Performance Evaluation


 Walter Matthews
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1 Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: Modling Baylik rputation systms: Analysis, charactrization and insuranc mchanism dsign Hong i, John C.S. Lui CSE Dpartmnt, Th Chins Univrsity of Hong Kong, Hong Kong articl info abstract Articl history: Availabl onlin xxxx Kywords: Rputation systm Ramp up tim Insuranc mchanism Drop out probability Long trm profit gains Ecommrc systms lik Bay ar bcoming incrasingly popular. Having an ffctiv rputation systm is critical bcaus it can assist buyrs to valuat th trustworthinss of sllrs, and improv th rvnu for rputabl sllrs and Ecommrc oprators. W formulat a stochastic modl to analyz an Baylik rputation systm and propos four masurs to quantify its ffctivnss: () nw sllr ramp up tim, (2) nw sllr drop out probability, (3) long trm profit gains for sllrs, and (4) avrag pr sllr transaction gains for Ecommrc oprators. By analyzing a datast from Bay, w discovr that Bay suffrs a long ramp up tim, low long trm profit gains and low avrag pr sllr transaction gains. W dsign a novl insuranc mchanism consisting of an insuranc protocol and a transaction mchanism to improv th abov four masurs. W formulat an optimization framwork to slct appropriat paramtrs for our insuranc mchanism. W conduct xprimnts on an Bay s datast and show that our insuranc mchanism rducs ramp up tim by 9%, improvs both th long trm profit gains and th avrag pr sllr transaction gains by 26.66%. It also guarants that nw sllrs drop out with a small probability (clos to 0). 205 Elsvir B.V. All rights rsrvd.. Introduction Ecommrc systms ar bcoming incrasingly popular and typical xampls includ Amazon [], Bay [2], and Taobao [3] of Alibaba (th largst Ecommrc systm in China), tc. Through an Ecommrc systm, buyrs and sllrs can transact onlin. Sllrs advrtis products in thir onlin stors (which rsid in th Ecommrc s wb sit), buyrs can purchas products from any onlin stors, and th Ecommrc systm can charg a transaction f from sllrs for ach compltd transaction. Not that in an Ecommrc systm, it is possibl to buy products from a sllr whom th buyr has nvr transactd with, and this sllr may not vn b trustworthy [4]. This situation rsults in a high risk of buying low quality products. To ovrcom such problms, Ecommrc systms usually dploy rputation systms [4]. Usually, Ecommrc systms maintain and oprat a rputation mchanism to rflct th trustworthinss of sllrs [2,3]. A high rputation sllr can attract mor transactions lading to highr rvnu [4]. Th Baylik rputation systm is th most widly dployd rputation policy, which is usd in Bay and Taobao, tc. This typ of rputation systm is a crditbasd systm. Mor prcisly, a sllr nds to collct nough crdits from buyrs in ordr to improv his rputation. Ths crdits ar obtaind in form of fdback ratings, which ar xprssd by buyrs aftr transactions ar compltd. Fdback ratings in Bay and Taobao ar of thr lvls: positiv ( ), nutral (0), and ngativ ( ). A rputation scor, which is a cumulativ sum of all th past fdback ratings of a sllr, can b usd to rflct th trustworthinss of a sllr. Furthrmor, Corrsponding author. addrsss: (H. i), (J.C.S. Lui) / 205 Elsvir B.V. All rights rsrvd.
2 2 H. i, J.C.S. Lui / Prformanc Evaluation ( ) th rputation scors and fdback ratings of all buyrs ar public information and thy ar accssibl by all buyrs and sllrs in such an Ecommrc systm. Considr this Baylik rputation systm, a nw sllr nds to spnd a long tim, or what w call a long ramp up tim, so to collct nough crdits to b considrd rputabl. This is bcaus nw sllrs ar initializd with a rputation scor of zro, and buyrs ar lss willing to buy products from a sllr with low rputation scors. Th ramp up tim is critical to an Ecommrc systm sinc a long ramp up tim discourags nw sllrs to join th Ecommrc systm. Furthrmor, a nw usr usually starts an onlin stor with crtain budgts, and maintaining such onlin stors involvs cost. If a nw sllr uss up his ntir budgt and has not yt rampd up his rputation, h may discontinu his onlin businss (i.., or drop out) du to low rvnu. Thrfor, a long ramp up tim incrass th risk that a nw sllr drops out and discourags potntial nw sllrs to join. Finally, a long ramp up tim also rsults in a low profit gain for a sllr. Bcaus bfor ramping up, a sllr can only attract fw transactions du to his low rputation scor. To an Ecommrc oprator, this also rsults in a rduction in rvnu. Rducing ramp up tim is challnging and to th bst of our knowldg, this is th first work which rvals th importanc of th ramp up tim in Baylik rputation systms. This papr aims to xplor th following two fundamntal qustions: () How to idntify ky factors which influnc th ramp up tim? (2) How to tak advantag of ths factors to rduc th ramp up tim? Our contributions ar: W rval th ramp up tim problm in Baylik rputation systms. W propos four prformanc masurs