Towards Incentive-Compatible Reputation Management

Transcription

1 Towards Incenive-Compaible Repuaion Managemen Radu Jurca, Boi Falings Arificial Inelligence Laboraory Swiss Federal Insiue of Technology (EPFL) IN-Ecublens, 115 Lausanne, Swizerland INTRODUCTION Sofware agens are a new and promising paradigm for open, disribued informaion sysems. However, besides he many pracical soluions his new paradigm provides, i also brings along a whole new se of unsolved quesions. One of he issues ha has araced a lo of aenion laely is securiy. Tradiional, cenralized approaches of securiy do no longer cope wih he challenges arising from an open environmen wih disribued ownership in which agens iner-operae. [McK1, Kag1, Kag] We focus in paricular on he problem of rus, i.e. deciding wheher anoher agen encounered in he nework can be rused, for example in a business ransacion. In closed environmens, rus is usually managed by auhenicaion schemes ha define wha agens are o be rused for a paricular ransacion. In an open environmen, fixed classificaions mus be replaced by dynamic decisions. One imporan facor in such decisions is an agen s repuaion, defined as informaion abou is pas behavior. The mos reliable repuaion informaion can be derived from an agen s own experience. However, much more daa becomes available when repuaion informaion is shared among an agen communiy. Such mechanisms have been proposed and also pracically implemened. The various raing services on he inerne are examples of such mechanisms. I is however no a all clear ha i is in he bes ineres of an agen o ruhfully repor repuaion informaion: by reporing any repuaion informaion, i provides a compeiive advanage o ohers, so i is no in is ineres o repor anyhing a all. by reporing posiive raings, he agen slighly decreases is own repuaion wih respec o he average of oher agens, so i is a disadvanage o repor hem ruhfully. by reporing fake negaive raings, he agen can increase is own repuaion wih respec o ohers, so i is an advanage o repor hem falsely. Thus, i is ineresing o consider how o make a repuaion mechanism incenive-compaible, i.e. how o ensure ha i is in he bes ineres of a raional agen o acually repor repuaion informaion ruhfully. This is he problem we address in his research. AN EXAMPLE OF AN INCENTIVE-COMPATIBLE MECHANISM As he firs sep in our research, we have consruced an example of a repuaion sharing mechanism ha is indeed incenive-compaible, hus showing ha such a mechanism is possible. From he consideraions given above, i is clear ha an incenive-compaible mechanism should inroduce side paymens ha make i raional

2 for agens o ruhfully share repuaion informaion. In our mechanism, hese side paymens are organized hrough a se of broker agens, called R-agens, ha buy and sell repuaion informaion. We assume ha no oher side paymens occur beween any agens in he sysem. As a firs sep, we show a mechanism which is incenive-compaible for a cerain scenario under he condiion ha all oher agens behave raionally, i.e. also repor he ruh. The problem of iniializaion is no sudied for now, bu raher, once ha he sysem sared, and assuming ha in he sysem here is a majoriy of agens reporing he ruh, we focus on a mechanism ha also makes i in he bes ineres of agens o share informaion ruhfully. The scenario is he following. We assume we have n agens: a i for i = 1..N, ha inerac pairwise in an ieraed Prisoner s Dilemma environmen. In each round, wo agens ogeher inves I unis of money in an idealized business ha pays of f(i) unis wih cerainy, where f is some funcion. The agens can cooperae, and each inves an equal amoun of money (I/), or can chea and no inves anyhing. A he end of each round he benefis are spli equally beween he wo parners, wheher hey have cheaed or no. Each agen will cooperae wih probabiliy p i,, or defec wih probabiliy 1- p i. Each agen can buy repuaion informaion abou anoher agen from an R-agen a a cos F, and laer sell repuaion informaion o any R-agen a a price C. Repuaion is represened as a single real number in he inerval [.,1.]. Agens repor eiher for a defecion or 1 for cooperaion, and he repuaion r i of an agen a i is compued as he mean of all he repors abou ha agen: k j= repor j ri = 1 ; (1) N where repor j, j=1 k are he k repors ha have been filed for agen a i and can ake he values or 1. In our scenario, agens sysemaically buy repuaion informaion before engaging in business wih anoher agen. Agens are only allowed o sell a repor for an agen when hey have previously bough repuaion informaion for ha agen. To make he repuaion mechanism incenive-compaible, we hen have he following condiions: 1. Agens ha behave as good ciizens, i.e. repor ruhfully he resul of every ineracion wih anoher agen, should no loose any money: E[F] E[C ruhful repor]. Agens ha repor repuaion incorrecly should gradually loose heir money: E[F] E[C false repor] To saisfy hese condiions, we propose he following mechanism. The basic idea is ha R-agens will only pay for repors if hey mach he nex repor filed by anoher agen. In order o prove he raionale behind his rule, suppose ha we consider he repuaion of agen a i and le us compue he probabiliies for he following evens: - agen a i cooperaes in wo consecuive rounds: p i - agen a i defecs wo consecuive rounds: (1-p i ) - agen a i cooperaes hen defecs: p i (1-p i ) - agen a i defecs hen cooperaes: p i (1-p i ) The probabiliy ha agen a i behaves he same way in consecuive rounds is hus:

