Reputation and Social Network Analysis in Multi-Agent Systems

Transcription

1 Repuaion and Social Neork Analyi in Muli-Agen Syem Jordi Sabaer IIIA - Arificial Inelligence Reearch Iniue CSIC - Spanih Scienific Reearch Council Bellaerra, Caalonia, Spain jabaer@iiia.cic.e Carle Sierra IIIA - Arificial Inelligence Reearch Iniue CSIC - Spanih Scienific Reearch Council Bellaerra, Caalonia, Spain ierra@iiia.cic.e ABSTRACT The ue of previou direc ineracion i probably he be ay o calculae a repuaion bu, unforunaely hi informaion i no alay available. Thi i epecially rue in large muli-agen yem here ineracion i carce. In hi paper e preen a repuaion yem ha ake advanage, among oher hing, of ocial relaion beeen agen o overcome hi problem. Caegorie and Subjec Decripor I.2.11 [Diribued Arificial Inelligence]: Muliagen yem; I.2.11 [Diribued Arificial Inelligence]: Inelligen agen; I.2.0 [General]: Cogniive imulaion General Term Algorihm,Deign,Theory 1. INTRODUCTION The udy and modeling of repuaion ha araced he inere of cieni from differen field uch a: ociology [10, 5], economic [7, 12], pychology [4, 11] and compuer cience [6, 3, 18]. According o he Oxford Englih Dicionary, repuaion i he common or general eimae of a peron ih repec o characer or oher qualiie. Thi eimae i necearily formed and updaed over ime ih he help of differen ource of informaion. Up o no, he compuaional model of repuaion have been conidering o differen ource: (i) he direc ineracion and (ii) he informaion provided by oher member of he ociey abou experience hey had in he pa [14, 15, 17, 18]. Thoe yem, hoever, forge a hird ource of informaion ha can be very ueful. A a direc conequence of he ineracion i i poible (even in imple ocieie) o idenify differen ype of ocial relaion beeen heir member. Sociologi and pychologi have been udying hee ocial neork in human ocieie for a long ime and Permiion o make digial or hard copie of all or par of hi ork for peronal or claroom ue i graned ihou fee provided ha copie are no made or diribued for profi or commercial advanage and ha copie bear hi noice and he full ciaion on he fir page. To copy oherie, o republih, o po on erver or o rediribue o li, require prior pecific permiion and/or a fee. AAMAS 02, July 15-19, 2002, Bologna, Ialy. Copyrigh 2002 ACM /02/ $5.00. alo ho hee ocial neork can be ued o analye ru and repuaion [8, 5]. Thee udie ho ha i i poible o ay a lo abou he behaviour of individual uing he informaion obained from he analyi of heir ocial neork. In hi paper e exend he Regre [14] yem o incorporae ocial neork in he repuaion model. In Secion 2 e inroduce he noion of ocial neork analyi and i applicaion o agen communiie. In Secion 3, a cenario i preened ha ill be ued in he re of he paper o ilurae ho he yem ork. Secion 4 8 decribe he yem in deail. Finally ecion 9 and 10 preen he relaed ork, concluion and fuure ork. 2. SOCIAL NETWORK ANALYSIS AND AGENT SOCIETIES Social neork analyi i he udy of ocial relaionhip beeen individual in a ociey. Social neork analyi emerged a a e of mehod for he analyi of ocial rucure, mehod ha pecifically allo an inveigaion of he relaional apec of hee rucure. The ue of hee mehod, herefore, depend on he availabiliy of relaional raher han aribue daa [16]. Relaional daa i repreened uing graph called ociogram. A differen ociogram i uually buil for each ocial relaion under udy. Depending on he ype of relaion e have a direced or non-direced ociogram, ih eighed edge or ihou. Obviouly, he more relaional daa he beer he neork analyi i. Hoever, hee daa can be difficul o obain. Sociologi uually obain hem hrough publicopinion poll and inervie ih he individual. Thi procedure i, of coure, no poible in agen ocieie. Moreover, he analyi of human ocial rucure i uually done by a ociologi exernal o he ociey. Thi exernal poiion give he analy a privileged achoer o make hi analyi. In our cae, a e an o ue ocial analyi a par of he repuaion yem o be included in each agen, each agen ha o do hi analyi from i on perpecive. I i beyond he cope of hi paper o propoe oluion abou he ay an agen build uch ociogram. From no on, e ill aume ha he agen on a e of ociogram ha ho he ocial relaion in i environmen. Thi ociogram are no necearily complee or accurae. We uppoe hey are buil by each agen uing he knoledge i ha abou he environmen. Therefore, ociogram are dynamic and agen dependen.

