+pincr(1󰀂󰀃incr)):

checkwithprobabilityrincr=

󰀃incrcRincr1󰀂󰀃incrGincr󰀂Wincr󰀂cRincr;

3Implications

Wenowstudyhowtheprobabilitiesofcommittingafraud,ofbeingdiscoveredandofnotbeingdiscovered,area¤ectedbyvariationsofthemainparametersofthemodel.Weshowthatobservedcasesoffraudsareunlikelytoberepresentative(nottomentionallcomprehensive)offraudsthatgoundetected.Theanalysisalsogenerateaseriesofclaimsandpredictionsthatqualifyandinsomecasescontradictcurrentproposalsandadoptedpoliciestodeterscienti…cfraud.The…ndingsarepresentedinthreesets,oneforeachofthefollowingsubsections.Adiscussionofthe…ndingsandtheirimplicationsconcludeseachofthethreesubsections.

3.1Typesoffraudulentresearchandoffraudulentscientists

A…rstquestionweposeconcernstherelationshipbetweentheextentofscienti…cmisconductandthetypeofresearchthatisperformed.Weshowthatforaneconomicallysigni…cantrangeofparametervalues,theremaybeamismatchbetweenthetypeofresearchthataremorelikelytobecaughtiffraudulent,andthetypeofresearchthataremorelikelytoactuallybefraudulentlyproduced.Toseethis,assume…rstthatGincr󰀅Wincr+Wrad+

cRrad1󰀂󰀃rad:

cRincr1󰀂󰀃incr

andGrad>

Thisimpliesthatapoolingequilibriumforincrementalresearchandasemi-

separatingequilibriumforradicalresearchareplayed.Theconditionsaremorelikelytobesatis…edifthebene…tsfromdiscoveringfraudsinradicalresearch(Brad)arehigh(whiletheyarelowforincrementalresearch),andtheprobabilityofagroundbreakingprojecttobesuccessful(󰀃rad)islow(whileishighforanincrementalproject).Inthiscase,theprobabilitythatafraudulentpaperwithincrementalresearchissubmitted,acceptedandcaughtiszero,whichislowerthantheprobabilityofaradicalfraudulentpapertobecaught–thisprobabilityisstrictly

13

positive.Theprobabilitythatafraudulentincrementalresearchpaperispublished,however,maybehigherorlowerthanthecorrespondingprobabilityforradicalresearchpaper.Itwillbehigherif:

󰀆incr(1󰀂󰀃incr)>

󰀆rad󰀃radcRrad

Grad󰀂Wrad󰀂cRrad

(1)

Inequality(1)ismorelikelytobesatis…edifBradishigh,i.e.whenbene…tsfromradicalresearchareparticularlyhigh.Iftheinequalityholds,weobservescienti…cmisconductmorelikelytobediscoveredinradicalresearch,whilebeingmorecommoninincrementalresearch.

cRincr1󰀂󰀃incr

Supposenowthatsemi-separatingequilibriaexistforbothtypesofresearch(Gincr󰀅Wincr+

andGrad󰀅Wrad+

cRrad1󰀂󰀃rad).

Inthiscase,theprobabilitythatafraudulentpaperis

submittedandpublishedishigherforincrementalresearchif:

󰀆rad󰀃radcRrad󰀆inc󰀃inccRinc

>;(2)

Ginc󰀂Winc󰀂cRincGrad󰀂Wrad󰀂cRrad

whiletheprobabilityoffraudulentpaperissubmitted,publishedandcaughtishigherforincre-mentalresearchif:

󰀆inc󰀃inccRincBincBrad󰀆rad󰀃radcRrad

>:

Ginc󰀂Winc󰀂cRincBinc+gincGrad󰀂Wrad󰀂cRradBrad+grad

(3)

Ifbene…tsfrompublishingradicalresearcharemuchhigherthanbene…tsfrompublishingin-crementalresearch,theprobabilitythatafraudulentpaperissubmittedandpublishedmaybehigherforincrementalresearch,whiletheprobabilityofbeingcaughtishigherforradicalresearch.Thefollowingnumericalexamplefurtherclari…estheseclaims.

Example3.1AssumeGrad=49;Gincr=43;Wrad=12;Wincr=40;cRrad=12;cRincr=6;Brad=89;grad=70;󰀆rad=:5;󰀆incr=:2;󰀃rad=:4;󰀃incr=:4:ThenGrad=49>Wrad+

cRrad

1󰀂󰀃rad

Rincr

=32;Gincr=43󰀃incr

c

:09:AssumefurtherthatBincr=15;cincr=2;crad=5:Then,󰀆rad󰀃radBrad󰀂crad=12:8>probabilityofapaperbeingfakedandpublishedis:09.Assumenow,instead,thatBincr=

󰀅rad󰀃radcRrad

Grad󰀂Wrad󰀂cRrad

=

󰀆incrBincr󰀂cincr=1;asemi-separatingequilibriumwithradicalresearchisplayedandthe60:Then,󰀆rad󰀃radBrad󰀂crad=12:8<󰀆incrBincr󰀂cincr=14;apoolingequilibriumwith

incrementalresearchisplayed.Theprobabilityofapaperbeingfakedandpublishedis:12>:09.

Themodelcanalsobeusedtopredictscienti…cmisconductinrelationtothecharacteristics

ofscientists.Wepointtoafurthersourceofmismatchbetweenobserved(detected)andactualamountandtypesoffraud.Whilehigh-reputationscientistsaremorelikelytomisbehave,averagescientistsaremorelikelytobecaught.Wemightthereforeobservemorefraudulentcasesbythosecategoriesofscientistswhoarelesslikelytocommitthem.

14

Characterizeahigh-reputationor\"star\"scientistasonemorelikelytosucceedinaproject,i.e.havingahigh󰀃;asonehavingahigherg,becausethelossofreputationishigher,andalowerB,ifBismeanttobethe\"utility\"ofamarginalpublication,comparedtoanaverage,lessknownscientist.;andasonehavingahigh󰀆;i.e.starsaremorelikelytohaveapaperpassedbyareferee.Indicatetheparametersreferringtothestarwiththesuperscripts;andthosereferredtotheaveragescientistwiththesuperscripta.Assume…nallythatbothtypesofscientistschoosethesametypeofresearch.OnecouldassumethatG󰀂Wismoredependingonthetypeofresearch(e.g.Grad>Ginc)ratherthanonthereputationofthescientistbeforethepaperispublished.Ifthatisthecase,theassumptionon󰀃onimplythattheconditionsrad/incrsubscriptsinceweassumethescientistschoosethesametypeofresearch).Therefore,wehaveapoolingequilibriumforthestarscientistandasemi-separatingequilibriumfortheaveragescientist.Itwillthereforebemorelikelyforareadertodiscoverafraudinthepaperbytheaveragescientistthanbythestar.However,theprobabilityofsubmittingandgetafakedpaperpublishedishigherforastarif:

󰀆a󰀃acRga

󰀆(1󰀂󰀃)󰀆a;

G󰀂Wa󰀂cRBa+gas

s

Gs󰀅Ws+

cR1󰀂󰀃sandGa>Wa+

cR1󰀂󰀃awillbetrueforalargesetofvaluesofcR(weomitthe

(4)

Ourassumptionon󰀃impliesthatboth(1󰀂󰀃s)and󰀃aarelow.However,wealsoassumedthatBaishighandgaislow,andthat󰀆s>󰀆a.Hence,inequality(4)willbesatis…edforlargesetofGa;WaandcR.

Theintuitionbehindthisresultisthataverage,unknownscientistshavemoretogainfromafraud.Asaconsequence,theyareunderstricterscrutinybypeers.Thisreducestheirincentivetosubmitfraudulentpapersinthe…rstplace.Atthesametime,papersbystarscientistsarenotcheckedbecause,exante,theirprobabilityofsuccessishigher,theyhavelessgainatthemarginandthepenaltyifcaught(i.e.lossinreputation)ishigher.3.1.1

Comment:\"real\"fraudsand\"real\"cheatersarenotastheyseem

Ontheonehand,this…rstsetofresultsconformwithmostoftheavailableaccountson(detected)scienti…cfraud.Mostfraudstories,suchasthosereportedintheIntroduction,describefraudsasbeingcommittedintheattempttogeneratepathbreakingadvancesinscience.Mostfraudulentresearchers,moreover,weredescribedasbeing\"ontherise\".Thefraudswerecommitted(andthendiscovered)whentheyhadnothadnotyetestablishedastrongreputation.Nothavingastrongreputationmadethemlesscredibleintheeyesoftheirpeersandmotivatedfurtherscrutiny.