3 (1-p i ) + p i =1 p i +p i which is bounded by [.5, 1]. On he oher hand, he probabiliy ha agen a i will change is behavior in wo consecuive rounds is: p i (1-p i ) which is bounded by [,.5]. Assuming ha he oher agens will repor he ruh, and ha a i will behave he same way on he nex ineracion, he omal sraegy for an agen is o repor behavior ruhfully, since his means i will be paid wih probabiliy of a leas.5. The remaining quesion is how much agens should be paid. For his, we need o consider ha agens can only file a repor if hey acually did business wih he agen, i.e. if hey rused he agen. Before each business begins, agens assess he rusworhiness of heir parner. The business is done only if boh parners agree. The expeced payoff an agen receives for a repor on anoher agen a i can be compued by analyzing he following siuaions: a) he repuaion of a i is oo low, which means ha no business will be conduced and no repor can be sold. In his case, he payoff is ; b) business is conduced, bu he parner agen changes is behavior in he nex round. Therefore, he agen s reporing will be considered as false. In his case, he payoff is also ; c) business is conduced and he parner agen behaves in he same way in he nex round. The payoff is C in his case; Therefore: E[payoff] = Pr(case a) + Pr(case b) + C Pr(case c) We assume ha an agen russ agen a i, and hus eners ino business wih a i, whenever i expecs i o yield a profi. Therefore q, he probabiliy ha an agen will rus anoher agen, is given as q=prob(ou>), where Ou is he expeced oucome of he business. 1 I Ou = (1 p ) f p f ( I ) I i i + ; () where f(i) is he business payoff funcion for I unis invesed. Assuming a monoone increasing funcion f, he condiion Ou> is equivalen o p i >?, where? is some consan ha depends only on he business payoff funcion f. Therefore, q=pr(p i >?). The probabiliy of conducing business is equal o he probabiliy ha boh agens rus one anoher. Therefore: Pr(case a) = (1- q ); Pr(case b) = q p j (1-p j ); Pr(case c) = q (1-p j +p j ); for differen p j. Because agens are seleced randomly wih uniform probabiliy o play he game, we can compue he mean value for he payoff: E [ payoff ] = C N j= 1 q (1 p j + p ) j ; (3) N There is a unique value for he price F of repuaion informaion ha would make he enire mechanism self-susaining (i.e. R-agens neiher loose nor win any money). The price of repuaion informaion F:

4 F = E[payoff]; (4) However, in a pracical implemenaion we can compue i simply as he moving average of he observed payoffs which mus converge o an equilibrium value given by (4). TESTING SCENARIO In his environmen we propose he inroducing of specialized review agens (R-agens) (he equivalen of professional survey companies) which are no allowed o play he game, bu which have as a goal o obain and sell informaion abou he repuaion of business agens. In he environmen we will have several such agens, so ha here is compeiion beween hem. One business agen will buy repuaion informaion from one R-agen, bu migh ge paid by all he R-agens. Therefore, we will divide he payoff C an agen receives for reporing correc repuaion by he number of R-agens in he sysem, and agens will sell repuaion informaion o all R-agens. In our presen work he fac ha here are more R-agens makes no difference. Business agens randomly selec he R-agen from which hey will buy repuaion. However, in fuure work we will also implemen a direc ineracion derived repuaion model of R-agens. Business agens will be able o develop preferences for R-agens ha correcly provide repuaion informaion. Anoher reason for he presence of more R-agens in he environmen is sysem robusness. We used a linear business payoff funcion in our experimens: f(i)=xi, where x is a coefficien greaer han 1. By uning x we modify he rading pariculariies of he environmen: a small value for x corresponds o harsh rading environmen where i is very imporan o rus your parner, while a big value for x would correspond o a friendly rading environmen, where posiive payoff is more probable, regardless of he parner s cooperaion. An average value for x would correspond o a rading environmen where agens make he decision of wheher or no o conduc business wih heir parners by evaluaing he inequaliy p i >? =.5. By replacing his in (), o obain he corresponding? =.5, we need o se x=1.33. The expeced payoff for filing repuaion repors would depend on he probabiliies p i of all he agens. The fac ha hese probabiliies are unknown can be solved by using for he price F of buying repuaion informaion he moving average of he payoffs obained by he agens for selling repuaion repors. The price F converges o he unique soluion of he equaion (4). EXPERIMENTS The simulaion of he above described environmen shows encouraging resuls. We have used en housand business agens in our environmen, and en R-agens. The firs es was o see wheher he rus model implemened can help he rading beween agens. Figure 1 shows he average wealh of cooperaing and cheaing agens. As i can be seen, he mechanisms implemened help cooperaive agens o successfully deec and isolae cheaing agens.

5 5 Wealh 15 cooperaive 1 cheaing Nr of rounds Figure 1: Average wealh of cooperaive and cheaing agens For our nex experimen, we ried o see if agens have an incenive o use he repuaion informaion in heir business. For ha, we inroduced in our sociey a percen of lonely agens ha do no use he rus model. Figure plos he average wealh of he social agens, who use he rus model, and he average wealh of he lonely agens agains he number of rounds. 3 Wealh Nr of rounds social agens lonely agens Figure : Evoluion of average wealh for lonely and social agens Finally, we were ineresed o see if agens have he incenive o repor rue repuaion. For ha, we inroduced in our environmen 1% of lying agens, i.e. agens ha do no repor he ruh when hey are asked. Figure 3 plos he evoluion of he average wealh for ruhful and lying agens. A more deailed analysis of he sysem s behavior in he presence of lying agens is presened in he following secion. These resuls allow us o believe ha our model can be successfully used for providing he agens wih he incenive o repor rue repuaion informaion. In fuure work we will ry o improve his model and find he combinaion of parameers ha yields he bes resuls. ANALYSIS OF SYSTEM ROBUSTNESS IN THE PRESENCE OF LYING AGENTS In Figure 3 we have seen saisfying resuls for he presence of 1% lying business agens in he sysem. In his secion we will analyze he sysem s behavior as his percenage increases. We will assume consisenly lying agens (i.e. agens ha lie all he ime) adong only one of he following hree differen sraegies: a) lying agens repor he opposie of he observed behavior of he parner b) lying agens always repor negaive repuaion for heir parner