2 3. RUNNING EXAMPLE The cenario for hi running example i a markeplace. To implify, he buyer buy one produc a a ime (i i no poible o buy in bulk) and he elemen ha are aken ino accoun for each ranacion are price, qualiy and delivery dae. The buyer chooe a eller. If he eller an o deal ih ha buyer, hen i end an offer. The buyer ha hen o decide if he an o accep he offer or no. If he buyer accep, he ranacion i performed. I i imporan o noe ha he acual reul of he ranacion may no necearily be equal o he iniial offer from he eller. A indler eller can increae he price, decreae he qualiy or deliver he produc lae. On he oher hand, he buyer can decide o pay le or even no o pay a all. We conider ha he proce of obaining he acual reul of he ranacion i aomic, ha i, he buyer and he eller have o decide heir raegy (o pay le, o overcharge he price, do hing exacly a pecified in he offer, ec.) before knoing he behaviour of he oher. Alhough hi aumpion i no very realiic, i make he example impler and allo u o focu our aenion only on repuaion. We can idenify many ype of relaionhip beeen agen in an e-commerce environmen and i i beyond he cope of hi paper o preen a urvey on all of hem. We ill refer ju o a e of relaion ha can be found in our cenario and ha ill help he reader o go hrough he explanaion of he yem. We aume ha in our cenario he grea majoriy of agen are raional and have a behaviour according o heir goal and affiliaion (in an environmen ih random or conradicory agen i make lile ene o ue ocial relaionhip o predic he behaviour of agen). We noe a nondireced relaion of ype rel beeen o agen a and b a rel(a, b). The hree relaion ype ha e conider o illurae hi cenario are: 1) Compeiion (comp). Thi i he ype of relaion found beeen o agen ha purue he ame goal and need he ame (uually carce) reource. In hi iuaion, agen end o ue all he available mechanim o ake ome advanage over heir compeior, for inance hiding informaion or lying. In our running example hi i he kind of relaion ha could appear beeen o eller ha ell he ame produc or beeen o buyer ha need he ame produc. 2) Cooperaion (coop). Thi relaion implie ignifican exchange of incere informaion beeen he agen and ome kind of predipoiion o help each oher if poible. Noice ha e alk abou incere informaion inead of rue informaion becaue he agen ho give he informaion believe i i rue. To implify, e conider ha o agen canno have a he ame ime a compeiive and a cooperaive relaion. 3) Trade (rd). Thi ype of relaion reflec he exience of commercial ranacion beeen o agen and i compaible eiher ih cooperaive or compeiive relaion. A e aid before, each agen on a ociogram for each of hee relaion ype. The hree ociogram are non-direced graph ih eighed edge. Weigh go from 0 o 1 and reflec he ineniy of he relaion. In our cenario, he variable ha appear in conrac beeen buyer and eller (price, qualiy and delivery dae) deermine he repuaion ype. To illurae he model, e conider four repuaion ype for he eller: o overcharge: A high repuaion value of hi ype mean ha he eller end o overcharge he price pecified in conrac. o deliver lae: A he name ugge, i he repuaion of delivering he produc laer han he delivery dae pecified in he conrac. qualiy indler: A eller ih a repuaion o deliver produc ih le qualiy han pecified in he conrac. indler: A indler i a eller ha overcharge he price and/or deliver produc ih a qualiy loer han he qualiy pecified in he conrac. For he buyer e illurae he model ih he ype: defauler: A high repuaion of hi ype mean ha he buyer doe no pay for he produc he buy. 4. THE REGRET SYSTEM The Regre yem rucure i baed on ha e call he hree dimenion of repuaion. If an individual i conidering only i direc ineracion ih he oher member of he ociey o eablih repuaion e ay ha he agen i uing he individual dimenion. If he individual alo ue he informaion coming from oher member of he ociey and he ocial relaion, e are alking abou he ocial dimenion. Finally, e conider ha he repuaion of an individual i no a ingle and abrac concep bu raher a muli-face concep. For example, he repuaion of being a good carrier ummarize he repuaion of having good plane, he repuaion of never loing luggage and he repuaion of erving good food. The differen ype of repuaion and ho hey are combined o obain ne ype i he bae of he hird dimenion of repuaion, he onological dimenion. In he folloing ecion e explain in deail each one of hee dimenion. In ecion 8 e ho ho hee dimenion are combined o obain a ingle value for he repuaion. Alhough repuaion alo have a emporal apec (he repuaion value of an agen varie along ime), e ill omi he reference o ime in he noaion in order o make i more readable. We ill refer o he agen ha i calculaing a repuaion a a (ha e call he ource agen ) and he agen ha i he objec of hi calculaion a b (ha e call he arge agen ). 5. INDIVIDUAL DIMENSION We define he oucome of a dialogue beeen o agen a: An iniial conrac o ake a paricular coure of acion and he acual reul of he acion aken. An iniial conrac o fix he erm and condiion of a ranacion and he acual value of he erm of he ranacion. An oucome i repreened a a uple of he form o = (a, b, I, X c, X, ) here a and b are he agen implied in he conrac, I a e of indexe ha idenify he iue of he conrac, X c and X o vecor ih he agreed value of he conrac and he acual value afer i fulfillmen repecively, and he ime hen he conrac a igned. We ue a ubindex i I o refer o he pecific value of iue i in vecor X c and X. For inance, in he example e have I = {P rice, Delivery Dae, Qualiy}. If e an o make reference o he P rice value in he vecor X c e ue he noaion X c P rice.