to xplor this problm: () nw sllr ramp up tim, (2) nw sllr drop out probability, (3) long trm profit gains for sllrs, and (4) avrag pr sllr transaction gains for an Ecommrc oprator. W dvlop a stochastic modl to idntify ky factors which influnc ths four prformanc masurs. W apply our modl to analyz a rallif datast from Bay. W discovr that th Bay systm suffrs a long ramp up tim, a high nw sllr drop out probability, low long trm profit gains and low avrag pr sllr transaction gains. W dsign a novl insuranc mchanism to improv ths four prformanc masurs. Our insuranc mchanism consists of an insuranc protocol and a transaction mchanism. W formulat an optimization problm to slct appropriat paramtrs for our insuranc mchanism, which aims to maximiz sllrs incntiv in subscribing our insuranc. W prsnt an fficint approach to locat th optimal insuranc paramtrs as wll. W conduct xprimnts using a datast from Bay. W infr modl paramtrs from th data and show that our insuranc mchanism rducs th ramp up tim by 9%, and it improvs both th long trm profit gains and th avrag pr sllr transaction gains by 26.66%. It also guarants that nw sllrs drop out with a small probability (vry clos to 0) and rducs th risk that buyrs transact with untrustworthy sllrs. This papr is organizd as follows. In Sction 2, w prsnt th systm modl for Ecommrc systms. In Sction 3 w formulat four masurs to xplor th ramp up tim problm. In Sction 4, w driv analytical xprssions for ths four masurs. In Sction 5, w prsnt th dsign of our insuranc mchanism. In Sction 6, w prsnt tradoffs in slcting insuranc paramtrs. In Sction 7, w prsnt xprimntal rsults using an Bay s datast. Rlatd work is givn in Sction 8 and w conclud in Sction Ecommrc systm modl An Ecommrc systm consists of usrs, products and a rputation systm. A usr can b a sllr or a buyr or both. Sllrs advrtis products in thir onlin stors and st a pric for ach product. Buyrs, on th othr hand, purchas products through onlin stors and provid fdbacks to indicat whthr a sllr advrtiss products honstly or not. A rputation systm is maintaind by Ecommrc oprators to rflct th trustworthinss of sllrs. A high rputation sllr can attract mor transactions lading to a high rvnu. Th rputation systm aggrgats all th fdbacks, and computs a rputation scor for ach sllr. Th rputation scors and fdbacks ar public information which ar accssibl by all buyrs and sllrs. Products ar catgorizd into diffrnt typs. For xampl, Bay catgorizs products into Fashion, Elctronics, Collctibls & Art, tc. [2]. W considr L typs of product. Considr a typ ` 2 {,...,L} product. A sllr sts a pric p` 2 [0, ] and th Ecommrc oprator chargs a transaction f of T, p`, whr 2 (0, ), aftr th product is sold. Thr is a pr unit manufacturing cost of c` 2 [0, ]. A sllr arns a profit of u` by slling on product, or u` = ( )p` c`. () For th as of prsntation, our analysis focuss on on product typ. Not that our analysis can b asily gnralizd to multipl product typs, but for clarity of prsntation, w omit th subscript unlss w stat othrwis. W can also considr a fixd transaction f modl and our analysis is still applicabl. But for brvity, lt us considr a transaction f which is proportional to th slling pric.
3 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 3 Tabl Notation list. p, c Pric and manufacturing cost of a product T, u Transaction f, unit profit of slling a product Q a, Q i, Q, Q p Advrtisd, intrinsic, stimatd, prcivd product quality d, C S Shipmnt dlay, shipmnt cost Critical factor in xprssing fdback ratings F, r Rputation profil, rputation scor for a sllr r h, Rputation thrshold, consistncy thrshold Discounting factor in stimating product quality P (Q, p) Probability that a buyr buys a product having stimatd quality Q and pric p P ba, P br Probability that a buyr buys a product from a sllr labld as avrag, rputabl, 2 Buyr s arrival rat bfor, aftr a sllr ramps up T w Th maximum tim that a sllr is willing to wait to gt rampd up T r, P d Ramp up tim, nw sllr drop out probability G s, G Long trm xpctd profit gains for a sllr, avrag pr sllr transaction gains for th Ecommrc oprator Discounting factor in computing long trm xpctd profit gains G s T ( ) Transaction s arrival rat at tim slot C I, D I, T d, T c Insuranc pric, dposit, duration tim and claring tim C, I D, I T, d T c Optimal insuranc pric, dposit, duration tim and claring tim b DI Insuranc dposit thrshold to rvok an insuranc crtificat I Transaction s arrival rat to an insurd sllr T I r, P I r Ramp up tim, nw sllr drop out probability whn subscribing an insuranc G I, s GI Long trm profit gains, avrag pr sllr transaction gains whn subscribing an insuranc G I Marginal profit gain improvmnt 2.. Transaction modl Sllrs advrtis th product quality in thir onlin stors. Lt Q a 2 [0, ] b th advrtisd quality. Th largr th valu of Q a implis th highr th advrtisd quality. Buyrs rfr to th advrtisd quality Q a in thir product