Ontheotherhand,however,theseresultspointtosomepitfallsofexcessivelyrelyingonobservedfraudsinordertounderstandtheoverallphenomenonofscienti…cmisconduct.Weshowthatheremaybeadivergencebetweentheprobabilitythatacertainkindoffraudisdiscovered

15

andtheprobabilitythatitiscommitted.Awholesetofequilibria,whereauthorscommitfraudandreadersdonotcheck(thepoolingequilibria)isnotcapturedbyempiricalanalyses.A\"goodnews\"fromthemodelisthatmajoradvancesinsciencearemorecloselyscrutinized,sothatfraudismorelikelytobedetected–andasaconsequence,lesslikelytobecommittedinthe…rstplace.Undetectedfraudinincrementalresearch,however,shouldnotbeundervalued.Entirelynewareasofresearchmayhaveoriginfromapparentlymarginaldiscoveries.Researchresultsthatthescienti…ccommunitywouldconsidermarginalimprovements,forexampleondrugdeliverymethodsorsidee¤ectsofdrugs,mayhavemajorimpactonpeople’slives.10Finally,thescienti…ccommunitiesofseveralcountriesarerelativelyisolatedandrecognitionisbasedonlocal,lessprominentjournals.Arguably,theoverallscrutinyonthesearticleswillbelessstrict(Maruši´c2007),thuspavingthewaytomoreundetectedfrauds.

Asaconsequence,policyimplicationsonscienti…cmisconductbasedondetectedfraudulentbehaviorcanbemisleading,intermsofboththetypesofresearchandofresearchersthesepolicieswouldaddress.Policiesmightbetailoredtothetypesofresearchthatarelesslikelytobefraudulent–forexamplebyfocusingonlyonsomejournalsor…elds.Theattentionmightbetoofocusedonlargerscienti…ccommunities,thusneglectinglocalcommunitieswherefraudmaybemorepervasive.Or,policiesmightbefocussedonlessknownresearchers(post-docs,juniorfaculty),whilethescienti…ccommunityalreadygenerates,withouttheneedforinterventions,therightincentivesfortheseclassesofresearcherstobescrutinized.

3.2Policyexperiments

Severalscholarsaswellasthepopularpresshaveadvocatedaseriesofinterventionsandreformsofthescienti…ccommunitythatwoulddeterscienti…cmisconduct.Someoftheseproposedpoliciescorrespondtochangesintheparametersofourmodel.Theanalysisthatfollowsassessesthee¤ectsofthesechanges.3.2.1

Misconductandcheckingcosts

Highcostsofreplicatingtheresultsinanarticleareindicatedamongthemaincausesoftheoccurrenceoffrauds.Itisperceivedthat,overtime,cheatinghasbecomeeasier(e.g.thankstotheeaseofmodifyingelectronicimages),butthecostsofcheckinghaveincreased.Datashouldbemademoreeasilyavailable,itisclaimed.Forexampleifauthorsshouldberequiredtosharetheirdatawiththeirpeersasaconditiontopublishonagivenjournal.Afewjournalsrequiretheauthorsofacceptedpaperstomaketheirdataavailableonline,andtoprovideanyadditionalmaterialofpotentialrelevancetofullyunderstandapaper(Hamermesh2007).Or,techniquescouldbedevelopedtocheckforfraudsmoreeasily(Hill1999,Sorokinaetal.2006,Giles2006).

10

AfewrecentexamplesonhowfraudsintheseareascanhaveseriousconsequencesareinSurowiecki(2007).

16

Whenwefullyconsiderthestrategicbehaviorofbothauthorsandtheirpeers,however,wecanshowthatareductionincheckingcostsdoesnotnecessarilyleadtolessmisconduct.Thisclaimisformalizedinthefollowingcorollaries(proofsareinAppendixB).

Corollary3.2.1AreductionincheckingcostscRi(i=rad,incr)neverleadstoahigherprob-abilityofundiscoveredfraudifitdoesnotinduceachangeinthetypeofresearch.

Corollary3.2.2IftheauthorAchangesthetypeofresearchfollowingareductionincheckingcosts,thentheprobabilityofanundiscoveredfraudcanincrease.

Thefollowingnumericalandgraphicalexampleclari…estheseresults.

Example3.2Figure3belowreportsanexampleofareductionincheckingcoststhatleadstoanincreaseinthelikelihoodofapaperbeingfraudulent,submitted,accepted,andnotcaught.

󰀅rad󰀃radcRradgrad

ConsiderthepointsinregionA.Inthisarea,Grad

󰀂Wrad󰀂cRradBrad+grad>󰀆incr(1󰀂󰀃incr)

cRrad(Brad+grad)(Grad󰀂Wrad)[󰀅incr(1󰀂󰀃incr)]

andGrad>Wrad+cRincr

(Grad󰀂Wrad)(1󰀂󰀃rad):Furthermore,Gincr󰀅Wincr+–equivalently,cRincr󰀆(Gincr󰀂

1󰀂󰀃incr

Wincr)(1󰀂󰀃incr).Theparametersarealsosuchthat󰀆incrBincr󰀂cincr>󰀆rad󰀃radBrad󰀂crad.

Thegraphrepresentsthe(cRrad;cRincr)spaceandfocusesontheregionwherecRrad󰀆cRincr.

Asaconsequence,Achoosesincrementalresearchandapoolingequilibriumisplayed(asfrompoint3.bofProposition2.4).Thelikelihoodofapaperbeingfraudulent,submitted,accepted,andnotcaughtis󰀆incr(1󰀂󰀃incr)(seeTable1atpage11above).

󰀆incr󰀃incrBincr󰀂cincr<󰀆rad󰀃radBrad󰀂crad.TheauthorAthereforechoosesradicalresearchandapaperbeingfraudulent,submitted,accepted,andnotcaughtis

󰀅rad󰀃radcRradgradGrad󰀂Wrad󰀂cRradBrad+grad

󰀅rad󰀃radcRradgrad

Grad󰀂Wrad󰀂cRradBrad+grad.

InregionB,theonly

cRincr

conditionthatchangeswithrespecttoregionAisthatGincr>Wincr+–equiva-1󰀂󰀃incr

lently,cRincr<(Gincr󰀂Wincr)(1󰀂󰀃incr).The…gureisdrawnforparametervaluessuchthat

asemi-separatingequilibriumisplayed(asfrompoint4.aofProposition2.4).Thelikelihoodof

Since

>󰀆incr(1󰀂󰀃incr)forthissetofparametervalues,andsinceregionB

liesbelowregionA,areductionofbothcRradandcRincrcanleadtoanincreaseintherateofcommittedandundetectedfraud.3.2.2

Misconductandcompetitionamongscientists

Itisfrequentlyclaimedthathighpoweredincentivestoscientistsmaybeconducivetofraud.Thehighbene…tsfrompublishingpapersandoutcompetingrivals(inawinner-takes-allcompetition)makesscientistsmorepronetomisbehave(List1985,Abelson1990,Giles2007).Again,ourmodelshowsthatthisclaimisnotnecessarilyborneout:morecompetitioncanactuallyserveasapowerfulmechanismtodeterfraud,asitincreasestheincentivesofpeersforscrutinizingeachother’swork.

17

Figure3:Exampleofareductionincheckingcoststhatleadstoanincreaseinthelikelihoodofapaperbeingfraudulent,submitted,accepted,andnotcaught.Thex-axisrepresentvaluesofcRrad,andthey-axisvaluesofcRincr:The…gureisdrawnforthefollowingsetofothervaluesoftheparame-ters:Grad=85;Gincr=62;Wrad=󰀂36;Wincr=󰀂25;Brad=89;Bincr=65;crad=16;cincr=1;grad=84;󰀆rad=:96;󰀆incr=:12;󰀃rad=:24;󰀃incr=:59:

Inthegame,thebene…tsfrompublications,andmoregenerallytheintensityofcompetitionamongscientists,arecapturedbyB(theauthor’sincentives)andG󰀂W.Iftheintensityofcompetitionishigh,A’sbene…tfrompublications(B)willbehigh;thesameisforthereturnfromdiscoveringafraud(G)andthelossfromothers’publications(󰀂W).Thecomparativestaticsfortheseparameters,justasinthepreviousexercises,cruciallydependonwhetherthetypeofresearchchosenbyauthorschangesornot.Ourresultsareformalizedinthefollowingcorollaries.

Corollary3.2.3Anincreaseincompetition(i.e.anincreaseinBiandGi󰀂Wi,i=rad,incr)typeofresearch.