3 oj ODB i defined a he e of all poible oucome. ODB a,b ODB i he e of oucome ha agen a ha igned ih agen b. We define ODB a,b {i 1,,i n} ODBa,b a he e of oucome ha have {i 1,, i n} a iue in he conrac. For example, ODB a,b {P rice} i he e of oucome ha ha agen a from previou ineracion ih agen b and ha fix, a lea, he value for he iue P rice. The individual dimenion model he direc ineracion beeen o agen. The repuaion ha ake ino accoun hi dimenion i he mo reliable. Thi i becaue i ake ino accoun all he peculiariie of he arge agen. We call oucome repuaion (noed a R O (ϕ) here ϕ i he a b repuaion ype) he repuaion calculaed direcly from an agen oucome daabae. The ube of iue of an oucome aken ino accoun o calculae a given repuaion ype ϕ i domain dependen. We define a grounding relaion (gr) a he relaion ha link a repuaion ype ϕ ih a li of iue. Thi e of iue allo u o elec he righ ube of oucome from he general oucome daa bae. Each iue i a uple ih he form (I i, {+, }, α i). The fir parameer (I i) i a label ha idenifie he iue. The econd parameer ({+, }) indicae ho an incremen of he value of he iue affec he repuaion, ha i, a + mean ha if he value of he iue increae, he repuaion alo increae hile a mean ha if he value of he iue increae, he repuaion decreae. Finally, he la parameer i he eigh ha ha iue ha in he general calculaion of he repuaion. A an example, he grounding relaion for a eller in our cenario i defined in he folloing able: ϕ gr(ϕ) o overcharge {(P rice, +, 1)} o deliver lae {(Delivery Dae, +, 1)} qualiy indler {(Qualiy,, 1)} Noe ha e only define he grounding relaion for he repuaion ype o overcharge, o deliver lae and qualiy indler. The repuaion ype indler i a complex repuaion ype calculaed from more baic repuaion a e ill ee in ecion 7. To calculae an oucome repuaion e ue a eighed mean of he oucome evaluaion, giving more relevance o recen oucome. 1 R a O b (ϕ) = ih ρ(, i) = o i ODB a,b gr(ϕ) f( i,) ODBa,b gr(ϕ) ρ(, i ) Imp(o i, gr(ϕ)) f( j,) here i he acual ime and f( i, ) i a ime dependen funcion ha give higher value o value cloer o. A imple example of hi ype of funcion i f( i, ) = i. Imp(o i, gr(ϕ)) i he evaluaion of he oucome o i aking ino accoun he acual value of a concree e of iue, hoe aociaed ih ϕ by he relaion gr. The evaluaion of an oucome o = (a, b, I, X c, X, ) i defined a a funion of he difference beeen he uiliy of he conrac and he uiliy of he fulfillmen of ha conrac: Imp(o, gr(ϕ)) = g(v (X ) V (X c )) 1 There are many pychological udie ha uppor recency a a deerminan facor [11]. here V (X c ) i he uiliy funcion over he vecor of value X c and X i a vecor = build uing he folloing formula: Xi X i if i gr(ϕ) oherie X c i In oher ord, e obain hi vecor from he X c vecor replacing he value pecified in he index gr(ϕ) by he value in he ame poiion in vecor X. Finally, g i a funcion ha model he behaviour of he agen according o he degree of decepion or reard obained afer he analyi of he oucome. An appropiae funcion i: g(x) = in( π 2 x) Uing hi funcion, an agen penalize a decepion in he fulfillmen of a conrac by giving value near 1 hen V (X ) < V (X c ) and value near 1 hen V (X ) > V (X c ). Beide he repuaion value, i i imporan o kno ho reliable i i. There are many elemen ha can be aken ino accoun o calculae ho reliable an oucome repuaion i bu e ill focu on o of hem: he number of oucome ued o calculae he repuaion value and he variabiliy of heir raing value. Thi approach i imilar o ha ued in he Spora yem [18]. The inuiion behind he number of oucome facor (noed a No) i ha an iolaed experience (or a fe of hem) i no enough o make a correc judgemen abou omebody. You need cerain amoun of experience before you can ay ho an agen i. A he number of oucome gro, he reliabiliy degree increae unil i reache a maximum value, ha e call he inimae level of ineracion (im from no on). From a ocial poin of vie, hi age i ha e kno a a cloe relaion. More experience ill no increae he reliabiliy of our opinion from hen on. The nex imple funcion i he one e ue o model hi: No(ODB a,b gr(ϕ) ) = π ODB in a,b gr(ϕ) ODB 2 im 1 oherie a,b gr(ϕ) im We believe ha he im value i domain dependen: i depend on he ineracion frequency of he individual in ha ociey. The oucome repuaion deviaion (noed a D) i he oher facor ha our yem ake ino accoun o deermine he reliabiliy of an oucome repuaion. The greaer he variabiliy in he raing value he more volaile ill he oher agen be in he fulfillmen of heir agreemen. To have a meaure of hi variabiliy e ake ino accoun he impac on he expeced uiliy of he acual execuion of he conrac. We calculae he oucome repuaion deviaion a: D(ODB a,b gr(ϕ) ) = ρ(, i ) Imp(o i, gr(ϕ)) R O (ϕ) a b o i Where o i ODB a,b gr(ϕ). Thi value goe from 0 o 1. A deviaion value near 1 indicae a high variabiliy in he raing value (ha i, a lo credibiliy of he repuaion value from he oucome repuaion deviaion poin of vie) hile a value cloe o 0 indicae a lo variabiliy (ha i, a high credibiliy of he repuaion value).