adoption. Each product also has an intrinsic quality which w dnot as Q i 2 [0, ] (i.., th ground truth of th product s quality). Th largr th valu of Q i implis th highr th intrinsic quality. Sinc sllrs aim to promot thir products, w hav Q a Q i. W mphasiz that th intrinsic quality Q i is a privat information,.g., it is only known to th sllr. On th othr hand, th advrtisd quality Q a is public information which is accssibl by all buyrs and sllrs. Buyrs stimat th product quality by rfrring to th advrtisd quality Q a (w will prsnt th stimating modl latr). Lt Q 2 [0, ] b th stimatd quality. Th largr th valu of Q implis th highr th stimatd quality. To purchas a product, a buyr must submit a paymnt p to th Ecommrc systm, which will b givn to th corrsponding sllr whn th buyr rcivs th product. Thr is usually a shipmnt tim (or dlay) in any Ecommrc systms. W dnot th dlay as d. Upon rciving a product, a buyr can valuat its quality and at that momnt, h has th prcivd quality, which w dnot as Q p 2 [0, ]. Th largr th valu of Q p implis th highr th prcivd quality. W assum that buyrs can prciv th intrinsic quality, i.., Q p = Q i. Buyrs ar satisfid (disappointd) if thy find out that th product is at last as good as (lss than) it is advrtisd, or Q p Q a (Q p < Q a ). To attract buyrs, an Ecommrc systm nds to incntiviz sllrs to advrtis honstly, i.., Q a = Q i. Many E commrc systms achiv this by dploying a rputation systm. W nxt introduc a popular rputation systm usd by many Ecommrc systms such as Bay [2] or Taobao [3]. Tabl summarizs ky notations in this papr Baslin rputation systm Th Baylik Ecommrc systm maintains a rputation systm to rflct th trustworthinss of sllrs. It consists of a fdback rating systm and a rating aggrgation policy. W first considr a baslin rputation mchanism. Buyrs xprss fdback ratings to indicat whthr a sllr advrtiss honstly or not. Th Baylik rputation systm adopts a fdback rating systm consisting of thr rating points, 2 i.., {, 0, }. A positiv rating (rating ) indicats that a product is at last as good as it is advrtisd, i.., Q p Q a. A nutral rating (rating 0) indicats that a buyr is indiffrnt about th product that h purchasd. This happns whn th prcivd quality is slightly lowr than it is advrtisd, i.., Q p 2 [Q a, Q a ), whr 2 [0, ] dnots th critical factor. Th smallr th valu of implis that buyrs ar mor critical in xprssing ratings,.g., = 0 mans that buyrs hav zro tolranc on sllr ovrstating th product quality. A ngativ rating (rating ) rprsnts that th prcivd quality is far smallr than th advrtisd quality, i.., Q p < Q a. W hav fdback rating = (, if Qp Q a, 0, if Q a appl Q p < Q a,, if Q p < Q a. 2 Not that w can asily gnraliz th modl to considr mor rating points.
4 4 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Fig.. Transition diagram of a sllr s rputation scor r. All th historical ratings ar known to all buyrs and sllrs. For th rating aggrgation policy, ach sllr is associatd with a rputation scor, which is th summation of all his fdback ratings. W dnot it by r 2 Z. A nw sllr who ntrs th Ecommrc systm is initializd with zro rputation scor, or r = 0. A positiv fdback rating incrass r by on, a ngativ fdback rating dcrass r by on, and a nutral fdback rating 0 dos not chang r. Fig. dpicts th transition diagram of a sllr s rputation scor. Not that th rputation scor r is a public information accssibl by all buyrs and sllrs. To assist buyrs to valuat th trustworthinss of a sllr, Ecommrc systms not only announc th sllr s rputation scor r, but also his rputation profil. Lt F, (r, n +, n 0, n ) b th rputation profil, whr n +, n 0, n rprsnt th cumulativ numbr of fdback ratings qual to, 0, rspctivly. Not that this form of rputation is commonly dployd, say in Bay [2] and Taobao [3]. Shipmnt dlay in ralworld Ecommrc systms usually rsults in crtain dlay in th rputation updat. To charactriz th dynamics of a rputation updating procss, w considr a discrt tim systm and divid th tim into slots, i.., [0, d), [d, 2d),..., whr d is th shipmnt dlay. W rfr to a tim slot 2 N as [ d,( + )d). Lt N( ) b th numbr of products sold by a sllr in th tim slot. Suppos N + ( ), N 0 ( ), N ( ) of ths transactions rsult in positiv, nutral and ngativ fdbacks rspctivly, whr N + ( )+N 0 ( )+N ( ) = N( ). Lt F ( ), (r( ), n + ( ), n 0 ( ), n ( )) b th rputation profil at tim slot. Initially, th rputation profil of this sllr is F (0) = (0, 0, 0, 0). Th rputation profil F ( ) is updatd as: n + ( + ), n 0 ( + ), n ( + ) = n + ( ) + N + ( ), n 0 ( ) + N 0 ( ), n ( ) + N ( ), r( + ) = r( ) + N + (2) ( ) N ( ). For simplicity, w drop th tim stamp in th rputation profil whn thr is no confusion. W nxt prsnt a probabilistic modl to charactriz th impact of sllrs rputation profils on buyrs product adoption bhavior. This modl srvs as an important building block for us to xplor th ffctivnss of this baslin rputation systm Modl for product