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DynamicsofTrustReciprocationinMulti-RelationalNetworks*AyushSinghal,KarthikSubbian,JaideepSrivastavaUniversityofMinnesota,Minneapolis,MN.ayush,karthik,srivastaTamaraG.Kolda,AliPinarSandiaNationalLaboratories,Livermore,CA.tgkolda,apinar@sandia.govUnderstandingthedynamicsofreciprocationisofgreatinterestinsociologyandcomputationalsocialscience.TherecentgrowthofMassivelyMulti-playerOnlineGames(MMOGs)hasprovidedunprecedentedaccesstolarge-scaledatawhichenablesustostudysuchcomplexhumanbehaviorinamoresystematicmanner.Inthispaper,weconsiderthreedifferentnetworksintheEverQuest2game:chat,trade,andtrust.Thechatnetworkhasthehighestlevelofreciprocation(33%)becausethereareessentiallynobarrierstoit.Thetradenetworkhasalowerrateofreciprocation(27%)becauseithas *fullversion:http://arxiv.org/abs/1303.6385https://www.everquest2.com/http://us.battle.net/wow/en/http://www.nickyee.com/daedalus/gateway demographics.html 0 5 10 15 20 25 0.55 0.6 0.65 0.7 0.75 0.8 ADDITIONAL DAYS OF TRADE INTERACTIONSAUC TRUST TRUST+TRADE TRUST+TRADE+HMPLY TRUST+HMPLY Fig.1:FigureshowsimprovementinAUCbyaddingtradeinteractionforpredictingtrustreciprocation.Dynamicsofthereciprocationvariesfromnetworktonetworkdependingonthelevelofbarrierforreciprocation.Thebarrierforreciprocatingatrustrelationshipcouldbelackofresourcesorhighriskinvolved.Needlesstosay,thesebarriersaffectthelevelsofreciprocationsignicantlyindifferentnetworks.Forinstance,inachatnetworkusershaveaverylowbarrierlevelfortrustingeachotherasthereisnocommitmentfromeithersidetoparticipateinanyinvolvedrelationshipor y sis and Minin g 661 A SONAM'13, August 25-29, 2013, Niagara, Ontario, CAN Copyright 2013 ACM 978-1-4503-2240-9 /13/08 ...$15.00 reciprocaledges,degree,andsizeofmodelednetwork.Duraketal.[]proposeanullmodelfordirectedgraphsthatcombinesthereciprocalandtheone-wayedgestogeneratedirectedgraphsthatmatchthein-,out-,andreciprocal-degreedistributions.Ahmadetal.[]usetheoriesofsocialexchangeasabasisforbuildingagenerativemodelGTPAformodelingtemporallyevolvingdirectednetworks.Thereareotherrecentworks,suchasGralaschelliandLoffredo[]thatusestatisticalmeasurestoconcludethatthereciprocationofanetworkisneveratrandomanditiseitherre-ciprocaloranti-reciprocal.Similarly,Zamora-Lopezetal.[proposeamethodtocomputetheexpectedreciprocationofthenetworkasafunctionofin-andout-degreedistributions.Reciprocationinweighteddirectednetworks,especiallyinlargescalemobilecommunicationnetworks,isdiscussedinin14],[].Szelletal.[]showthatnegativeinteractionshavealowerreciprocationcomparedtothepositiveinteractions.Reciprocationhasalsobeenusedforlinkprediction[],[[19].II.MMOGDATAInthissection,wedescribethenetworksusedinourexperiments.A.TrustNetworkInEQII,playersformteamsinordertocompletethegametasks.Astheplayersarelimitedbythenumberofitemstheycancarryatatime,playersbuyhousesasatemporarystoragetoretaintheirarmoryandotheraccessories.Throughthetrustnetwork,playerssharetheirhouseaccesswithotherplayers.Forthisreason,wealsorefertothisnetworkasthetrustnetwork.Wehave9monthsofdatafromJan-01-2006toSep-11-2006with63684nodesand140514edges.Eachnodeinthenetworkisaplayercharacterinthegame,andeachedgeisapermissionlevelgrantedbythecharactertoanothercharacter.Eachedgehasatimestampwhentheaccesswasgranted.Thetrustlevelsaredescribedasfollows.Trustee:Playercanstore,touch,move,add,andre-movethings,andhasalmostsameaccessastheowner.Friend:Playercanstore,touch,andmovethings.Visitor:Playercanenterthehouseandviewthings.:Playercanseethehouseexternallybutcannotenterit.B.TradeNetworkIntheEQIItradenetwork,playersexchangegoodsforcoinsorgoods.Inthisactivity,atradelinkisestablishedbetweentheseller(initiator)andthebuyer(acceptor)inthetradenetwork.Weanalyzedsuchatradenetworkcontaining295,055nodesand11,913,994edgesoveraperiodof9monthsfromJan-01-2006andSep-11-2006.C.ChatNetworkThechatnetworkisacommunicationmediumwhereplay-ersexchangeinstantmessages.Thenumberofnodesinthisnetworkis349,654,andthenumberofedgesis86,948,748,spanningoveraperiodofonemonthfromJul-29-2006toSep-D.NetworkProlesWepresentthedegreedistributionofthesenetworksin.Thedistributionswereconstructedusingsnapshotsofdifferentnetworksovertheentireobservationperiod.ThedistributionsseemtofollowthepowerlawwithexponentTABLEI:Statisticsofreciprocationintrade,chatandtrustnetworks. Network AllForward First Total Type(period) Edges Reciprocation Reciprocation Chat(1month) 1840492 441039(23.9%) 599548(32.6%) Trade(9months) 520861 74137(14.23%) 136809(26.3%) Trust(9months) 62674 8452(13.5%) 8083(14.0%) ofthepowerlawrangingfrom1to3.Theexponentwascalculatedusingtheslopeofaleastsquarestinthelog-logIII.RECIPROCATIONINIFFERENTETWORKSThereciprocationofanetworkistheratioofforwardedges(sayfromplayer)thathaveacorrespondingbackwardedge(fromplayer),i.e.,theratioofmutualinteractions.A.BarriersofReciprocationBarriersofreciprocationcanbebroadlygroupedintoriskandutility.Theriskfactorsincludeloosinganasset,in-gamepoints,orin-gametime;andtheutilityinclude,immediategainsintermsofpointsandassetsandlongtermfutureprospects.Eachnetworkhasspeciccharacteristicsthatleadtolow,mediumorhighbarriersforreciprocation.Accordingly,trustnetworkhasthelevelofbarrier.Inthecaseoftradenetwork,thebarrierofreciprocationfallintobarriercategory.ThechatnetworkfallsintothelowbarrierB.MultiplereciprocationsTherecanbeseveraloverlappingforwardandbackwardarcsbetweeneachpairofplayers.Forthepurposeofmeasur-ingthereciprocationandresponsetime,werstpartitionthetimelineintoseveralpartitions.Weconsiderthestarttimeofrstforwardedgeandthecorrespondingendtimeoftherstresponseastherstpartition.Similarly,thesecondforwardarcanditsresponsemarkstheendofthesecondpartitionandsoon.Fortheremainderofthispaper,unlessspecied,wealwaysrefertotheoverallreciprocationrate.InTableshowmultiplereciprocationrateforthreedifferentnetworks.C.ReciprocationinTrust,ChatandTradeNetworksInthissection,westudythereciprocationbehaviorintrust,chatandtradeasindependenthomogenousnetworks.Then,inthenextsection,weanalyzetheinteractionsofchatandtraderelationshipsinaffectingthereciprocationofthetrustnetwork.Thechatandtradenetworkshavesimpleedgetypeswithnoattributesexcepttimestamps.Forthetrustnetwork,theTrustlevelcorrespondstobeingaTrustee.Wecollapsethelowertrustlevels,(Friend,Visitor,andNone),toasingleNot-Trustlevel.WesummarizethetotalreciprocationforeachnetworktypeinTable.Inthetrustnetwork,beingahighbarrierrelationship,only14.0%oftheforwardtrust(8803one-way)linksreceiveatrustresponse(reciprocation)backandtheirresponsetimedistributionisshowninFigure.Asthechatnetworkisalowbarrieractivity,ithasthehighestamountofreciprocationwith32.6%offorwardedgesreciprocated.Thelowbarrierinthisnetworkisduetotheinstantnatureofthecommunicationandminimalriskinvolvedinmakingachatreciprocation.Oncontrary,inthemediumbarriertradeactivitiesthereciprocationrateis26.3%,lowerthanchatbutmorethanthetrustnetwork.Thereasonswhyaplayermaynot y sis and Minin g 662 100 101 102 100 101 102 103 104 105 DEGREEFREQUENCY INDEGREE OUTDEGREE 100 101 102 103 104 100 101 102 103 104 105 DEGREEFREQUENCY INDEGREE OUTDEGREE 100 101 102 103 100 101 102 103 104 105 DEGREEFREQUENCY INDEGREE OUTDEGREE Fig.2:Degreedistributionsoftrust(left),trade(right-top)andchatnetworks(right-bottom). 100 101 102 100 101 102 103 104 RESPONSE TIME IN DAYSNUMBER OF RESPONSES RESPONSE TIME m=27.304 s=42.812 #examples= 8803 (a)Trust 100 101 100 101 102 103 104 105 106 RESPONSE TIME IN DAYSNUMBER OF RESPONSES RESPONSE TIME m=0.317 s=1.397 #examples=599548 (b)Chat 100 101 102 100 101 102 103 104 105 NUMBER OF RESPONSESRESPONSE TIME IN DAYS RESPONSE TIME m=12.587 s=25.954 #examples=136809 (c)TradeFig.3:Theresponsetimedistributionforthethreenetworks.reciprocateinthisnetwork,couldbelackofeitherresourcesoraneedfordoingso.Further,wewishtoanalyzetheresponsetimedistributionsofthesenetworkstounderstandsomekeyquestions,suchas,doesallreciprocationsoccurwithinacertainnumberofdaysoraretheyspreaduniformlyoveralongerperiodoftime?showstheresponsetimedistributionforthetrustrelationship.Wendthattheresponsetimedistributionfollowsapowerlaw,withameanresponsetimeof27days.FortheChatactivity,theresponsetimedistributionisshowningure.Thedistributionroughlyfollowsapowerlaw.Thereisanoutlierregionaround45days.Weinvestigatedthisregionandfoundthatthesearersttimeuserswhoarenotfamiliarwiththesystem.Wenotethatsuchusersareextremelyrareinthedataset(lessthan0.01%).Thegurealsoshowsthatmostoftheusersinthelowbarrier,chatnetworkreciprocatewithinthesamedayoratmostthenextday.Thisisevidentsincethemeanrstresponsetimeinthechatnetworkislessthanoneday(0.317).Inthechatnetworkthereisasharptruncation[after7days,asthesignicanceofamessagebeyondaweekbecomescompletelyirrelevanttothecontextofthegame.Forthetradenetwork,weshowtheresponsetimedistribu-tioninFigure;thedistributionhasaheavytailandseemstofollowapowerlaw.Theslopeofthisdistributionisnotassteepasthatofthechatnetwork,implyingthetradereciprocationisnotasquickasinchat.Asthebarrierforreciprocationinthetradenetworkismorethanchat,theaverageresponsetimeintradeis43Xslowerataround13days.IV.RECIPROCATIONINETEROGENEOUSNETWORKSWewillnowoverlaythetrust,chat,andtradenetworkstoanalyzetheinteractionsamongheterogeneousedges.AsTABLEII:Thereciprocationcountsforrstinteraction(rstforwardrequestandrstreply)inaheterogeneousMMOGnetworkforaperiodofonemonth. Forward FirstForward Chat Trade Trust Type Edges Reciprocation Reciprocation Reciprocation Chat 1645623 435758 1187 105 Trade 74428 7953 11402 335 Trust 10502 