4 Finally, e define he reliabiliy of an oucome repuaion a a convex combinaion of he funcion No and he oucome evaluaion raing deviaion D. RL O (ϕ) = (1 µ) No(ODB a,b ) + µ (1 D(ODBa,b a b gr(ϕ) gr(ϕ) )) 6. SOCIAL DIMENSION Alhough direc ineracion i he mo reliable ource of informaion, unforunaely i i no alay available. No only becaue he agen can be a necomer o a ociey bu alo becaue he ociey can be very large. Therefore, hen he ineracion ih anoher agen are carce i i no poible o aign i a repuaion baed ju on direc experience. I i in hee iuaion hen he ocial dimenion of an agen may help by uing informaion coming from oher agen. In he Regre yem e ue hree ype of ocial repuaion depending on he informaion ource: Wine Repuaion. Baed on he informaion abou he arge agen coming from oher agen. We noe hi repuaion a: R W (ϕ) a b Neighbourhood Repuaion. Ue he ocial environmen of he arge agen, ha i, he neighbour of he arge agen and heir relaion ih i. Noed a: R N (ϕ) a b Syem Repuaion. I i a defaul repuaion value baed on he role played by he arge agen. Noed a: R S (ϕ) a b Each one of hee repuaion require a differen degree of knoledge of he agen ociey and he arge agen. The Syem Repuaion i he eaie o calculae. We are auming ha he role an agen i playing i alay viible informaion ha i available o all he agen in he ociey. Hoever, he role alone doe no convey enough informaion o compue a repuaion on all imaginable apec. Alo, he reliabiliy of hi ype of repuaion end o be lo becaue i doen ake ino accoun he peculiariie of he individual and i environmen. Thi i he kind of repuaion ha an agen can ue hen i i a necomer and here i an imporan lack of ineracion ih he oher agen in he ociey. The Wine Repuaion and he Neighbourhood Repuaion, on he oher hand, demand from he agen a moderae o hard knoledge of he ocial relaion in he agen communiy. Sociologically peaking, hi diviion i far o be complee. Hoever, e conider ha ih hee hree ype e mainain a good compromie beeen he complexiy of he model and he requiremen ha an agen can have in an e- commerce environmen. We explain belo ho o calculae hee repuaion value. 6.1 Wine repuaion Belief abou he repuaion of oher can be hared and communicaed by he member of a ociey. The repuaion ha an agen build on anoher agen baed on he belief gahered from ociey member (inee) i ha e call ine repuaion. In an ideal orld, ih only homogeneou and rued agen, hi informaion i a relevan a he direc informaion. Hoever, in he kind of cenario e are conidering, i may happen ha: The informaion i fale. Eiher becaue he oher agen are rying o lie or becaue he informaion hey on i no accurae, an agen ha o be prepared o deal ih fale informaion. Agen hide informaion. An agen canno aume ha he informaion i complee. Beide ha, he informaion ha come from oher agen can be correlaed (ha i called he correlaed evidence problem [13]). Thi happen hen he opinion of differen inee are baed on he ame even() or hen here i a coniderable amoun of hared informaion ha end o unify he inee ay of hinking. In boh cae, he ru on he informaion houldn be a high a he number of imilar opinion may ugge. Becaue he even() ha have generaed he opinion for each agen may be hidden, he agen canno idenify direcly hich agen are correlaed. Schillo e. al [15] propoe a mehod baed on he analyi of lying a a ochaic proce o implicily reconruc ine obervaion in order o alleviae hi problem. We ake a differen approach baed on he ocial relaion beeen agen. Analying hee relaion, an agen can obain ueful informaion o minimize he effec of he correlaed evidence problem. We aume ha he informaion o be exchanged beeen agen i a uple here he fir elemen i he repuaion value of he arge agen from he poin of vie of he ine, and he econd elemen i a value ha reflec ho confiden he ine i abou he repuaion value. A e aid before, he ine can give rong value or imply can decide no o give i opinion even if he ha enough informaion o do o. We ill noe he uple a R c b (ϕ), RL c b (ϕ), here c i he agen giving he informaion o a Idenifying he inee The fir ep o calculae a ine repuaion i o idenify he e of inee (W). The iniial e of poenial inee migh be he e of all agen ha have ineraced ih he arge agen in he pa. In he example, he iniial e i compoed by all he agen ha had had a rade relaion ih he arge (i eem logical o hink ha he be inee abou he commercial behaviour of he arge agen are hoe agen ha had a rade relaion ih i before). Thi e, hoever, can be very big and i member probably uffer from he correlaed evidence problem. We ake he ance ha grouping agen ih frequen ineracion among hem and conidering each one of hee group a a ingle ource of repuaion value minimize he correlaed evidence problem. Moreover, auming ha aking for informaion ha a co, i ha no ene o ak he ame hing o agen ha e expec ill give u more or le he ame informaion. Grouping agen and aking for informaion o he mo repreenaive agen ihin each group reduce he number of querie o be done. A domain dependen ociogram i ha Regre ue o build hee group and o decide ho i heir mo repreenaive agen (in our example he ociogram of he cooperaive relaion). There are many heuriic ha can be ued o find group and o elec he be agen o ak. In he Regre yem e ue a heuriic baed on he ork by Hage and Harary [9]. Taking he ube of he eleced ociogram over he agen ha had had ineracion ih he arge agen a he iniial graph, he heuriic ha Regre follo i: 1. To idenify he componen of he graph. A componen i defined a a maximally conneced ubgraph. 