Corollary3.2.4IftheauthorAchangesthetypeofresearchfollowinganincreaseincompe-tition,thentheprobabilityofanundiscoveredfraudcanincrease.3.2.3

Misconductandthepenaltiesofbeingcaught

neverleadstoahigherprobabilityofundiscoveredfraudifitdoesnotinduceachangeinthe

Anotherfrequentlyproposedremedyagainstmisconductinscienceistostrengthentheseverityofthepenaltiesforthosescientistswhoarecaughtcommittingfraud.Thiswoulddeterscien-18

tistsfrommisbehaving.Infact,asmentionedabove,penaltiescanbeassevereasleadingtoimprisonment.However,justastheincreasedabsolutevalueofthepunishmentshoulddeteranauthorfromcheating,thiscouldalsoreducetheincentivesforpeerstocheck,countervailingthedeterrencee¤ect.Inthepublishinggameabove,theparametergrepresentsthecost,whichcanbepecuniaryornot,su¤eredbyAifafraudulentpaperisdiscovered.Thisparameterappearsasrelevantonlyinasemi-separatingequilibrium,a¤ectingtheprobabilityofdiscoveringafraud-ulentpaper.Thederivativesignisnegative,i.e.aincreaseingincreasestheprobabilitythatafraudulentpaperisnotcaught.Thisapparentlycounterintuitiveresultisduetothefactthat,ifgishigh,thenalowerprobabilityofcheckingbyRisrequiredtogeneratetheindi¤erencebetweensubmittingafakedpaperornotbyA.3.2.4

Comment:deterrencepoliciescanback…re

Aseriesofcounterintuitiveinsightsemergefromthissecondsetofresults.Ofkeyimportanceinthemodelarethemultiplerolesplayedbyascientist’speers.Theyareusers,competitors,andevaluatorsatthesametime.Thesedi¤erentpositionscorrespondtodi¤erentbene…tsandcosts.Weshowthat,ifcheckingpublishedresultsbecomeseasier,thiscanmodifythetypeofresearchactivitiesscientistsundertakeinthe…rstplace.Inturn,fraudulentactivitieswillconcentrateinsometypesofresearch.

Themodelalsoquali…estheclaimthatamajorcauseofmisbehaviorinscienceisrepresentedbyanexcessofcompetitionamongresearchers.High-poweredcompetitioncanstimulatemoremonitoring,thusdeterringfrauds.Onemightobservemorecasesoffraudinmorecompetitive…elds,but,aspointedoutabove,thisdoesnotmeanthattheoverallamountoffraudisgreater.Thisjustsaysthatfraudismorelikelytobecaught,thusdeterringscientiststomisbehaveinthe…rstplace.Infact,itmaywellbethattoolittlecompetitionisconducivetomisconduct.Severalscholarshavepointedoutthatreplicationofexistingresultsistoopoorlyrewardedbythescienti…ccommunity.InEconomics,forexample,Hamermesh(2007)documentsadeclineinthenumberofjournalsthathaveasectiondedicatedtocommentariesofpreviousworks.Thislimitedrecognitionforreplicationcanbeseenasalimittocompetition.Oncearesulthasbeenfoundbyascientist,heestablishesasortof\"monopoly\"overit.Anysubsequentworkthatjustreplicatesthisresultisconsideredunworthyofrecognition.11

Establishinghigherrewardsforworksthatreplicateexisting…ndingsandcouldpossiblydetectmisconductepisodesthusemergesasapowerfuldevicetodeterfraud.Thecostofsuchapolicymightbeanexcessiveincentivetoinvestinthiskindofresearchinsteadofengagingingenuinelynovelactivities.Inthelate1980s,forexample,WalterW.StewartandNedFeder,twoscientistsatNIH,gainednotorietyandsomescienti…crecognitionforhavingunveiledseveral

Engaginginactivitiesaimedatquestioningexistingworkscanevenbedetrimentaltoascientist’scareer,asthecaseoftheMITpost-doctoralstudentsMargotO’Toolewitnesses(seefootnote8atpage8above).

11

19

casesofmisconduct.Thetwoscholarsengagedinthese\"checkingactivities\"almostonafull-timebasis,atthecostofapoorproductivityinthegenerationofnewresearch.12

3.3AnactiveroleforEditors?

Aspreviouslynoticed,neithereditorsnorrefereesaretypicallyrequiredtocontrolforthetruthof…ndingsinthemanuscriptstheyreceive.Suspicionsoffraudmostoftenemergeafterapaperispublished.Colleaguesandcollaboratorsofanauthor,ormostfrequently,readersofanarticlecontacttheeditorofthejournaltoexpresstheirconcerns.Onlythendoeditorialboardshavearole.Theytakepartinacontrolprocessthatcaninvolvetheorganizationwheretheauthorworksandpossiblyalsopublicagencies(LaFollette1992).Themodelasdescribedsofarrepresentsthisstateofa¤airs.However,afewmajorjournalshaverecentlyimplementedpracticesthatimplyagreaterinvolvementofeditorialboardintheattempttodeterandreducefraud.AtNatureImmunology,forexample,anarticleisrandomlyselectedamongthoseacceptedforpublicationbeforeeachissueisreleased,andgoesthroughadditionalcontrols.Asimilarprocedure,concerningeveryacceptedmanuscript,hadbeenpreviouslyintroducedattheJournalofCellBiology(Rossner2006,NatureImmunology2007).

Inwhatfollows,weattempttoreplicatetheseeditorialinnovationsbyextendingthepubli-cationgame.Refereesarestillassumedtohavenoroleincheckingforfrauds.Now,however,editorsandrefereesareseparatedagents.Ifapaperisacceptedbyareferee(calledRef),theeditorE,withsomeprobability󰀄,performsacheckbeforepublication.Thisisacommitmentbytheeditor:hehasnochoicebutperformingtherandomcheck.13Theeditor,therefore,doesnotactstrategically;henceherpayo¤sareirrelevant.Asfortheinformationstructure,imperfectinformationisassumedbythereaderonwhethertheeditorhasperformedthecheck.Thisisconsistent,forexample,withthepracticesintheaforementionedjournals,wheretheidentityofthecheckedpapersiskeptsecret.ThefullgameinextendedformisrepresentedinFigure4.We…rstanalyzethetwopropersubgamesstartingwhennatureNmovesseparately,andthendealwiththewholepublicationgamethusmodi…ed.TheanalysismirrorsthatofSection2above.Wefocusonthepeculiaritiesofthiscase,andleavethederivationsandproofsoftheresultstoAppendixBbelow.

SeeBo¤ey1988,Greenberg1988,Okie1988,LaFollette1992.

BothatNatureImmunologyandattheJournalofCellBiology,forexample,thisisaclearlystatededitorialpolicy,withnodiscretionallowed.Noticealsothat,di¤erentlyfromthepracticeatNatureImmunology,checksaresupposedtoberunoneachandeveryacceptedpaperattheJournalofCellBiology,beforepublication.However,itisstillreasonabletoincludesuchacaseinthemodel’sversiondevelopedhere,wheretheprobabilityofcheckingcanalsobelessthanone.First,inthemodelwhatmattersistheprobabilityofcheckingandspottingafraud.Evenwhenallpapersarechecked,somefraudscangoundetected.Second,bothinthecaseofNatureImmunologyandtheJournalofCellBiology,thesechecksarelargelyfocusedonimagemanipulationonly(Rossner2006).Therefore,othertypesoffraudscangoundetected.Conversationswithjournaleditorscon…rmedthatonlysomefraudscanbedetectedwiththemethodsandresourcescurrentlyinuse.

1312

20

A)ncr(1-βi lifaNsuccincr (βradAsubmno incr)submsubA-cincr; 0mno submRefncr)rej (1-incr)-cincr; 0incr)N)-βrad1( lfai (1rejππi-πinacc (acc (π-cincr; 0eck ch)on-γ(1-cincr; 0-cincr; 0succcr)Asubm (βcheck (γ)no rad)-gincr-cincr; 0Rckcheck chno-γ)(1Refno checksubmeckEcheck(γ)submA-crad; 0no submno acc (πrad)cheacc (chead)cherej (1)-crad; 0-rad) (1rejckckπcheckπr-πrano Bincr-cincr;-gincr-cincr;WincrGincr-cRincrBincr-cincr;Bincr-cincr;WincrWincr-cRincrBincr-cincr;WincrBincr-cincr;Wincr-cRincreck ch)on-γ(1-crad; 0Echeck (d-crad; 0check(γ)γ)-grad-crad; 0ckeck ch)on-γ(1ERno checkcheno no checkcheckcheckBrad-crad;-grad-crad;WradGrad-cRradFigure4:Gamewithrandomchecksbytheeditor.

checkBrad-crad;Brad-crad;WradWrad-cRradBrad-crad;WradBrad-crad;Wrad-cRrad3.3.1Equilibriaofthepropersubgames

Themaindi¤erencefromthecasewithoutcheckbytheeditoristhat,now,aseparatingequi-libriumexistswhenthecheckingprobabilitybyEissu¢cientlyhigh.Considerthefollowingproposition.