adoption bhavior A rputation systm forgs trust among sllrs and buyrs. This trust plays a critical rol in product adoption. Mor prcisly, buyrs valuat th trustworthinss of sllrs from sllrs rputation profils. Buyrs sk to minimiz thir risk in product purchas and thy prfr to buy from rputabl sllrs. Basd on th rputation profil F, our modl classifis sllrs into two typs: rputabl and avrag. To b labld as rputabl, a sllr s rputation profil must satisfy two conditions. Th first on is that a sllr nds to collct nough crdits, i.., positiv fdbacks from buyrs. Mor prcisly, his rputation scor must b at last gratr than or qual to som positiv rputation thrshold r h, i.., r r h. A nw sllr is initializd with zro rputation scor, i.., r = 0. To accumulat a rputation scor of at last r h, a sllr nds to accomplish sufficint numbr of honst transactions. Th scond condition is that a sllr should b consistntly honst. Mor concrtly, th fraction of positiv fdbacks should b largr than or qual to a consistncy thrshold 2 (0, ], i.., n + /(n + + n + n 0 ). Th largr th valu of implis that an ECommrc oprator is mor critical about th honst consistncy. W formally dfin a rputabl sllr and an avrag sllr as follows. Dfinition 2.. A sllr is labld as rputabl if and only if th following two conditions ar mt C: r r h and, C2: n + /(n + + n + n 0 ). Othrwis, a sllr is labld as an avrag sllr. Rmark. Th rputation thrshold r h and consistncy thrshold quantify how difficult it is for a sllr to arn a rputabl labl. Th largr th r h and, th mor difficult it is to arn a rputabl labl. An Ecommrc oprator can control r h and. Som Ecommrc systms may not st r h and xplicitly, whr our modl is still applicabl bcaus w can infr r h and from historical transaction data. A buyr stimats th product quality by rfrring to th advrtisd quality Q a and th rputation profil of a sllr. If a sllr s rputation profil indicats that this sllr is rputabl, thn a buyr blivs that this sllr advrtiss honstly.
5 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 5 This buyr thrfor stimats th product quality as th advrtisd quality, i.., Q = Q a. On th contrary, if th rputation profil indicats that a sllr is avrag, a buyr blivs that this sllr is likly to ovrstat th product quality. Hnc th stimatd quality is lowr than th advrtisd quality, i.., Q = Q a, whr 2 [0, ] dnots th discounting factor. Th smallr th valu of implis that buyrs ar lss willing to trust an avrag sllr. W hav Q = Q a, if r r h and n + /(n + + n + n 0 ), Q a, othrwis. A buyr maks th purchasing dcision basd on th stimatd quality Q and th product pric p. Mor concrtly, th probability that a buyr buys a product incrass in Q and dcrass in p. Formally, w hav Pr[adopts a product], P (Q, p), (3) whr P can b any function as long as it incrass in Q and dcrass in p. 3. Problms formulation W us four prformanc masurs to quantify th ffctivnss of th baslin rputation systm mntiond in Sction 2. Ths masurs ar: () ramp up tim T r, (2) nw sllr drop out probability P d, (3) long trm xpctd profit gains for a sllr G s, and (4) avrag pr sllr transaction gains for th Ecommrc systm oprator G. W prsnt our problm formulations and our objctiv is to idntify ky factors which can influnc ths masurs. Lastly, w xplor an intrsting qustion of whthr thr ar othr mchanisms which can rduc th ramp up tim and th nw sllr drop out probability, and improv th long trm xpctd profit gains and avrag pr sllr transaction gains. 3.. Ramp up tim Sllrs and Ecommrc systm oprators ar intrstd in th minimum tim that a nw sllr nds to collct nough crdits, i.., positiv fdbacks from buyrs, so that th sllr can b classifid as rputabl. For on thing, a rputabl sllr can attract mor buyrs which may rsult in mor transactions, and highr transaction volum implis highr transaction gains to th Ecommrc oprator. W nxt formally dfin th ramp up procss and th ramp up condition. Dfinition 3.. A nw sllr s rputation is initializd as r = 0. H nds to collct nough crdits, i.., positiv fdbacks from buyrs, so that his rputation r can incras to at last r h. Th procss of incrasing his rputation to r h is calld th ramp up procss. Furthrmor, whn r r h, thn w say that th ramp up condition is satisfid. Rcall that r( ) dnots th rputation scor of a sllr at tim slot. W now formally dfin th ramp up tim. Dfinition 3.2. Ramp up tim is th minimum tim that a sllr must spnd to accumulat a rputation scor of r h. Lt T r dnot th ramp up tim, w hav T r, d arg min {r( ) r h }. (4) Th ramp up tim quantifis how long it will tak to collct nough crdits from buyrs. It is critical to th sllr s profit gains. To s this, w nxt quantify how th ramp up tim can affct th transaction s arrival rat. A sllr can attract mor buyrs whn h satisfis th ramp up condition bcaus his onlin stor will rciv highr click rat by buyrs, thrfor incrasing his profit gains. Lt ( 2 ) b th buyr s arrival rat bfor (aftr) a sllr satisfis th ramp up condition. W