907 1016 722 thechatdataisavailableonlyforamonth,werestricttheotherdatasetsalsotothisonemonthperiod.Thefocusofthissectionistoanswerquestions,suchas:Howmanytimesdoesatrustgrantingfromplayerresultinatrustreciprocation?Doesaplayerprefertoreciprocatewithtradeorsomeotherlowbarrierinteractionsuchaschatbeforegrantingahighbarrierrelationshipsuchastrusttoplayer.Therstinteraction,asnotedearlierinFigure,capturesallthecharacteristicsoftheadditionalinteractions,henceweconsideronlytherstinteractionforthisexperiment.Foreachforwardedgetype,wecountthenumberofrstreciprocationbetweenpairsofplayersintheconsolidatednetwork.Inthecaseoftiereciprocationsacrossmultipleedgetypes,weincludeallthetiededgeswhilecounting.WehavesummarizedthereciprocationsforeachforwardinteractiontypeinTableAsweseefromTable,theplayerswhoperformchatpre-dominantlymakeareciprocationusingthechatlink(26.48%).Thesameobservationismadeforthetradeactivity,whichisalsoalowbarrieractivity(buthigherthanchat).Herealsowendthattraderesponsesarethepredominanttypeofresponsesforatraderelationship.However,thisisnotthesameinthe y sis and Minin g 663 caseofatrustforwardedgetypesincetrustisahighbarrierrelationshipandamoretimeconsumingactivity.Sopeopleareverycarefulbeforereciprocatingforsuchrelationshipsandreciprocationsarerstinitializedthroughlowbarrieractivitiesbeforereciprocatingwithahighbarrierrelationship,suchastrust.Thereciprocationsfortrustforwardedgeispredominantlythroughchat(8.63%)ortrade(9.67%).Wenowanalyzethedependencybetweentrustrelationshipagainsttradeandchatinteractions.Theaimofthisexperimentistoquantifyhowchatandtrade,lowbarrierrelationships,inuencereciprocationinahighbarrierrelationship.Foranytwonodesinthetrustnetwork,westartouranalysisfromthetimewhenaforwardTRUSTedgefromisestablished.ForsuchaforwardedgetherecaneitherbeaTRUSTreplytocompletetheTRUSTrelationshipornoTRUSTreply(incompleteTRUSTrelationship).TheTRUSTrelationshipisdeterminedasincompleteifthereisnotrustresponsefromwithintheaveragetrustresponsetimewhichis4.6daysinthiscase.Inotherwords,wetruncatetheresponsetimefortheincompletereciprocationsbythemeanresponsetime(4.6days)anduseonlytheperiodbeforethismeanresponsetimeforfurtheranalysis.Therecanalsobeseveralotherresponses(lowbarrierinteractions)fromreplieswithaTRUSTlink.Understandingtheseotherrelationships,suchaschatandtrade,beforeaTRUSTreplyisformedfromiscrucialtodecipherthenatureofsocializationrequiredforahealthymutualtrustrelationship.Asaresultofthisexperiment,wendthatcompleteandincompleteTRUSTdifferfromeachotherintermsofchatandtraderesponses.Weobservethattheresponsesareexactlyinanoppositeorderinthetworows.ForthecompleteTRUSTweobservethattherewere743forwardsedgesthatwererespondedbackwithTRUST.However,beforetheTRUSTiscompletedbetween,weseethatthereare408traderesponsesfrom.Thesetraderesponsesaccountfornearly63%ofthetotalresponses.Wehaveonly243chatresponses,whichiscomparativelysmallerthanthetraderesponses.Surprisingly,theamountoflowbarrierresponsesfortheincompleteTRUSTgetscompletelyreversed.Thereare9145forwardTRUSTedgeswhichdonotgetaTRUSTreplybackandremainonesided.FortheseTRUSTrequests,wendthatthechatresponsesfromnow6962(approximately75%ofthetotalresponses)whilethetraderesponsesaresignicantlylower(aslowas25%).ThisexperimentconrmsthataTRUSTrelationshipbe-ismorelikelytocompleteiftherearemoretraderesponsesthanchatresponsesfrom.ThisinterestingresultcanbeusedtoinferthefutureTRUSTrelationshipsbasedonsomelowbarrierrelationshipssuchaschatandtrade.V.PREDICTINGTRUSTRECIPROCATIONInthissectionweevaluatehowwellcanwepredictahighbarrierrelationship,suchasatrust,usinginformationaboutthemediumbarrieractivitiesbetweenthenodes.Theempiricalanalysisintheprevioussectionshowedthatthesuccess(completion)ofhighbarriertrustrelationshipdependsonsomemediumbarrierrelationshipliketrade.Weusethisasourmotivationtoquantifyhowwellthemediumbarrierrelationshipcanhelptopredicthighbarrierrelationshipcom-pletion.However,weusetheentire9monthsofdatainordertomakeanyconclusionsforthetrustreciprocationprediction.ThechatrelationshiphastobeexcludedfromthisexperimentTABLEIII:Tablecomparingreciprocationpredictionaccuracyusingdifferentfeaturesets. Average Average Classier CWA AUC Precision Recall F-measure onlytrust 0.515 0.659 0.800 0.863 0.806 trust+trade(K=0) 0.526 0.637 0.825 0.866 0.816 trust+homophily 0.519 0.604 0.788 0.849 0.808 trust+trade(K=0)+homophily 0.527 0.636 0.826 0.866 0.817 trust+trade(K=20) 0.588 0.714 0.871 0.885 0.851 becauseofitslimitedavailabilityforasinglemonth.ButweaddseveralotherfeaturestomaketheexperimentmoreForthetrustnetworkdatafor9months,thereareatotalof61006trustrequests(forwardsedges).Thetrustlinksthatarereciprocatedis8252whereas52574forwardsedgesremainedincomplete.Fortheforwardrequests,weignoredtherequeststhatstartedinthelast(9th)monthbecauseitishardtodeterminewhethertherequestswerecompleted.Thusthenumberoftrustrequestsareslightlylessthanthosementionedinearliersections.Sothecompletedtrustlink(reciprocated)formsoneclassandtheincompletetrustlinks(unreciprocated)formsthesecondclass.Thefollowingfeatureswillbeusedtobuildthepredictionmodel.Featuresfromhighbarrierrelationship(trust):Thesefeaturescharacterizethepositionofplayers(nodes)inthetrustnetwork.ForthereciprocationlinksA,Bweconsidertwostructuralfeatures.Therststructuralfeaturedescribestheconnectivityoftoothernodesinatrustnetwork.Thesecondstructuralfeatureistheconnectivityofwithothernodesinthetrustnetwork.Forconvenience,wereferthesefeaturesastrustfeatures.Featuresfrommediumbarrierrelationship(trade)Thisfeaturesetconsistsoffeaturesfromthreesub-categoriesnamely,structural,past-behavioralandfuture-behavioral.ForaA,Bthestructuralfeaturecorrespondstothedegreeofanddegreeofinthetradenetwork.Thepast-behavioralfeaturesforalinkA,Bcorrespondtothecountofthetradeinteractionofthetypebeforethetrustrequestfromstarted.Thisfeaturetakesintoaccountthetradebehaviorbetweenbeforeanytrustinteractionstartedbetweenthem.Thefuture-behavioralfeaturestakesintoaccountthebehavioroftradeinteractionbetweenoncethetrustrequestissentfrom.Hereweuseatimewindow(indays)startingfromthetimewhentrustrequestwasinitiatedfrom.WecountthenumberoftradeinteractionsinthistimewindowFeaturesfromplayerdemography(homophily):Inthisfeaturesetwetakeintoaccountthetwotypesofhomophilies.Thersttypeofhomophilyisgenderhomophily.Thegenderhomophilybetweenis1ifhasthesamegender,and0otherwise.Theseconddemographicfeatureistheexperiencehomophilybetween.ItiscomputedA,BtheexperiencelevelofAsmentionedearlier,theaimofthisexperimentistoquantitativelycomparetheimpactofusingdifferentfeatures(describedabove).Weusedthesefeaturesetstobuildbinaryclassier(randomforestdecisiontree)topredictwhetheratrustreciprocationwithhappenornot.Tablecomparesthetrustreciprocationaccuracyforvariousfeaturesets.Theadditionoftradefeaturesbooststheperformanceofthepredictivemodeloverthecasewhenno y sis and Minin g 664 0 5 10 15 20 25 0.5 0.52 0.54 0.56 0.58 0.6 0.62 ADDITIONAL DAYS OF TRADE INTERACTIONCWA TRUST TRUST+TRADE TRUST+TRADE+HMPLY TRUST+HMPLY (a)Classweightedaccuracy 0 5 10 15 20 25 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 ADDITIONAL DAYS OF TRADE INTERACTIONF1 MEASURE TRUST TRUST+TRADE TRUST+TRADE+HMPLY TRUST+HMPLY (b)F1measure 0 5 10 15 20 25 0.75 0.8 0.85 0.9 0.95 ADDITIONAL DAYS OF TRADE INTERACTIONPRECISION TRUST TRUST+TRADE TRUST+TRADE+HMPLY TRUST+HMPLY (c)Precision 0 5 10 15 20 25 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 ADDITIONAL DAYS OF TRADE INTERACTIONRECALL TRUST TRUST+TRADE TRUST+TRADE+HMPLY TRUST+HMPLY (d)RecallFig.4:Comparingclassweightedaccuracy,precision,andrecallfortrustreciprocationprediction.tradefeaturesareused.Weextendthisexperimenttoincludethevariationoffuturetimewindowsize(K)forallfeaturesandmonitoritsimpactintermofaccuracyofthepredictionmodel.Figureshowstheresultsofthisexperiment.Asmentionedearlier,westudytheimpactofvaryingthetimewindowssize(from0to25days)forallthefeatures.AsshowninFigures,usingtradeasanadditionalfeatureinthepredictionmodeloutperformsthemodelwhichusesonlytrustortrustandhomophilyonly.Wealsondthatadditionofhomophilyfeaturesdonothaveasignicantimpactinpredictingreciprocationintrustnetwork.Thisisaninterestingndingfortrustreciprocationpredictionbecauseitisageneralnotionthathomophilyissignicantinpredictingtrustlinks[].Apossibleexplanationofthisob-servationisthatthereciprocationphenomenonissignicantlydifferentfromanormaltrustformationphenomenon.Asweknow,inreciprocationthereisalreadyaonesidedrelationshipestablishedandareciprocationmightdependonentirelyotherdynamicssuchastradeinteractions.VI.CWehavestudiedvarioussocialfactorsaffectingrecip-rocationinthreedifferentinteractionnetworksfromSonyEverQuestIIMMOG.We,usingresponsetimeanalysis,showthatpeopleareslowinbuildingmutualhightrustrelationshipscomparedtolowbarrierones.Weextendouranalysisfromsingle-typenetworkstoheterogeneousnetworks,whereweconrmthathighdegreeofmediumbarrieractivitiesiscrucialforreciprocationinhighbarrierrelationships.CKNOWLEDGMENTSThisworkwasfundedbytheGRAPHSprogramatDARPA.SandiaNationalLaboratoriesisamulti-programlaboratorymanagedandoperatedbySandiaCorporation,awhollyownedsubsidiaryofLockheedMartinCorporation,fortheU.S.DepartmentofEnergysNationalNuclearSecurityAdministrationundercontractDE-AC04-94AL85000.[1]D.Lazer,A.Pentland,L.Adamic,S.Aral,A.-L.Barabsi,D.Brewer,N.Christakis,N.Contractor,J.Fowler,M.Gutmann,T.Jebara,G.King,M.Macy,D.Roy,andM.V.Alstyne,Computationalsocialscience,vol.323,no.5915,pp.721 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