6 c) lying agens give random repors for heir parners. All lying agens lie according o he same sraegy, and hey do no change heir sraegy during he lifeime of he sysem Wealh ruhfull Nr of rounds Figure 3: Evoluion of average wealh for ruhful and lying agens (1%) lying p i p i q q α Le us denoe by: he real repuaion of agen a i (i.e. he number of imes he agen cooperaed divided by he oal number of ineracions he agen had, aka. cooperaion level of he agen); he perceived repuaion of he agen a i as known a ime insance by R-agens. In our sysem, has he meaning of number of proposed businesses; he real percen of cooperaive agens (i.e. he percen of agens whose cooperaion level p i is greaer han a hreshold θ); he percen of perceived cooperaive agens (i.e. he percen of agens whose perceived repuaion p i is greaer han a hreshold θ); he percen of lying agens. Assuming ha p i = 1 (i.e. agens are iniially considered rusworhy), he evoluion of p i in each of he hree lying sraegies enumeraed above is given by he following equaions: (1 ) + ( α + α) = (1 α ) + α = ; for case (a) ( α) = (1 α ) + α = ; for case (b) (5) ( α +.5α ) = (1 α ) + α = ; for case (c) The convergence value of p i when approaches depends only on he rue cooperaion level of ha agen, p i, and on he percen of lying agens, α. The equaions above also show he impac differen lying behaviors have on he perceived repuaion of he agens wihin he sysem. In he firs case, as he value of α increases from o.5, he perceived repuaion p i is biased owards he value.5. Cooperaive agens will have a slighly lower repuaion, while defecive agens will have a slighly beer repuaion. For α=.5, he repuaion informaion becomes compleely useless because all agens will

7 have a perceived repuaion of.5. Moreover, as α grows bigger han.5, repuaion informaion is misleading since defecive agens are perceived as cooperaive and cooperaive agens are perceived as defecive. In he second case, as he value of α increases, he perceived repuaion p i of all agens converges o. The advanage over he previous case is ha cooperaive agens will always have higher perceived repuaion han defecive agens. In he hird case, as he value of α increases, he values for perceived repuaion approach he value.5. However, cooperaive agens will always have perceived repuaion higher han.5, while defecive agens will always have perceived repuaion lower han.5. In his case he sysem will be able o build he mos accurae repuaion informaion since he error p i - p i has he smalles increase wih he increase of α. The effec of he error inroduced by lying agens in he perceived repuaion of he business agens is refleced in he average increase of he wealh of he agens. Since on he average he repuaion paymens sum o zero (i.e. overall, he amoun of money paid for rerieving repuaion informaion is equal o he oal amoun of money received for filing repuaion repors) we will consider only he wealh increase resuled from business beween wo agens. Le us consider wo agens a i and a j having he opporuniy o do business. The probabiliy ha business is conduced, Pr(business), is: Pr(business) = Pr(p i >θ) Pr(p j >θ) q The expeced payoff of his paricular business opporuniy is: ( X 1) I [ payoff ] = q ( p p ) E i + j (6) where f(i) = x I is he business payoff funcion, I is he proposed invesmen and p i and p j are he cooperaion levels of he wo agens. Because agens are chosen randomly, we can compue an average expeced payoff as: E [ payoff ] = q ( X 1) I p (7) where p is he average real cooperaion level of he agens who are perceived as cooperaive, I is he average invesmen, and wealh increase for one business round will be: [ payoff ] q = lim q. Therefore, he average E Av. WealhInc = (8) N where N is he oal number of agens in he sysem. The AvWealhInc is always posiive, and is affeced by he presence of lying agens only hrough he values of q and p. Knowing he disribuion of he values of p i, and considering he equaions in (5), (6), (7) and (8), we can deermine he heoreical dependence of AvWealhInc on α. Figure 4 plos he heoreical dependence agains he observed values in he simulaion.