assum that th buyr s arrival procss, both bfor and aftr a sllr satisfis th ramp up condition, follows a Poisson counting procss with paramtr (bfor ramping up) and 2 (aftr ramping up) rspctivly, whr < 2 to indicat that a rampd up sllr can attract mor buyrs. Rcall that in Eq. (3) w xprss th probability that a buyr purchass a product as P (Q, p). If a buyr purchass a product, w say a sllr obtains a transaction. Basd on th Poisson proprty, it is asy to s that th transaction s arrival procss is also a Poisson counting procss. Lt T ( ) b th transaction s arrival rat at tim slot. Lt P (Q ( ), p) b th probability that a buyr adopts a product at tim slot, whr Q ( ) dnots th stimatd quality at tim slot. W can xprss th transaction s arrival rat as T ( ), P (Q ( ), p), if r( ) <r h, 2P (Q ( ), p), if r( ) r h. Eq. (5) srvs as an important building block for us to xplor th ky factors which influnc th ramp up tim T r. Lt us formulat our first problm. Problm. Idntify ky factors which influnc th ramp up tim T r, and dsign a mchanism which can tak advantag of ths factors to rduc T r. (5)
6 6 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 3.2. Nw sllr drop out probability In ralworld Ecommrc systms, a nw sllr may drop out, or mov to anothr Ecommrc systm, if h dos not collct nough crdits (i.., ramp up) within crtain tim bcaus h cannot obtain nough transactions. For xampl, a nw sllr in Bay may drop out if h dos not ramp up in on yar. This is bcaus a nw sllr starts an onlin stor with crtain budgts, and thr ar costs associatd with maintaining this onlin businss. To modl this scnario, lt T w > 0 dnot th maximum tim that a nw sllr is willing to wait to gt rampd up. In othr words, if th ramp up tim is longr than T w,a nw sllr will drop out from that Ecommrc systm. W assum T w /d 2 N to accommodat th dlay (d) in rputation updat. Dfinition 3.3. A nw sllr drops out, if and only if T r > T w. Lt P d dnot th probability that a nw sllr drops out. W formally hav P d, Pr[T r > T w ]. (6) Sllrs and th Ecommrc oprator ar intrstd to know this nw sllr drop out probability. Th smallr th valu of P d implis that sllrs ar mor likly to continu his onlin businss in th Ecommrc systm. This is an important masur sinc a small P d can attract mor nw sllrs to join th Ecommrc systm, which will rsult in highr transaction gains for th Ecommrc oprator. On th othr hand, a larg P d discourags nw sllrs to participat and can lad to som transaction gain losss for th Ecommrc systm oprator. W thrfor considr th scond problm. Problm 2. Idntify ky factors which influnc th nw sllr drop out probability P d, and dsign a mchanism which can tak advantag of ths factors to rduc P d Long trm profit gains and transaction gains Th profit gain and transaction gain ar critical to sllrs and Ecommrc systm oprators rspctivly. W focus on th scnario that sllrs ar long livd and thy aim to maximiz thir long trm profit gains. Rcall that u, th unit profit of slling on product, is xprssd in Eq. (). Also rcall that N( ) dnots th numbr of products sold in th tim slot. W mphasiz that N( ) is a random variabl and it follows a Poisson distribution with paramtr T ( )d, whr T ( ) is drivd in Eq. (5). A sllr arns a profit of un( ) in th tim slot. W considr a discountd long trm profit gain with a discounting factor of 2 (0, ]. Dfinition 3.4. Lt G s dnot th long trm xpctd profit gains for a sllr, which can b xprssd as " # G s, E un( ). (7) Not that whn a sllr arns a profit u, h also contributs a transaction f T = p to th Ecommrc oprator. Dfinition 3.5. Lt G dnot th avrag pr sllr transaction gains that a sllr pays to th Ecommrc oprator. W can xprss it as " # " # G, E TN( ) = E pn( ) = p u G s. (8) Not that G s is important to a sllr whil G is important to th Ecommrc oprator. Problm 3. Idntify ky factors which influnc th profit gains G s and th avrag pr sllr transaction gains G, and dsign a mchanism to us ths factors to improv G and G s. W nxt driv E[T r ], P d, G s, and G. Through this analysis, w idntify ky factors which influnc th abov mntiond prformanc masurs. Ths insights will srv as important building blocks for us to dsign a mchanism. 4. Analyzing th baslin rputation systm Hr, w driv analytical xprssions for th xpctd ramp up tim (E[T r ]), th nw sllr drop out probability (P d ), th long trm xpctd profit gains (G ) and th avrag pr sllr transaction gains (G ). Through this w idntify that th rputation thrshold (r h ), as wll as th probability that a buyr buys a product from an avrag labld sllr (P ab ) ar two critical factors which influnc T r, P d, G s and G. Our rsults indicat that th baslin rputation mchanism dscribd in Sction 2, suffrs a long ramp up tim, a high nw sllr drop out probability, and small long trm profit gains or transaction gains. Ths insights show that on nds to hav a nw mchanism to rduc T r, P d, and to improv G s and G. W will prsnt this nw mchanism in Sction 5.