2. To find he e of cu-poin (CP ) for each componen. A cu-poin i a node hoe removal ould increae he

5 b a componen g c cenral poin i i cu-poin h e d f j CP = {b,d} LCP = {h} W = {b,d,h} compeiive relaion cooperaive relaion - ine - arge agen - ource agen Figure 1: Wine elecion ihin Regre. Figure 2: Relevan ocial rucure in he example. number of componen by dividing he ub-graph ino o or more eparae ub-graph among hich here are no connecion. A cu-poin can be een from a ociological poin of vie a indicaing ome kind of local cenraliy. Cu-poin are pivoal poin of ariculaion beeen he agen ha make up a componen [16]. 3. For each componen ha doe no have cu-poin, o chooe a a repreenaive for ha componen he node ih he larger degree. If here i more han one node ih he maximum degree, chooe one randomly. Thi poin i called a cenral poin. The degree can be regarded alo a a meaure of local cenraliy [16]. We refer o hi e of node a LCP. 4. The e of eleced node i he union beeen he e of cu-poin and he e of LCP. Tha i, W = CP LCP. Figure 1 ho an example of he applicaion of he heuriic. A hi poin, he agen ha o ak for informaion o all he agen in he o calculaed e of inee W Who can I ru? Once he informaion i gahered e obain { R i b(ϕ), RL i b(ϕ) i W W} here W i he ube of agen ha anered a query. The nex ep i o aggregae hee value o obain a ingle value for he Wine Repuaion. Hoever, a e aid before, i i poible ha hi informaion be fale o he agen ha o be careful o give he righ degree of imporance and reliabiliy o each piece of informaion. The degree of imporance relie on he ru ha each ine ha. The yem ue o differen mehod o calculae hi ru: ocial ru and oucome ru repuaion. We define ocialt ru(a, i, b) a he ru degree ha agen a aign o i hen i i giving informaion abou b and aking ino accoun he ocial relaion among a, i and b. Regre ue fuzzy rule [19] o deermine ho a ocial rucure provide a reliabiliy degree on he informaion coming from a given agen in ha rucure. The aneceden of each rule i he ype and degree of a ocial relaion and he conequen i he reliabiliy of he informaion from he poin of vie of ha ocial relaion. In our cenario, a poible rule ould be: lo (l) moderae (m) high (h) Figure 3: Ineniy of a ocial relaion. IF coop( i, b) i high THEN ocialtru(a, i, b) i very bad ha i, if he level of cooperaion beeen i and b i high hen he ru from he poin of vie of a on he informaion coming from i relaed o b i very bad. The heuriic behind hi rule i ha a cooperaive relaion implie ome degree of compliciy beeen he agen ha hare hi relaion o he informaion coming from one abou he oher i probably biaed. From he e of ocial relaion in our cenario, only he cooperaive relaion and he compeiive relaion are relevan o calculae a meaure of reliabiliy. Which relaion are relevan o calculae he reliabiliy depend on he meaning ha each relaion ha in he pecific agen ociey. In our cenario, for inance, a rade relaion canno ca any ligh on he reliabiliy of an agen from he poin of vie of ocial analyi. In oher ocieie, hoever, hi could be he oher ay around. Hence, ogeher ih he no relaion poibiliy and ih he fac ha he mo relevan link are beeen he ine and he agen and he ine and he arge, here are 9 ocial rucure o be conidered a hon in Figure 2. Figure 3 conain he fuzzy e value -defined over he ineniy label on he arc in he ociogram- for he variable coop( i, a), coop( i, b), comp( i, a), and comp( i, b), imilarly e can define he fuzzy e value for he variable ocialtru(a, i, b). Alhough a hi momen he kind of influence of each ocial rucure i aic and baed in human common ene, e plan o improve he yem ih a rule learning mechanim. A econd ay o calculae he degree of ru of an agen i uing he oucome ru repuaion of he ru ha oher agen deerve, ha i, R a O b (ru). The oucome ru repuaion i calculaed like any oher oucome repuaion (ee ecion 5). In our running example he grounding relaion