Proposition3.1Thesubgames\"rad\"and\"incr\"havethefollowingequilibria:1.Aseparatingequilibrium(subm,nosubm;nocheck;1)for󰀄󰀆2.Apoolingequilibrium(subm,subm;nocheck;󰀃)for1󰀂i=rad;incr:

BiBi+gi

(1󰀂󰀃i)Wi+cR󰀃i(Gi󰀂cRi)(1󰀂󰀃i)󰀅󰀄<

BiBi+gi;

3.Asemi-separatingequilibrium(submwithprobabilityp=1ifprojectissuccessful;submwith

󰀃iprobabilitypi=1󰀂󰀃󰀄Bi1

Bi+gi1󰀂󰀄󰀂1󰀂󰀄;

ci(G󰀂c)(1󰀂󰀄)󰀂Wiiftheprojectisunsuccessful;checkwithprobabilityr=iRi

󰀃i(1󰀂󰀃i)Wi+cR󰀃iBi)existsfor󰀄21

3.3.2Detectedandundetectedmisconduct

Theprobabilitythatfraudulentpapersarewrittenandpublishedwithoutbeingcaught,andthattheyarewritten,publishedandcaughtarereportedinthefollowingtables.Noticethat,for󰀄=0(i.e.nocheckbytheeditor),weobtaintheprobabilitiesforthebasicgame,asreportedintables1,2,and3atpage11above.

poolingeq.Typeofresearch:

radincr

󰀆rad(1󰀂󰀄)(1󰀂󰀃rad)󰀆incr(1󰀂󰀄)(1󰀂󰀃incr)

semi-separatingeq.󰀅rad󰀃radcradgrad

(Grad󰀂cRrad)(1󰀂󰀄)󰀂WradBrad+grad

󰀅incr󰀃incrcincrgincr

(Gincr󰀂cRincr)(1󰀂󰀄)󰀂WincrBincr+gincr

Table4:Probabilitythatafraudulentpaperissubmitted,published,andnotcaught

poolingeq.Typeofresearch:

radincr

󰀆rad(1󰀂󰀃rad)󰀄󰀆incr(1󰀂󰀃incr)󰀄

semi-separatingeq.󰀅rad󰀃radcradBrad󰀂󰀄(Brad+grad)Brad+grad(Grad󰀂cRrad)(1󰀂󰀄)󰀂Wrad

󰀅incr󰀃incrcincrBincr󰀂󰀄(Bincr+gincr)Bincr+gincr(Gincr󰀂cRincr)(1󰀂󰀄)󰀂WincrTable5:Probabilitythatafraudulentpaperissubmitted,publishedandcaught

3.3.3Thechoiceofthetypeofresearchandtheequilibriumofthewholegame

Bybackwardinduction,theauthorAchoosesthetypeofresearchtoperform,inordertomaximizehisexpectedpayo¤.WederivethefollowingProposition,whoseproofisimmediategiventheresultsandpropositionsabove.Proposition3.2

n

󰀃rad)Wrad+cRrad󰀃rad1.Ifmax1󰀂(1(󰀂Grad󰀂cRrad)(1󰀂󰀃);1󰀂

rad

󰀃inc)(Bincr+gincr)󰀂cincr;incrementalotherwise.Thesubgameshavepoolingequilibria.

no

(1󰀂󰀃incr)Wincr+cRincr󰀃incr(1󰀂󰀃rad)Wrad+cRrad󰀃radBradBincr2.If1󰀂(Grad󰀂cRrad)(1󰀂󰀃)󰀅󰀄rad

incr

Achoosesradicalresearchif󰀆rad(Brad󰀂󰀄(1󰀂󰀃rad)(Brad+grad))󰀂crad>󰀆inc(Binc󰀂󰀄(1󰀂

(1󰀂󰀃incr)Wincr+cRincr󰀃incr

(Gincr󰀂cRncr)(1󰀂󰀃incr)o

󰀅󰀄n

BradBinc;grad+Bradginc+Binc

o

;

crad>󰀆incr󰀃incrBincr󰀂cincr,incrementalotherwise(withasemi-separatingequilibrium).

on

(1󰀂󰀃incr)Wincr+cRincr󰀃incr(1󰀂󰀃rad)Wrad+cRrad󰀃radBrad3.If󰀄rad

incr

Achoosesradicalresearch(withpoolingonsubm)if󰀆rad(Brad󰀂󰀄(1󰀂󰀃rad)(Brad+grad))󰀂

onsubmit).

crad>󰀆incr(Bincr󰀂󰀄(1󰀂󰀃inc)(Bincr+gincr))󰀂cincr,incrementalotherwise(withpooling

Achoosesradicalresearch(withasemi-separatingequilibrium)if󰀆rad󰀃radBrad󰀂

22

4.If󰀄erwise.Thesubgameshavesemi-separatingequilibria.

no

BradBincr5.If󰀄󰀆maxgrad+Brad;gincr+Bincr;Achoosesradicalresearchif󰀆rad󰀃radBrad󰀂crad>curring.

(1󰀂󰀃incr)Wincr+cRincr󰀃incr(Gincr󰀂cRncr)(1󰀂󰀃incr)Achoosesradicalresearchif󰀆rad󰀃radBrad󰀂crad>󰀆incr󰀃incrBincr󰀂cincr,incrementaloth-

n

Bradgrad+Brad;1

󰀂

(1󰀂󰀃rad)Wrad+cRrad󰀃rad(Grad󰀂cRrad)(1󰀂󰀃rad)o

and󰀄n

Bincrgincr+Binrc;1

󰀂

(1󰀂󰀃incr)Wincr+cRincr󰀃incr(Gincr󰀂cRncr)(1󰀂󰀃incr)o,

󰀆incr󰀃radBincr󰀂cincr,incrementalotherwise,withseparatingequilibriaandnofraudoc-Bradgrad+Brad

6.If󰀄󰀆and1󰀂

incremental(pooling)otherwise.

n

BradBincr7.If󰀄󰀆grad+Bradand󰀄+Bincr;1󰀂separating)otherwise.

research(separating)if󰀆rad󰀃radBrad󰀂crad>󰀆inc(Binc󰀂󰀄(1󰀂󰀃inc)(Brad+grad))󰀂cinc,

(1󰀂󰀃incr)Wincr+cRincr󰀃incr(Gincr󰀂cRncr)(1󰀂󰀃incr)󰀅󰀄<

Bincginc+Binc,

Achoosesradical

research(separating)if󰀆rad󰀃radBrad󰀂crad>󰀆incr󰀃incrBincr󰀂cincr,incremental(semi-Bradgrad+Brad

o

,Achoosesradical

󰀃rad)Wrad+cRrad󰀃rad8.If1󰀂(1(󰀂Grad󰀂cRrad)(1󰀂󰀃)󰀅󰀄<

rad

and󰀄󰀆

Bincrgincr+Binr,

Achoosesradicalresearch

(separating)otherwise.

n

Brad9.If󰀄+Brad;1󰀂(separating)otherwise.

(pooling)if󰀆rad(Brad󰀂󰀄(1󰀂󰀃rad)(Brad+grad))󰀂crad>󰀆incr󰀃incrBincr󰀂cincr,incremental

(1󰀂󰀃rad)Wrad+cRrad󰀃rad(Grad󰀂cRrad)(1󰀂󰀃rad)research(semi-separating)if󰀆rad󰀃radBrad󰀂crad>󰀆inc󰀃incrBincr󰀂cincr;incrementalComment:checkalotornotcheckatall?

o

and󰀄󰀆

Bincrgincr+Bincr,

Achoosesradical

3.3.4

Basedontheseresults,wecananalyzeanddiscusstheimpactofvariationsin󰀄;ourmeasureofthedegreetowhicheditorsparticipateincheckingforfrauds.Weconsiderinparticularthee¤ectanincreaseofthisparameter.Wecanshowthatanincreasein󰀄doesnotnecessarilyleadtoareductioninscienti…cmisconduct.ConsiderthefollowingcorollariesofPropositions3.1and3.2above(proofsinAppendixB).Corollary3.3.1If󰀄󰀆

BiBi+gi

(i=incr,rad),thenthereisnofraudinequilibrium.