7 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 7 Tabl 2 Expctd ramp up tim E[T r ] in days (P ba = 0.02, d = 3) E[T r ] (r h = 200) E[T r ] (r h = 50) E[T r ] (r h = 00) Driving th xpctd ramp up tim E[T r ] Lt us driv th analytical xprssion for th xpctd ramp up tim E[T r ]. This masur quantifis on avrag, how long it will tak to ramp up a nw sllr undr th baslin rputation mchanism mntiond in Sction 2. W considr th scnario that buyrs advrtis th product quality honstly, i.., Q a = Q i. As to how an Baylik rputation mchanism can guarant rational sllrs to advrtis honstly, on can rfr to [5]. W lik to point out that nw sllrs can achiv th lowst ramp up tim by advrtising honstly (Q a = Q i ). This is bcaus ovrstating th product quality, i.., Q a > Q i, lads to nutral or ngativ ratings. Undrstating th product quality, i.., Q a < Q i, rsults in a dcras in transaction s arrival rat. Hnc, th assumption that Q a = Q i can b viwd as driving th bst cas of T r for th baslin rputation systm. W dfin th following notations to simplify our analysis. Dfinition 4.. Lt P ba, P ( Q i, p) and P br, P (Q i, p) dnot th probability that a buyr buys a product from an avrag labld sllr and a rputabl sllr rspctivly. Thorm 4.. Th xpctd ramp up tim is E[T r ]=d h P ba ( ( )d P ba ( )d) k. (9) = Furthrmor, E[T r ] incrass in th rputation thrshold r h, and dcrass in th transaction s arrival rat P ba. Proof. Plas rfr to Appndix for drivation. Rmark. A nw sllr is mor difficult to gt rampd up if th ECommrc oprator sts a high rputation thrshold r h, or th transaction s arrival rat to an avrag labld sllr ( P ba ) is low. Th computational complxity in valuating E[T r ] drivd in Eq. (9) is ( P = r h) = (). W nxt stat a Thorm to approximat E[T r ]. P rh P ba ( )d ( P ba ( )d) k Thorm 4.2. Lt b E[Tr ]= P d = dnot an stimation of E[T r ] drivd in Eq. (9). If > n o max ln( 0.8 P bad ) + ln /(0.8 P ba d), 25 r h, thn P ba b E[Tr ] E[T d r ] appl. Proof. Plas rfr to Appndix for drivation. Tabl 2 prsnts numrical xampls on E[T r ], whr w fix P ba = 0.02, i.., buyrs purchas products from an avrag labld sllr with probability 0.02, and fix d = 3, i.., th rputation updating dlay is thr days. W vary th buyr s arrival rat from 5 to 25, i.., on avrag ach day an avrag labld sllr attracts 5 to 25 buyrs to visit n his onlin stor. W vary th rputation thrshold o (r h ) from 00 to 200. Applying Thorm 4.2 w st = max ln( ) + ln 0.0 /(0.048 ), 25 r h to guarant b E[Tr ] E[T r ] appl 0.0. Whn r h = 200, as 0.06 incrass from 5 to 25, th xpctd ramp up tim (E[T r ]) drops from to 40.5 days, a dduction ratio of 80%. Whn th buyr s arrival rat is low, say = 5, as th rputation thrshold r h drops from 200 to 00, th xpctd ramp up tim E[T r ] drops from to 00.5 days, a rduction ratio of 50%. Ths rsults show that th xpctd ramp up tim (E[T r ]) is larg in gnral. Namly, it is difficult for nw sllrs to quickly gt rampd up undr th baslin rputation systm. W nxt xplor th nw sllr drop out probability Driving th nw sllr drop out probability P d W now driv th analytical xprssion for P d. This probability quantifis how difficult it is for a nw sllr to surviv in an Ecommrc systm. Not that P d is also crucial for nw sllrs bcaus a potntial nw sllr can us it to dcid whthr or not to opn an onlin stor in that Ecommrc systm. Thrfor, a low drop out probability P d is attractiv to nw sllrs, whil a high P d discourags nw sllrs to join. Thorm 4.3. Th nw sllr drop out probability is P d = P r h P ba Tw ( P ba Tw) k. Th P d dcrass in P ba,t w and incrass in r h. Proof. Plas rfr to Appndix for drivation.