6 n for hi repuaion ype could be: ϕ gr(ϕ) ru {(P rice,, 0.3), (Qualiy, +, 0.4), (Delivery Dae,, 0.3)} Tha i, an agen ha repec he price, he qualiy and he delivery dae of a conrac i a ruy agen. We could alo ake he informaion coming from a ine ino accoun a ell a ho accurae are hee informaion. Thi could become he e of oucome ued o calculae he oucome ru repuaion for ha ine. The ru value calculaed uing an oucome ru repuaion are more ueful han hoe baed on ocial relaion (ocialtru) becaue an oucome ru repuaion i baed on he individual experience and hu ake ino accoun i pariculariie hile he analyi of ocial rucure rely on global expeced behaviour. Hoever, in hoe iuaion here here i no enough informaion o calculae a reliable oucome ru repuaion, he analyi of ocial relaion can be a good oluion. Uually, ocial relaion are eaier o obain han a e of oucome (neceary o calculae an oucome ru repuaion) epecially if he agen ha ju arrived o a ne cenario. Given ha, e define a ru degree for an agen i hen i i giving informaion abou b a: ru(a, i, b) = RL a O i (ru) R a O i (ru) + (1 RL a O i (ru)) ocialt ru(a, i, b) Tha i, he agen ue he ru repuaion baed on direc ineracion if i i reliable, if no, i ue he ocial ru. No e have all he neceary ool o calculae he ine repuaion and i reliabiliy conidering ha he informaion coming from he inee can be fale. The formulae e propoe o calculae hee value are: R W (ϕ) = ω ib R i a b b(ϕ) i W RL W (ϕ) = ω ib min(ru(a, i, b), RL i a b b(ϕ)) i W ru(a, i,b) here ω ib = j W ru(a, j,b) Thee formulae require ome explanaion. To calculae he ine repuaion he agen ue he normalized ru of he ine o eigh each opinion in he final value. For he calculaion of he reliabiliy, e an ha in he final value, he conribuion of each individual reliabiliy be in he ame proporion ha i relaed repuaion. Therefore, he agen ue he ame eigh in he reliabiliy formula a in he repuaion formula. Finally o calculae he reliabiliy of an individual repuaion, he agen ue he minimum beeen he ru of he ine ha en he repuaion and he reliabiliy ha he ine himelf give o ha repuaion. We ue hi mehod o model he idea ha if he ine i a ruy agen, hen e can ue hi/her on meaure of reliabiliy for he repuaion, if no, e canno rely on hi/her informaion and e have o calculae our on meaure of ruorhine for ha repuaion baed on he oucome and he ocial relaion of ha ine. 6.2 Neighbourhood repuaion The repuaion of he individual ha are in he neighbourhood of he arge agen and heir relaion ih him are he elemen ued o calculae ha e call he Neighbourhood Repuaion. Neighbourhood in a MAS i no relaed ih he phyical locaion of he agen bu ih he link creaed hrough ineracion. The main idea i ha he behaviour of hee neighbour and he kind of relaion hey have ih he arge agen can give ome clue abou i poible behaviour. The e of neighbour of an agen b i noed a N b = {n 1, n 2,, n n}. To calculae a Neighbourhood Repuaion e ue fuzzy rule a ell. Thee rule, ha are domain dependen, relae he oucome repuaion of a arge neighbour and he ocial relaion hey have, ih a repuaion of he arge agen. The applicaion of hee rule generae a e of individual neighbourhood repuaion noed a R n i (ϕ). For inance, a b uing again our running example, one rule could i) be: IF R a ni (indler) i X AND coop(b, n lo THEN R n i a (indler) i X b IF RL a ni (indler) i X AND coop(b, n i) i Y THEN RL n i (indler) i T(X, Y ) a b In oher ord, e are aying ha if he neighbour of he arge agen i a indler and here i a relaion of cooperaion beeen he arge and hi neighbour, hen he arge i alo (aummed o be) a indler. Finally able 1 ho a poible e of value for funcion T. X Y l m h vl vl vl vl l vl vl l m vl l m h l m h vh m h vh Table 1: Funcion T ued in reliabiliy rule. The general formulae e ue o calculae a neighbourhood repuaion and i reliabiliy are: R N (ϕ) = ω n ib a b n i R n (ϕ) i a b N b RL N (ϕ) = ω n ib RL n (ϕ) i a b a b n i N b here ω n ib = RL n (ϕ) i a b j N RL n b j (ϕ) a b In hi cae e are uing he reliabiliy of each individual neighbourhood repuaion o eigh he conribuion o he final reul, boh for he repuaion and for he reliabiliy. 6.3 Syem repuaion The idea behind Syem repuaion i o ue he common knoledge abou iniuional rucure and he role ha he agen i playing for ha iniuional rucure a a mechanim o aign defaul repuaion o he agen. An iniuional rucure i a ocial rucure he member of hich have one or everal obervable feaure ha unambiguouly idenify hem a member of ha ocial rucure. The fac ha here are obervable feaure o idenify i member i ha differeniae an iniuional rucure from oher ocial rucure. Example of iniuional