(1󰀂󰀃i)Wi+cR󰀃i(Gi󰀂cRi)(1󰀂󰀃i)Corollary3.3.2Considereachpropersubgameinisolation.Suppose1󰀂

BiBi+gi

;i=rad;incr;bothbeforeandafteranincreaseof󰀄.Then,theprobabilitythatfrauds

󰀅󰀄<

arediscoveredincreases,followinganincreasein󰀄:

Corollary3.3.3Considereachpropersubgame.Suppose󰀄(1󰀂󰀃i)Wi+cR󰀃iBi

(Gi󰀂cRi)(1󰀂󰀃i);Bi+gi);

i=rad;incr,bothbeforeandafteranincreaseof󰀄:Then,theincreasein󰀄leadstoanincrease

23

Corollary3.3.4Considereachpropersubgame.Supposethatinitially󰀄=󰀄0(1󰀂󰀃i)Wi+cR󰀃iBi(Gi󰀂cRi)(1󰀂󰀃i);Bi+gi);i=rad;incr;and

i

󰀄00anincreasein󰀄=󰀄0issuchthat1󰀂fraudisnotcaughtincreasesif:

0

(1󰀂󰀃i)Wi+cR󰀃i(Gi󰀂cRi)(1󰀂󰀃i)<

󰀆󰀃cRg

<󰀆(1󰀂󰀃)(1󰀂󰀄00):0(G󰀂cR)(1󰀂󰀄)󰀂WB+g

(5)

Corollaries3.3.1and3.3.2depict\"expected\"scenarioswherethescrutinybyanadditionalactorreducestheoverallchanceofundetectedfrauds.Corollaries3.3.3and3.3.4,incontrast,showthatalsotheoppositecanbetrue.Corollary3.3.3,forexample,saysthatwhenRobservesapublishedpaper,hecannotexcludethattheeditorhasactuallycheckedit.ThisreducestheincentivestocheckforR,sinceRfacestheriskofa\"doublecheck\"ofasuccessfulpaper:

Withrespecttothewholegame,fromProposition3.2weseethatvariationsin󰀄canactuallyleadtoachangeinthetypeofresearchperformedbyA.Suchchangesmayinducechangesintheprobabilitythatafraudiscommittedanddiscovered.SimilarlytothecaseofareductionincheckingcostsbyR,anincreasein󰀄caninduceanincreaseintheprobabilitythatafraudiscommittedandnotcaughtviaachangeinthetypeofresearch.Consideravariationin󰀄thatmovestheequilibriumfromregion4(bothsubgameswithsemi-separatingequilibria)toregion3(subgameradwithasemi-separatingequilibrium,subgameincrwithapoolingequilibrium)in3.2.Since

󰀆inc(Binc󰀂󰀄(1󰀂󰀃inc)(Brad+grad))󰀂cinc>󰀆inc󰀃incBinc󰀂cinc;

when󰀄<

Bincginc+Binc

(6)

theauthorAmayswitchfromradicaltoincrementalresearch.Inthiscase,

theprobabilitythatfraudsarecommittednotdiscoveredincreasesif:

󰀆incr(1󰀂󰀃incr)>

󰀆rad󰀃radcRradgrad

(Grad󰀂cRrad)(1󰀂󰀄)󰀂cRradBrad+grad

(7)

ThisisthecasewheneverBradissu¢cientlyhigh.

Weconcludethatanactiveroleofeditorsintocheckingformisconductunambiguouslyleadstoalowerchanceoffraudulentpapersbeingleftuncheckedonlywhensuchaninvolvementislarge.Iftheinvolvementisonlyonasmallscale(e.g.onlyonasmallshareofpapersoronlyforsomespeci…ctypesoffrauds),thenthecheckingactivitiesbyjournalsmaycrowdouttheincentivetothoroughlycheckbyreaders,andleadtoanoverallincreaseofthechancesofhavingfraudulentpaperspublishedandnotscrutinized.Thebene…tsfromalargescaleinvolvementofjournalinpre-publicationcheckforfraudwillneedtobeweightedagainstsuchcostsasadditionalpersonnel,time,andpossiblydelaysinpublication.

24

4Conclusion

Theobjectiveofthispaperwastoprovideaframeworkforthestudyofscienti…cmisconduct.Fraudinscienceoccursandisamajorproblem.Individuals,…rmsandgovernmentsincreas-inglyrelyonscienti…cknowledgefortheirwelfare.Theyoperateundertheassumptionthatthisknowledgehasbeenhonestlyandtruthfullygenerated.Nonetheless,examplesofscientistswhofalsi…ed,fabricatedorplagiarizedtheir…ndings,andwerestillabletopublishandgetrecognitionformthem(beforebeingfoundout)abound.Thescienti…ccommunityisacom-plex,self-regulatinginstitutionwhereseveralactorsinteractindi¤erentforms–ascompetitors,complementors,andevaluators.Littleisknownonhowthosesameinstitutionalfeaturesthatleadtoknowledgecreationalsoleadtothefabricationoffakeinformation.Withthispaper,wehopetohavemadeprogresstowardsanunderstandingofthesephenomena.Webuiltagame-theoreticmodeloftheresearchadpublicationprocessthatcapturesthesemaincharacteristicsofthescienti…ccommunity,andalsoallowsauthorstocommitfraud.

Themodelgeneratesthreesetsofresults.First,thetypesofresearchthataremorelikelytobefraudulent,andthetypeofscientiststhataremorelikelytocommitfraud,aredi¤erentfromthetypeofresearchandscientiststhatarediscoveredasfraudulent.Second,somepoliciesaimedatreducingundetectedfraud,suchasareductioninthecostsofreplicatingotherscientists’researchandsofteningcompetitionamongresearchers,canback…reandinduceanincreaseinundetectedmisbehavior.Third,addinglayersofcontrolformisconduct,forexamplethroughadirectinvolvementjournals;editorialsta¤inpolicingformisconductbeforepublication,doesnotnecessarilyincreasetheoverallamountofdetectionandpreventionofmisconduct.

Theseresultsimplythattheremaybeagooddealoffraudsthescienti…ccommunityisnotawareof,andmostofthesefraudsareofadi¤erentnaturethantheonesthatareinfactsdiscovered.Wemaythereforehaveonlyalimitedanddistortedsenseoftheamountandtypeofscienti…cmisconduct,ifwerelyonreportsandanecdotesofscientistswhowere,indeed,caughtcheating.Inaddition,policiesdeemedtounequivocallydiscouragefrauds,suchasfacilitatingreplicationanddatasharing,softeningcompetition,andinvolvingjournals’editorialboardsintocheckingforfrauds,donotnecessarilyelicittheexpectedvirtuousbehaviors.

Somelimitsofthemodel,togetherwiththeirdiscussions,havebeenreportedinthepaperalready.Furtherextensionsarepossible.Oneavenueforextensionsconcernsthebehavioralassumptions.Inthemodel,scientistsare\"sel…sh\"andhavenoethicalconcerns.Whilethesociologicalliteratureiscontroversialontheissue,itcanbearguedthatscientistsderiveutilityfromproducingknowledgehonesty,andnotonlyformthepublicationofanyresults.14Aninterestinginterpretationofourresultisthat,ifethicalconcernarelimitedornon-existent,thenfraudisaninherentcharacteristicofthescienti…ccommunity.Cheating,moreover,can

14

AppendixCbelowcanbeseenasanattempttoincludeethicalconcernsintothecurrentsetup.

25

alsobeseenasa\"compulsive\"behavior,andnotastheoutcomeofarationalchoice.Themodelcouldalsobeimprovedinordertodrawclearernormativeconclusions.Wedonotcompletelyconsider,forexample,thecostsrequiredtoimplementsomepoliciesthatdeterfrauds.Aninvolvementofjournals’editorialboardsintocheckingforfraudsmayrequiremorepersonnel,moretime,andpossiblydelaysinpublication.Similarly,increasingrecognitionforreplicationworkscandeviatesomescientiststowardtheseactivities,thusmakingexistingknowledgemorereliablebutalsoslowingdownthecreationofnewknowledge.

References

[1]Abelson,P.,1990:\"MechanismsforEvaluatingScienti…cInformationandtheRoleofPeerReview\

JournaloftheAmericanSocietyforInformationScience,41,3,216-222.

[2]AssociatedPress,2006:\"DisgracedKoreanCloningScientistIndicted\May12.

[3]BBC,2004:\"TheDarkSecretofHendrikSchön\TVShow\"Horizon\"broadcastonFebruary5th

(transcriptavailableathttp://www.bbc.co.uk/science/horizon/2004/hendrikshontrans.shtml).

[4]Bell,R.,1992:ImpureScience.Fraud,Compromise,andPoliticalIn‡uenceinScienti…cResearch,

JohnWiley&Sons.

[5]Bo¤ey,P.M.,1988:\"TwoCriticsofScienceRevelintheRole\TheNewYorkTimes,April18.[6]CBS,2005:\"MenopauseDocFudgedData\CBSNewsJune21st.