8 8 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Tabl 3 Nw sllr drop out probability P d ( = 20, T w = 80, d = 3). P ba P d (r h = 200) P d (r h = 50) P d (r h = 00) Tabl 4 Long trm xpctd profit gains G s and avrag pr sllr transaction gains G ( = 20, 2 = 50, u =, T = 0., = 0.99, T w = 80, P br = 0., d = 3). P ba G s (r h = 200) G s (r h = 50) G s (r h = 00) G (r h = 200) G (r h = 50) G (r h = 00) Rmark. Thorm 4.3 stats that a nw sllr can rduc th drop out probability by xtnding his ramp up dadlin lin (T w ), and a nw sllr is mor likly to drop out if th rputation thrshold (r h ) incrass or th transaction s arrival rat to an avrag labld sllr ( P ba ) dcrass. Tabl 3 prsnts numrical xampls on th nw sllr drop out probability P d, whr w st = 20, i.., on avrag, ach day an avrag labld sllr attracts 20 buyrs to visit his stor, d = 3, and T w = 80, i.., sllrs drop out if thy do not ramp up in 80 days. W vary P ba, th probability that a buyr buys products from an avrag labld sllr, from 0.0 to 0.05, and vary th rputation thrshold r h from 00 to 200. Considr r h = 200. As P ba incrass from 0.0 to 0.05, th nw sllr drop out probability P d dcrass from to This implis a vry high drop out probability. Considr P ba = As th rputation thrshold r h drops from 200 to 00, w s that P d drops from to , a rduction ratio of around 80%. It is intrsting to obsrv that whn th P ba is small, th nw sllr drop out probability is quit high. In fact whn P ba = 0.0, P d is vry clos to. In othr words, if buyrs ar lss willing to buy from avrag labld sllrs, nw sllrs will b mor likly to drop out. W nxt xplor ky factors which influnc long trm xpctd profit gains and avrag pr sllr transaction gains Driving th long trm profit gains G s and G Lt us now driv analytical xprssions for th long trm xpctd profit gains G s and th avrag pr sllr transaction gains G rspctivly. Thy ar important masurs bcaus a larg G s is attractiv to nw sllrs and a small G s discourags nw sllrs to join th Ecommrc systm, whil th avrag pr sllr transaction gains G is crucial to th Ecommrc systm oprator. Thorm 4.4. Th long trm xpctd profit gains for a nw sllr can b xprssd as G s = 2 P br d h Furthrmor, G = p u G s. P ba Tw ( P ba T w ) k Proof. Plas rfr to Appndix for drivation. 2P br d T w/d + Tw/d h P ba ( d P ba d) k ( P ba 2 P br )d. (0) Rmark. Thorm 4.4 quantifis th impact of various factors on th long trm xpctd profit gains (G s ) and avrag pr sllr transaction gains (G ),.g., th rputation thrshold r h, th buyr s arrival rat, 2, tc. W nxt prsnt som numrical xampls to illustrat thir impact. Tabl 4 prsnts numrical xampls on th long trm xpctd profit gains (G s ) and th avrag pr sllr transaction gains (G ), whr w st = 20, T = 0., 2 = 50, u =, T w = 80, d = 3, P br = 0. (i.., buyrs buy products from a rputabl sllr with probability 0.). W vary P ba, th probability that a buyr purchass products from an avrag labld sllr, and th ramp up thrshold r h rspctivly to xamin thir impact on G s and G. Considr r h = 200. As P ba incrass from 0.0 to 0.05, G s improvs from 27.7 to , an improvmnt ratio of 7.29 tims. Similarly, th avrag pr sllr transaction gains G is also improvd by 7.29 tims. This implis that P ba is critical to both sllrs profit gains and th Ecommrc systm oprator s transaction gains. Considr P ba = As r h drops from 200 to 00, G s improvs from to , an improvmnt ratio of This improvmnt ratio also holds for th avrag pr sllr transaction grains G. It is intrsting to obsrv that whn P ba is small, both G s and G ar quit small. In fact whn P ba = 0.0, th G s
9 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 9 is around 27.7 and G is around Namly, if buyrs ar lss willing to buy from avrag labld sllrs, sllrs (Ecommrc oprators) will hav low long trm profit gains (avrag pr sllr transaction gains). Summary: Th rputation thrshold r h and P ba ar critical to th ramp up tim, th nw sllr drop out probability, th long trm profit gains and th avrag pr sllr transaction gains. Th baslin (or Baylik) rputation systm prsntd in Sction 2 suffrs a long ramp up tim, a high nw sllr drop out probability, low long trm profit gains and low avrag pr sllr transaction gains. Hnc, it is important to ask whthr w can dsign a nw mchanism that an Ecommrc systm can us to improv all th prformanc masurs E[T r ], P d, G s and G. W nxt xplor this intrsting qustion. 