7 rucure in human ocieie are he police, a company, a club, or a family. We aume ha he role ha an agen i playing and he iniuional rucure i belong o i omehing viible and ruorhy for each agen. Each ime an agen perform an acion e conider ha i i playing a ingle role ihin he iniuional rucure. An agen can play he role of buyer and eller bu hen i i elling a produc only he role of eller i relevan. Alhough e can hink up ome iuaion here an agen can play o or more differen role a a ime, e conider ha here i alay a predominan role o he oher can be diregarded. In Regre he repuaion aociaed o each role ihin an iniuional rucure are domain dependen and par of he iniial knoledge of he agen. The value for hee repuaion can be differen depending on hich iniuional rucure he agen belong o. Thi model he idea ha group (in our cae iniuional rucure) influence he poin of vie of heir member [11]. Anoher imporan poin i ha an iniuional rucure doe no alay aociae a repuaion value o each conrac iue. Syem repuaion are calculaed uing a able for each iniuional rucure here he ro are he poible role, and he column he repuaion ype ha canno be ubdivided in more pecialized repuaion ype (ee ecion 7). Table 2 ho an example of yem repuaion for agen ha belong o company B from he poin of vie of an agen of company A. A you noice, in hi cae he opinion of company A oard agen in company B i no very good. defauler o overcharge o deliver lae qualiy indler eller buyer Table 2: Example of yem repuaion. Uing a imilar able e ould define he reliabiliy for hee repuaion. Syem repuaion are noed a R S (ϕ) and i reliabiliy a RL S (ϕ). Hence, for example, uing he able a b defined above, e have ha R S (defauler) = 0.7 here a b b i a eller ha belong o company B. Given ha hi a b i a defaul value for repuaion ued hen oher informaion ource are miing, he reliabiliy ha o be necearily moderaely lo. 7. ONTOLOGICAL DIMENSION Along he individual and ocial dimenion, repuaion i alay linked o a ingle behavioural apec (a conrac iue). Wih he onological dimenion e add he poibiliy of combining repuaion on differen apec o calculae complex repuaion. To repreen he onological dimenion e ue graph rucure. Figure 4 ho an onological dimenion for a eller in he running example. In hi cae, he repuaion of being a indler i relaed ih he repuaion of overcharging price and he repuaion of delivering produc ih le qualiy han pecified in he conrac. For he oner of hi onological rucure, he delivery dae i omehing ha i no relevan o be conidered a indler. Hence, o calculae a given repuaion aking ino accoun he onological dimenion, an agen ha o calculae he repuaion of each of he relaed apec ha, in urn, can be he node of anoher ubgraph ih oher aociaed apec. The repuaion of hoe node ha are relaed o_deliver_lae 0.6 o_overcharge indler 0.4 qualiy_indler Figure 4: Onological rucure for a eller. ih an aomic apec of he behaviour (in he example: o deliver lae, o overcharge and qualiy indler), are calculaed uing he individual and ocial dimenion. The repuaion of an inernal node ψ in an onological graph i compued a follo (he compuaion of leave remain a preened before): R a b (ϕ) = RL a b (ϕ) = ψ children(ϕ) ψ children(ϕ) ω ϕψ R a b (ψ) ω ϕψ RL a b (ψ) For inance, uing he onological rucure in figure 4 e can calculae he repuaion of b a a indler from a perpecive uing he formula: R a b (indler) = 0.6 R a b (o overcharge) R a b (qualiy indler) Noe ha he imporance (ω ϕψ ) of each apec i agen dependen and no necearily aic. The agen can change hee value according o i menal ae. 8. PUTTING IT ALL TOGETHER: THE REGRET SYSTEM. The Regre yem i an experimenaion ool here he repuaion of he paricipaing agen i modeled aking ino accoun all he apec menioned in hi paper. In paricular i define a repuaion meaure (and i reliabiliy) ha ake ino accoun he individual dimenion, he ocial dimenion and he onological dimenion a: R a b (ϕ) = RL a b (ϕ) = ξ i R i (ϕ) a b i {O,W,N,S} if ϕ i a leaf ω ϕψ R a b (ψ) Oherie ψ children(ϕ) ξ i RL i (ϕ) if ϕ i a leaf a b i {O,W,N,S} ω ϕψ RL a b (ψ) Oherie ψ children(ϕ) A e have argued, he mo reliable repuaion i he oucome repuaion folloed by he ine and he neighbourhood repuaion and finally by he yem repuaion. Therefore, e an he agen o give more relevance o he oucome repuaion in derimen of he oher. If he oucome repuaion ha a lo degree of reliabiliy (for inance becaue he agen doe no have enough informaion) hen he agen ill ry o ue he ine and he neighbourhood repuaion. Finally, if i knoledge of he ocial relaionhip i hor, he agen ill ry o ue he yem repuaion. Given ha, he facor {ξ I, ξ W, ξ N, ξ S} in he general formulae are:

8 ξ I = RL a O b (ϕ) ξ W = RL a W b (ϕ) (1 ξ I )/2 ξ N = RL a N b (ϕ) (1 ξ I )/2 ξ S = 1 (ξ I + ξ W + ξ N ) 9. RELATED WORK The idea of uing he opinion of oher agen o build a repuaion i no ne. The ork of Michael Schillo, Pera Funk and Michael Rovao [15] and he ork of Bin Yu and Munindar P. Singh [17] are good example of hi. In boh cae hey ue a ru-ne for eighing he oher agen opinion. Our rucure o calculae he ine repuaion can be conidered alo a ru-ne. In our cae, hoever, beide he previou experience ih he inee e alo conider he informaion abou he agen ocial relaion. The model propoed by Yu and Singh [17] merge informaion ha come from agen ha have good repuaion. Schillo e al [15] conider ha he ame agen ha can provide you ih informaion are alo compeing ih you. Alhough agen are aumed o never lie, hey can hide informaion or bia i o favour heir goal. We go one ep furher and conider ha he agen can alo lie. In elecronic markeplace, he repuaion ha a uer ha i he reul of aggregaing all he experience of he oher uer ha ineraced ih him/her in he pa. Amazon Aucion [1] and ebay [2] for inance, are online aucion houe here uer buy and ell good. Each ime a ne ranacion i finihed, he buyer rae he eller. Thee raing are ued o build he repuaion of a eller. Spora [18] i an evolved verion of hi kind of repuaion model. Spora inroduce he noion of reliabiliy of he repuaion and i more robu o change in he behaviour of a uer han repuaion yem like Amazon Aucion, baed on he average of all he raing given o he uer. In all hee yem each uer ha a global repuaion hared by all he oberver inead of having a repuaion biaed by each oberver. Hio [18], alo oriened o elecronic commerce, i a more peronalized repuaion yem here repuaion depend on ho make he query, and ho ha peron raed oher uer in he online communiy. Finally, e ould like o re ha unlike Regre, all he previou model conider repuaion a a ingle concep inead of a muli-face concep. 10. CONCLUSIONS AND FUTURE WORK In hi paper e have preened ho ocial neork analyi can be ued in a repuaion yem ha ake ino accoun he ocial dimenion of repuaion. The yem ha alo a hierarchical onology rucure ha allo o conider everal ype of repuaion a he ame ime. The combinaion of complemenary mehod ha ue differen apec of he ineracion and ocial relaion, allo he agen o calculae repuaion value a differen age of i knoledge of he ociey. The ue of he ocial neork analyi echnique a par of a repuaion yem open a ne field for experimenaion. Our fir objecive i o validae he yem in a realiic e-commerce environmen here ocial relaion are an imporan facor. To be able o exploi all he capabiliie of he Regre yem e need environmen more ophiicaed han he acual e-marke like Amazon Aucion or ebay. We are orking in everal ool ha allo he pecificaion and implemenaion of hee kind of e-marke. Once you inroduce he ocial dimenion in repuaion yem and he agen ar o ake ino accoun ocial relaion, i become more and more imporan o conider no only hich i he repuaion of he oher agen, bu ha can an agen do o ge and mainain a good repuaion. Uing he Regre yem, e an o udy repuaion from hi ne perpecive. Finally, i i imporan o udy mechanim ha allo agen o build and mainain ociogram. 11. ACKNOWLEDGMENTS Thi ork ha been uppored by he European projec SLIE, IST , and he Spanih MCYT projec e- INSTITUTOR, MCYT REFERENCES [1] Amazon Aucion. hp://aucion.amazon.com. [2] ebay. hp://.ebay.com. [3] A. Abdul-Rahman and S. Haile. Supporing ru in virual communiie. In Proceeding of he Haaii In. Conference on Syem Science, Maui, Haaii, [4] D.B. Bromley. Repuaion, Image and Impreion Managemen. John Wiley & Son, [5] V. Buken. The ocial rucure of ru. Social Neork, (20): , [6] C. Caelfranchi and R. Falcone. Principle of ru for ma: Cogniive anaomy, ocial imporance, and quanificaion. In Proceeding of he 3h Inernaional Conference on Muli-Agen Syem, page 72 79, [7] M. Celenani, D. Fudenberg, D.K. Levine, and W. Pendorfer. Mainaining a repuaion again a long-lived opponen. Economerica, 64(3): , [8] P. Dagupa. Tru a a commodiy. In D. Gambea, edior, Tru: Making and Breaking Cooperaive Relaion, page Blackell, [9] P. Hage and F. Harary. Srucural Model in Anhropology. Cambridge Univeriy Pre, [10] P. Hage and F. Harary. Iland Neork. Cambridge Univeriy Pre, [11] M. Karlin and H. Abelon. Peruaion, ho opinion and aiude are changed. Croby Lockood & Son, [12] R. Marimon, J.P. Nicolini, and P. Tele. Compeiion and repuaion. In Proceeding of he World Conference Economeric Sociey, Seale, [13] J. Pearl. Probabiliic Reaoning in Inelligen Syem: Neork of Plauible Inference. Morgan Kaufmann, [14] J. Sabaer and C. Sierra. Regre: A repuaion model for gregariou ocieie. In Proceeding of he Fourh Workhop on Decepion, Fraud and Tru in Agen Socieie, Monreal, Canada, page 61 69, [15] M. Schillo, P. Funk, and M. Rovao. Uing ru for deecing deceiful agen in arificial ocieie. In Applied Arificial Inelligence, Special Iue on Tru, Decepion and Fraud in Agen Socieie, [16] J. Sco. Social Neork Analyi. SAGE Publicaion, [17] Bin Yu and M.P. Singh. A ocial mechanim of repuaion managemen in elecronic communiie. In Cooperaive Informaion Agen, CIA-2000, Boon, MA, USA, page , [18] G. Zacharia. Collaboraive repuaion mechanim for online communiie. Maer hei, Maachue Iniue of Technology, Sepember [19] L.A. Zadeh. Fuzzy logic and approximae reaoning. Synhee, 30: , 1975.