[7]Chang,K.,2002:\"OnScienti…cFakeryandtheSystemstoCatchIt\TheNewYorkTimes,October

15.

[8]Chang,K.,2004:\"ResearcherLosesPh.D.OverDiscreditedPapers\TheNewYorkTimes,June

15.

[9]Cyranowski,D.,2006:\"YourCheatin’Heart\NatureMedicine,12,5,490.

[10]Deichmann,U.&Müller-Hill,B.,1998:\"ThefraudofAbderhalden’sEnzymes\Nature393,109-111.

[11]Dennis,M.A.,1987:\"AccountingforResearch:NewHistoriesofCorporatelaboratoriesandthe

SocialHistoryofAmericanScience\SocialStudiesofScience,17,3,479-518.

[12]Dyck,A.,Morse.A.andZingales,L.,2007:\"WhoBlowstheWhistleonCorporateFraud?\working

paper.

26

[13]Fi…eld,A.andCookson,C.,2006:\"SeoulSearching:KoreansFindTheirRapidDevelopmentHas

HardScienti…cLimits\FinancialTimes,January19.

[14]Fisher,P.,1999:\"TheEndoftheBenvenisteA¤air?\TheBritishHomeopathicJournal,88,4.[15]FreelanJudson,H.,2004:TheGreatBetrayal.FraudinScience,Harcourt.[16]Fuller,S.,2006:

syndicate.com).

\"TheConundrumofScienti…cFraud\ProjectSyndicate(www.project-

[17]Giles,J.,2006:\"PreprintAnalysisQuanti…esScienti…cPlagiarism\Nature,444,524-525.[18]Giles,J.,2007:\"BreedingCheats\Nature,445,7125,242-243.

[19]Glaeser,E.L.,2006:\"ResearcherIncentivesandEmpiricalMethods\NBERWorkingPapert0329.[20]Goodstein,D.,2002:\"Scienti…cMisconduct\Academe,Jan-Feb.,28-31.

[21]Greenberg,D.S.,1988:\"Lab-Scam:HowScienceGoesBad\WashingtonPost,April24.

[22]GrossLevi,B.,2002a:\"BellLabsConvenesCommitteetoInvestigateQuestionsofScienti…cMis-conduct\PhysicsToday,July.

[23]GrossLevi,B.,2002b:\"InvestigationFindsthatOneLucentPhysicistEngagedinScienti…cMis-conduct\PhysicsToday,November.

[24]Hamermesh,D.S.,2007:\"ReplicationinEconomics\CanadianJournalofEconomics,forthcoming.[25]Hill,T.,1999:\"Thedi¢cultyoffakingdata\Chance,26,8-13.

[26]Huelsnitz,W.,2005:\"Scienti…cLiteracyandEducationReform\AmericanPhysicalSocietyNews,

14,8,5.

[27]Kolata,G.,2005:\"ACloningScandalRocksaPillarofSciencePublishing\TheNewYorkTimes,

December18.

[28]Kintisch,E.,2006:\"PoehlmanSentencedto1YearofPrison\ScienceNOWDailyNews,June28.[29]LaFollette,M.C.,1992:StealingIntoPrint.Fraud,PlagiarismandMisconductinScienti…cPub-lishing,UniversityofCaliforniaPress.

[30]List,C.J.,1985:\"Scienti…cFraud:SocialDevianceortheFailureofVirtue?\Science,Technology

andHumanValues,10,4,27-36.

[31]Maruši´c,A.,2007:\"SmallJournals\presentationtotheESF-ORIFirstWorldConferenceon

ResearchIntegrity.

27

[32]Mialon,H.andMialon,S.,2002:\"Scienti…cOriginalityandtheEconomicsofPublishing\working

paper.

[33]NationalAcademyofSciences,NationalAcademyofEngineersandInstituteofMedicine,1992:

ResponsibleScience,NationalAcademyPress.

[34]NatureImmunology,2007:\"SpotChecks\8,3,215.

[35]Odling-Smee,L.,Giles,J.,Fuyuno,I.,Cyranoski,D.andMarris,E.,2007:\"WhereareTheyNow?\

Nature,445,7125,244-245.

[36]O¢ceofResearchIntegrity,2005:\"Dr.EricT.PoehlmanPressRelease\March17.

[37]Okie,S.,1988:\"WhenResearchersDisagree:Whistle-BlowingWasCostlyforScientist\Washing-tonPost,April11.

[38]Pollak,R.,1997:TheCreationofDr.B:ABiographyofBrunoBettelheim,Simon&Schuster.[39]Pozzi,A.andDavid,P.,2007:\"EmpiricalrealitiesofScienti…cMisconductinPubliclyFunded

Research\presentationtotheESF-ORIFirstWorldConferenceonResearchIntegrity.

[40]Reuters,2006:\"KoreanScientistPaidMa…aforMammoth\October25.

[41]Rivoire,K.,2003:\"TheGrowingThreattoResearch:Scienti…cMisconduct\M.I.T.Undergraduate

researchJournal,8,21-26.

[42]Robin,R.,2004:ScandalsandScoundrels.SevenCasesthatShooktheAcademy,Universityof

CaliforniaPress.

[43]Romer,P.,1990:\"EndogenousTechnologicalChange,\"JournalofPoliticalEconomy,98,S71-S102.[44]Rossner,M.,2006:\"HowtoGuardAgainstImagefraud\TheScientist,Marchissue.

[45]Rothwell,P.M.andMartyn,C.N.,2000:\"ReproducibilityofPeerreviewinClinicalNeuroscience\

Brain,123,1964-1969.

[46]Sorokina,D.,Gehrke,J.,Warner,S.,andGinsparg,P.:\"PlagiarismDetectioninarXiv\Proceedings

ofthe6thIEEEInternationalConferenceonDataMining,forthcoming.

[47]Surowiecki,J.,2007:\"ADrugontheMarket\TheNewYorker,June25.

[48]Wible,J.,1998:TheEconomicsofScience:MethodologyandEpistemologyasifEconomicsReally

Mattered,Routledge.

[49]Zuckermann,H.,1984:\"NormsandDeviantBehaviorinScience\Science,TechnologyandHuman

Values,9,1,11-12.

28

ANotation

PlayersANERefR

Movesrad,incrfail,succacc,rejcheck,nocheckProbabilities󰀃incr;󰀃rad󰀆incr;󰀆rad

󰀄

Payo¤sparametersBincr;Brad2(0;+1)

cincr;crad2(0;+1)gincr;grad2(0;+1)

Wincr;Wrad2(󰀂1;+1)cRincr;cRrad2(0;+1)Gincr;Grad2(0;+1)AuthorNature

Editor/referee(basicgame),Editor(extendedgame)Referee(extendedgame)Reader

ChoicesbyAofincrementalvs.radicalresearch

Failureorsuccessoftheproject,asdeterminedbyNatureAcceptanceorrejectionofthepaperbyE(basicgame),orbyref(extendedgame)

Choiceofwhethercheckingornotcheckingapaperforfraud–byR(basicgame),andbyeitherRorE(orboth)(extendedgame)ProbabilitiesofsuccessofanincrementalorradicalprojectProbabilitiesofacceptancebytherefereeofanincrementalorradicalproject

ProbabilitythatEchecksapaperformisconduct(extendedgame)Bene…tforAfromhispaperbeingpublishedandnotchecked(orcheckedandfoundclean),forincrementalandradicalresearchCosttoperformincrementalorradicalresearch

PenaltytoAfromhispaperbeingdetectedasfraudulentBene…tforRfromA’spaperbeingpublishedandnotchecked(orcheckedandfoundclean),forincrementalandradicalresearch

CostforRtocheckanincrementalorradicalpaperformisconductBene…ttoRfromA’spaperbeingdetectedasfraudulentTable6:Summaryofthenotationusedinthemodel

BProofs

We…rstprovetheexistenceofthepoolingequilibrium.Theexpectedpayo¤

ProofofProposition2.1

ofRfromnotcheckingishigherthanthepayo¤fromchecking,giventheposteriorbeliefsofR.Since

RassumespoolingbyA,shedoesnotupdateherbeliefsonthestateofnature.Therefore,thebest

responsetopoolingonsubmisnocheckifandonlyif:

󰀃W+(1󰀂󰀃)W󰀆󰀃(W󰀂cR)+(1󰀂󰀃)(G󰀂cR)

fromwhichweobtaintheresult.15

(8)

Inthethecasewhereexpression(8)holdswithequality,weassumethattheindi¤erencecaseisincludedinto

thepoolingequilibrium.AppendixCbelowo¤ersamoretechnicalexplanationforthischoice.