8 5 AvWealhInc heoreical value real value 5 AvWealhInc heoreical value real value alpha case a) case b) alpha 5 AvWealhInc heoreical value real value alpha case c) Figure 4: Average Wealh Increase depending on he percen of lying agens RELATED WORK In [McK1] he auhors presen a definiion of rus by idenifying is consrucs: rus-relaed behavior, rusing inenions, rusing beliefs, insiuion-based rus and disposiion o rus. On he oher hand, he Social Audior Model, presened in [Kra1], accouns for he process humans undergo when aking rusing decisions. Combining he wo, a framework is obained in which differen rus and repuaion models can be compared and classified. In he presen paper, we presen a simple rus model wihin his framework ha uses only he rusing beliefs consruc (he exen o which one believes ha he oher person has characerisics beneficial o one) from he definiion in [McK1] under he name of repuaion, and a simple decision process in which agens can ake binary decisions (yes or no) abou wheher o inerac or no wih oher agens. For simpliciy, we also combined he four differen aspecs of repuaion (compeence, benevolence, inegriy and predicabiliy) ino one number. Mui [Mui] presens an exensive repuaion ypology classified by he means of collecing he repuaion informaion. As saed before, we employ only wo caegories from he ypology in our rus model: he direc ineracion-derived repuaion and he propagaed (from oher agens) indirec repuaion. There are a number of sysems ha implemen rus mechanisms based only on direc ineracion-derived repuaion: [Birk], [Birk1], [Kra1], [Wi1], [Bis]. However, all hese sysems deal wih an environmen wih a relaively small number of agens where direc repuaion can be build. These models will no work in a very large environmen because he ime necessary for building direc repuaion would be oo large. [Sch] proposes a soluion ha akes ino consideraion he repuaion informaion repored by oher agens. However, his soluion we believe is no realisic because i does no provide any incenive for he agens o repor he repuaion informaion. Besides, each agen has o implemen a raher complicaed mechanism for judging he informaion i has received from is peers.

9 CONCLUSION In our work, we buil a successful rus model in an environmen where a big number of rading agens conduc business. We have done so by using a repuaion-based rus model in which boh direc ineracion-derived repuaion and propagaed indirec repuaion is used. Special care was dedicaed o he problem of incenive compaibiliy. By inroducing a mechanism of paymens, and a separaion of goals hrough wo kind of agens (business and review agens) we have shown ha i is possible o make i in he bes ineres of he agens o share repuaion informaion and o share i ruhfully. ACKNOWLEDGEMENTS We hank Monique Calisi for her help and consrucive remarks while wriing his paper. REFERENCES [Birk] Birk, A. Boosing Cooperaion by Evolving Trus, Applied Arificial Inelligence, 14: , [Birk1] [Bis] [Kag1] [Kag] [Kra1] Birk, A. Learning o Trus In R. Falcone, M. Singh and Y.-H. Tan (Eds.): Trus in Cybersocieies, LNAI 46, pp. 7-54, 1 Springer-Verlag Berlin Heidelberg 1 Biswas, A., Sen, S., Debnah, S. Limiing Deceon in a Group of Social Agens, Applied Arificial Inelligence, 14: , Kagal, L., Finin, T., Anupam, J. Moving from Securiy o Disribued Trus in Ubiquios Compuing Environmens, IEEE Compuer, December 1 Kagal, L., Finin, T., Anupam, J. A Delegaion-based Disribued Model for Muli Agen Sysems Sysems hp:// Kramer, R. Trus Rules for Trus Dilemmas: How Decision Makers Think and Ac in he Shadow of Doub, In R. Falcone, M. Singh and Y.-H. Tan (Eds.): Trus in Cyber-socieies, LNAI 46, pp. 9-6, 1 Springer-Verlag Berlin Heidelberg 1 [McK1] McKnigh, H. Chervany, N. Trus and Disrus: One Bie a a Time, In R. Falcone, M. Singh and Y.-H. Tan (Eds.): Trus in Cyber-socieies, LNAI 46, pp. 7-54, 1 Springer-Verlag Berlin Heidelberg 1 [Mui] [Sch] [Wi1] Mui, L. Noions of Repuaion in Muli-Agen Sysems: A Review MIT LCS Memorandum, hp://hongkong.lcs.mi.edu/lmui/docs/repuaionnoions.ps Schillo, M., Funk, P., Rovasos, M. Using Trus for deecing Deceiful Agens in Arificial Socieies, Applied Arificial Inelligence, 14:85-848, Wikowski, M., Arikis, A., Pi, J. Experimens in building Experienial Trus in a Sociey of Objecive-Trus Based Agens In R. Falcone, M. Singh and Y.-H. Tan (Eds.): Trus in Cyber-socieies, LNAI 46, pp , 1 Springer-Verlag Berlin Heidelberg 1