15

29

Second,considertheconditionsfortheexistenceofasemi-separatingequilibrium.Notice,…rst,thatInordertohaveasemi-separatingequilibrium,bothAandrandomize.IfRchoosescheck,thenAhasnoincentivetosubmitincaseoffailure:hewouldbecaughtcheatingwithprobability1.nosubmwilldominatesubm.Inotherwords,thetwooptionswillnotleaveAindi¤erentforanymixingprobabilityintheunitinterval.IfRdoesnotcheck,thenAhasanincentivetopoolonsubmratherthanrandomizing.

ThereaderRchoosesrsoastomakeAindi¤erentbetweenbetweensubmittingandnotsubmitting,whentheprojectisunsuccessful:

󰀆[r(󰀂g󰀂c)+(1󰀂r)(B󰀂c)]+(1󰀂󰀆)[󰀂c]=󰀂c;

fromwhichweobtainr=

BB+g.

(9)

Considernowtheindi¤erenceconditionforR,whichdeterminesthe

mixingprobabilityforA.Risindi¤erentbetweencheckingandnotchecking,givenher(updated)beliefsonthesuccessoftheresearch,ifthefollowingconditionholds:

󰀅(W󰀂cR)+(1󰀂󰀅)(󰀂cR+G)=󰀅(W)+(1󰀂󰀅)(W);

where󰀅=prob(projectissuccessfuljpaperpublished)

(10)

=

prob(paperpubljprojsucc)*prob(projsucc)

prob(paperpubljprojsucc)*prob(projsucc)+prob(paperpubljprojnotsucc)*prob(projnotsucc)󰀃cR

1󰀂󰀃G󰀂W󰀂cR.

=

󰀅󰀄󰀃

󰀅󰀄󰀃+󰀅p(1󰀂󰀃):

Substitutinginto(10),weobtainp=

Inorderforptobenonnegative,GhastobesuchthatG>W+cR.Also,inorderforptohavepositiveandmeaningfulvalues,i.e.withintheunitinterval,itmustbethatEquivalently:(1󰀂󰀃)(W󰀂G)<󰀂c;orG>W+

cR

:1󰀂󰀃

󰀃c1󰀂󰀃G󰀂W󰀂c<1.

ProofofCorollaries3.2.1and3.2.2Supposethereisnochangeinthetypeofresearchchoseninequilibrium,followingareductionincheckingcosts.Threecasesneedtobeconsidered:

i)Theequilibriumofthepropersubgameispoolingbeforeandafterthereductionincheckingcosts.Inthiscase,theprobabilityofundiscoveredmisconductdoesnotchange,asitis󰀆(1󰀂󰀃)beforeandafterthechangeincheckingcosts.

ii)Theequilibriummovesfrompoolingtosemi-separating.Theprobabilityofundiscoveredmiscon-ductmovesfrom󰀆(1󰀂󰀃)to󰀆(1󰀂󰀃)p(1󰀂r).Sincepandraresmallerthan1,then󰀆(1󰀂󰀃)p(1󰀂r)<

󰀆(1󰀂󰀃).

iii)Theequilibriumissemi-separatingbeforeandafterthereductionincheckingcosts.ItcanbeseenfromProposition2.3thattheprobabilityofundiscoveredfrauddecreases.

Toseehowtheprobabilityofanundiscoveredfraudcanactuallyincreasefollowingareductionincheckingcosts,assume…rstthatGrad>Wrad+

cincr>󰀆rad󰀃radBrad󰀂crad:Thismeansthatequilibriumfallsinregion3.bofProposition2.4above

reductioninbothcRradandcRincrsuchthatGrad󰀅Wrad+

cRradcRincr

,Gincr󰀅Wincr+and󰀆incrBincr󰀂

1󰀂󰀃rad1󰀂󰀃incr

cRradcRincr

andGincr󰀅Wincr+:

1󰀂󰀃rad1󰀂󰀃incr

(page12):anincrementaltypeofresearchischosen,andapoolingequilibriumisplayed.Considernowa

30

Amayswitchtoaradicaltypeofresearch,sincetherearevaluesoftheparametersforwhichboth

󰀆incrBincr󰀂cincr>󰀆rad󰀃radBrad󰀂cradand󰀆incr󰀃incrBincr󰀂cincr<󰀆rad󰀃radBrad󰀂cradare

true:Ifthishappens,wemovefromapoolingequilibriuminwhichincrementalresearchischosentoasemi-separatingequilibriuminwhicharadicalpathischosen.Theprobabilitythatafraudulentpaperissubmitted,published,andnotcaughtishigherafterthereductioninthecheckingcostsif:

grad󰀆rad󰀃radcRrad

>󰀆incr(1󰀂󰀃incr)

Grad󰀂Wrad󰀂cRradBrad+grad

researchpaperismorelikelytoacceptedthananincrementalpaper.

(11)

Inequality(11)issatis…ediftheprobabilityofsuccessofradicalresearchissu¢cientlyhighandifradical

ProofofCorollaries3.2.3and3.2.4Consider…rstthecaseinwhichthechoiceofresearchtypeisuna¤ectedaftertheincreaseintheintensityofcompetition.Inthiscase,threesituationsmayoccur:

i)Theequilibriumispoolingbeforeandaftertheincreaseincompetition.ii)Theequilibriummovesfrompoolingtosemi-separating.

iii)Theequilibriumissemi-separatingbeforeandaftertheincreaseincompetition.

Inthe…rsttwocases,thereasoningisthesameasinthepreviousproof.Inthethirdcase,weseethattheprobabilityofundiscoveredfrauddecreasesfromProposition2.3(page11),sincebothand

@P(subm;acc;nc)

@B@P(subm;acc;nc)

@(G󰀂W)arenegative.

Inordertoseetheoppositee¤ectatwork,supposethattheequilibriumisinregion1.binProposition2.4(i.e.Grad󰀅Wrad+

crad):Thismeansthatanincrementaltypeofresearchischosen,andapoolingequilibriumisplayed.

Considernowasigni…cantincreaseintheincentivestoconduceradicalresearch(i.e.anincreaseinbothBradandGrad󰀂Wrad),whichmovestheequilibriumfromregion1toregion3asdescribedinProposition2.4above(Grad>Wrad+

cRradcRincr

;Gincr󰀅Wincr+and󰀆incrBincr󰀂cincr󰀆󰀆radBrad󰀂

1󰀂󰀃rad1󰀂󰀃incr

cRradcRincr

andGincr󰀅Wincr+).Supposethat,

1󰀂󰀃rad1󰀂󰀃incr

beforethechange,incrementalresearchwaschosen.IftheincreaseinBradissu¢cientlyhigh,aradical

typeofresearchwillnowbechosen.Wemovefromapoolingequilibriumwithincrementalresearch,toasemi-separatingequilibriumwithradicalresearch.Wesawinthepreviousproofthat,forsomecon…gurationoftheparameters,theprobabilityofundiscoveredfraudmayincrease.

ProofofProposition3.1Weprove,insequence,theexistenceofaseparating,pooling,andsemi-separatingequilibrium.

First,Aprefersnottosubmitafakedpaperif󰀆󰀄(󰀂g)+󰀆(1󰀂󰀄)B󰀂c<󰀂c,fromwhichthe

conditionontheexistenceofaseparatingequilibriumfollow.

Withrespecttotheexistenceofapoolingequilibrium,wecheck…rstthattheexpectedpayo¤ofRfromnotcheckingishigherthanthepayo¤fromchecking,giventheposteriorbeliefsofR.IfRobserveapaperbeingpublished,sheexcludesthatthepaperisfakedandtheeditorhascheckedit.Thisoccurswithprobability(1󰀂󰀃)󰀄.Therefore,theprobabilitythattheresearchwassuccessful,conditionalon

31

thearticlehavingbeenpublished,isif

󰀃

1󰀂(1󰀂󰀃)󰀄=

successful,conditionalonthearticlehavingbeen

󰀃

󰀃+(1󰀂󰀄)(1󰀂󰀃):Theprobabilitythat

(1󰀂󰀃)(1󰀂󰀄)

published,is󰀃+(1󰀂󰀄)(1󰀂󰀃).Therefore,

(1󰀂󰀃)(1󰀂󰀄)

󰀃+(1󰀂󰀄)(1󰀂󰀃)(G

theresearchwasRdoesnotcheck

W󰀆

Thecondition󰀄<

BB+g󰀃

󰀃+(1󰀂󰀄)(1󰀂󰀃)(W

󰀂cR)+󰀂cR)

(12)

derivesfromtheresultontheexistenceofaseparatingequilibrium.

Finally,considertheconditionsfortheexistenceofasemiseparatingequilibrium.RchoosesrsoastomakeAindi¤erentbetweenbetweensubmittingandnotsubmitting,whentheprojectisunsuccessful:

󰀆󰀄(󰀂g)+󰀆(1󰀂󰀄)[r(󰀂g)+(1󰀂r)(B)]󰀂c=󰀂c;

or:r=

1B

B+g1󰀂󰀄(13)

andcheckedbytheE.Withprobability󰀆(1󰀂󰀄),thepaperispublishedbutnotcheckedbyE.Inthiscase,withprobabilityrthereisacheckbyR,whilewiththecomplimentaryprobabilitythereisnocheck.Considernowthentheindi¤erenceconditionforR.Risindi¤erentbetweencheckingandnotcheckingif:

󰀄󰀂1󰀂󰀄:Ifthepaperisfakedandsubmitted,withprobability󰀆󰀄thepaperispublished

󰀅(W󰀂cR)+(1󰀂󰀅)(󰀂cR+G)=󰀅(W)+(1󰀂󰀅)(W);

where󰀅=prob(projectissuccessfuljpaperpublished)

(14)

prob(paperpubljprojsucc)*prob(projsucc)󰀅󰀄󰀃

prob(paperpubljprojsucc)*prob(projsucc)+prob(paperpubljprojnotsucc)*prob(projnotsucc)=󰀅󰀄󰀃+󰀅p(1󰀂󰀃)(1󰀂󰀄):

󰀃cRSubstitutinginto(14),weobtainp=1󰀂󰀃(G󰀂cR)(1󰀂󰀄)󰀂W.Inorderforrtobenonnegative,itmustbe󰀄=

orequivalently,g>0,whichistruebyassumption.Inorderforptobenonnegative,Ghastobe

W+cR

G:Also,inorderforptohavepositive󰀃cRandmeaningfulvalues,i.e.withintheunitinterval,weneed1󰀂󰀃(G󰀂cR)(1󰀂󰀄)󰀂W<1.Equivalently:

(1󰀂󰀃)(1󰀂󰀃)W+cR󰀃

(G(1󰀂󰀄)󰀂W)or󰀄<1󰀂cR<󰀃+(1󰀂󰀄)(1󰀂󰀃)(G󰀂cR)(1󰀂󰀃):Itturnsoutthatthissecondconditionis

(1󰀂󰀃)W+cR󰀃

stricterthanthe…rstone,sothatasemi-separatingequilibriumrequires󰀄<1󰀂(G󰀂c)(1󰀂󰀃):R

largeenough,i.e.G>1W󰀂󰀄+cR,orequivalently,󰀄<1󰀂

ProofofCorollary3.3.1If󰀄󰀆paperissubmitted.

BiBi+gi,

thesubgameshaveaseparatingequilibriumwherenofailed

ProofofCorollary3.3.2Ifmin(1󰀂

increase,thenthesubgamesareplayedinpoolingequilibria.Inthiscase,thereisnocheckbyA,andtheoverallprobabilitythatafraudisdiscoveredis󰀆i(1󰀂󰀃i)󰀄i(seeTable4),fromwhichthecorollarydirectlyfollows.

ProofofCorollary3.3.3If󰀄(1󰀂󰀃i)Wi+cR󰀃iBi(Gi󰀂cRi)(1󰀂󰀃i);Bi+gi)

(1󰀂󰀃i)Wi+cR󰀃iBi(Gi󰀂cRi)(1󰀂󰀃i);Bi+gi)

󰀅󰀄<

BiBi+gi

beforeandafterthe

beforeandaftertheincrease,then

@r@󰀄thesubgamesareplayedinsemi-separatingequilibria.Itisimmediatetoverifythat<0;sothatan

increasein󰀄leadstoareductioninthecheckingprobabilitybyR:Thise¤ectmorethancompensates

32

thedirect,fraud-reducinge¤ectofanincreaseof󰀄;sothattheoverallprobabilitythatafakedpapergoesuncheckedincreases,ascanbeseenfromTable4above.

ProofofCorollary3.3.4Weillustratethiscorollarythroughthefollowingnumericalexample:

ExampleB.1SupposecR=1;G=5;W=2;󰀃=0:5and

gg+B=0:5:Itmustbe󰀄<0:5for

aseparatingequilibriumnottobeplayed.If󰀄0=0:2;asemi-separatingequilibriumisplayed.Then,for0:25<󰀄00<0:5,theequilibriumbecomespoolingandtheprobabilitythatthefraudisnotcaughtincreases.

CEthic-basedtremblingequilibrium

Inthebasicset-upofthemodelweexcludethepossibilitythattheauthorofthepaper(A)behavesethically,i.e.itdoesnotsubmitapaperwhenitisnotsuccessful,evenifthisactionispro…table.Theaimofthissectionistoinvestigatetherobustnessofequilibriawhenthereisa(small)probabilitythattheauthorbehavesethically.

First,weconsiderthenotionofethic-perturbatedgame.Intheoriginalgame,anequilibriumisde…nedbyps,theprobabilityofAsubmittingapaperwhichissuccessful(thisprobabilitybeingalwaysequalto1);bypns,theprobabilityofAsubmittingapaperwhenitisnotsuccessful;byr,theprobabilityofacheckingbyR;and,…nally,bytheupdatebeliefbyRonA0saction.

Intheethic-perturbatedgame,Asubmitsanunsuccessfulpaperwithprobabilitypns(1󰀂\"),where

0<\"<1.Thismustbeinterpretedasfollows.Thereisaprobability\"thatAisirrational,in

thesensethathefollowstheruleofneversubmittingafakedpaper,whateverarethepayo¤s.Withthecomplementarityprobability,instead,itis\"rational\".Updatebeliefsare

󰀃

󰀃+pns(1󰀂\")(1󰀂󰀃):

pns(\")istheactionbyA.Thechecking

probabilitybyRisr(\").BothareingeneralfunctionoftheprobabilityofanethicalbehaviorbyA:

󰀄De…nition1Intheoriginalgame,aPerfectBayesianEquilibriumisuniquelyidenti…edbyp󰀄ns;rand󰀃+p󰀄ns(1󰀂\")(1󰀂󰀃)󰀃

:Consideradecreasingsequence\"k;k=1;2;:::;1,withlim\"k=0:Inthepertur-k!1

󰀄pns(\");r󰀄(\")

batedgame,aPerfectBayesianEquilibriumisidenti…edbyatriple

󰀄ThePBEidenti…edbyp󰀄ns;randk!1

k!1

󰀄󰀄󰀄limp󰀄ns(\"k)=pnsandlimr(\"k)=rforanysequence\"k:

󰀃+p󰀄ns(1󰀂\")(1󰀂󰀃)󰀃

and

󰀃

:󰀃+p󰀄(1ns󰀂\")(1󰀂󰀃)isanethic-basedtremblingequilibrium(EBTE)if

Thisde…nitionhasaclearinterpretation.APerfectBayesianEquilibriumisaEBTEifsmallpertur-bationsintroducedbyethical(irrational)behaviordonotleadtosigni…cantdepartureintheequilibriumoftheoriginalgame.

RIfG󰀄Inthisrange,intheperturbatedgame,p󰀄ns(\")=1andr(\")=0:IfRassumespooling,itwilldecide

33

nottocheckifG󰀄Risnotchecking.Inthiscase,itisobviouslythatlimr󰀄(\"k)=r󰀄andlimp󰀄ns(\"k)=pns.Then,we

cR󰀃1󰀂1󰀂\"(1󰀂󰀃),whichisalwaystrueinthecaseweareconsidering.Awillpoolif

k!1

k!1

haveaEBTE.

IfG>W+

cR1󰀂󰀃;

weareintherangeofparameterswheretheequilibriumissemi-separating(

p󰀄ns1󰀂\"󰀄p󰀄ns<1):Intheperturbatedgame,theindi¤erenceconditionrequirespns(\")=

k!1

k!1

whiler󰀄(\")=r󰀄.

󰀄Weclearlyhavelimr󰀄(\"k)=r󰀄andlimp󰀄ns(\"k)=pns:Therangeofparametersforwhichasemi-

separatingPBEexistsintheperturbatedgameisthesameforwhichthistypeofequilibriumexistintheoriginalgame.Then,wehaveaEBTEintheoriginalgame.

RIfG=W+1c󰀂󰀃;inanyperturbatedgameRprefersnottocheck,ifitassumespooling.Awillpool

ifRdoesnotcheck.Thisimpliesthatonlyr=0isaEBTE.Forr>0,instead,wehaver󰀄(\")=0

8\">0,andthenlimr󰀄(\"k)=r󰀄:W+

cR1󰀂󰀃;

Asare…nement,EBTEleadstoauniqueequilibriumforanyvalueoftheparameters.ForG󰀅

theequilibriumispooling.ForG>W+

cR1󰀂󰀃;

theequilibriumissemi-separating.

34