5. Insuranc mchanism dsign Th objctiv of our insuranc mchanism is to hlp nw sllrs ramp up quickly. Our insuranc mchanism consists of an insuranc protocol and a transaction mchanism. W first dscrib th insuranc protocol. Th Ecommrc systm oprator provids an insuranc srvic to nw sllrs. Each insuranc has a pric of C I > 0, a duration tim of T d > 0, and a claring tim of T c > 0. Without loss of gnrality, w assum T d 2 N and T c 2 N in ordr to accommodat th dlay (d) in rputation updat. Th insuranc claring tim d d taks ffct whn an insuranc xpirs. To buy an insuranc, a sllr must provid th Ecommrc oprator an insuranc dposit of D I. Hnc, th total paymnt by th nw sllr to th Ecommrc systm oprator is C I + D I. W rfr to this insuranc as th (C I, T d, T c, D I )insuranc. Only nw sllrs can subscrib to this insuranc. If a sllr subscribs an insuranc, th Ecommrc systm oprator issus an insuranc crtificat to him, and this crtificat is known to th public (i.., all buyrs and sllrs). This crtificat only taks ffct within th insuranc duration tim T d. Th Ecommrc systm oprator trats a sllr with an insuranc crtificat as trustworthy. To guarant that such sllrs will advrtis thir product quality honstly, th Ecommrc systm oprator rquirs such sllrs oby th following ruls basd on our transaction mchanism. W now dscrib th transaction mchanism. Only sllrs with an insuranc crtificat hav to oby ths transaction ruls. Lt us focus on a sllr with an insuranc crtificat. Whn ordring a product from this sllr, a buyr snds his paymnt p to th Ecommrc systm oprator. Aftr rciving th product, if this buyr provids a positiv fdback, thn this transaction complts, i.., th Ecommrc oprator forwards th paymnt ( )p to th sllr and chargs a transaction f of p. This transaction also complts if this buyr xprsss a nutral fdback. A nutral fdback mans that a sllr slightly ovrstatd his product quality, i.. Q i < Q a < Q i +. To avoid such ovrstating, th Ecommrc company rvoks a sllr s insuranc crtificat onc th fraction of positiv fdbacks falls blow th consistncy factor ( ), i.., n + /(n + + n 0 + n )<. A ngativ fdback rsults in th transaction bing rvokd. Mor concrtly, th E commrc oprator givs th paymnt p back to th buyr and dos not charg any transaction f from th sllr (providd that it is within th duration tim T d or th claring tim T c ). Th buyr nds to ship th product back to th sllr but th buyr dos not nd to pay for th shipmnt cost C S, bcaus it will b dductd from a sllr s insuranc dposit D I. If th insuranc dposit is not nough to covr C S, th Ecommrc oprator maks a supplmntal paymnt. To avoid this undsirabl outcom, th Ecommrc company rvoks a sllr s insuranc crtificat, onc a sllr s dposit falls blow a thrshold b DI < D I. Th insuranc claring tim taks ffct whn an insuranc is invokd. At th nd of th claring tim, th Ecommrc company rturns th rmaining dposit (if it is not dductd to zro) to th sllr. Rmark. Not that sllrs may collud with buyrs to inflat thir rputation by fak transactions [6]. On way to avoid such collusion is by incrasing th transaction f such as [7]. Th shipmnt cost may xcd D I du to a larg numbr of products to b rturnd. This can b avoidd with high probability by stting a larg b DI (rfr to Thorm 5.2). W also driv th minimum claring tim (T c ) to guarant that a sllr with an insuranc crtificat nds to oby th transaction mchanism (rfr to Thorm 5.2). 5.. Analyzing th insuranc mchanism W first show that buyrs trat a sllr having an insuranc crtificat as trustworthy. W driv th transaction rat for a sllr who has an insuranc crtificat. W thn driv th improvd E[T r ], P d, G s and G. Buyrs trat sllrs having an insuranc crtificat as trustworthy. This is an important proprty of our insuranc mchanism bcaus it influncs th probability that a buyr adopts a product from a sllr. Suppos in tim slot, a sllr has an insuranc crtificat. If this sllr advrtiss honstly Q a = Q i, thn th buyr who buys a product from this sllr will b satisfid (xprss positiv fdback rating). In this cas, th paymnt from th buyr will b forwardd to th sllr. Hnc this sllr arns a profit of u. If this sllr ovrstats his product quality byond th lnint factor ( ), i.., Q a > Q i +, thn according to our insuranc mchanism, th paymnt by th buyr will b rturnd to th buyr. Th sllr nds to pay a shipmnt cost of C S to ship back th product and C S will b dductd from his insuranc dposit D I. Hnc, if a sllr ovrstats th product quality byond th lnint factor, h will los a total shipmnt cost of at last min{b DI, C S N( )} in tim slot, whr N( ) dnots th numbr of product slling. A sllr with an insuranc crtificat must oby th sam consistncy factor ( ) as rputabl sllrs in bing honst, i.., n + /(n + +n 0 +n ), bcaus if not his insuranc crtificat will b rvokd by th Ecommrc oprator. Givn ths proprtis, buyrs trust a sllr with an insuranc crtificat.
10 0 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Tabl 5 Impact of our insuranc on E[T r ], P d, G s and G. r h = 00 r h = 50 r h = 200 E[T r ] P d G s G E[T r ] P d G s G E[T r ] P d G s G Baslin Insuranc Improvmnt 87% 00% 95% 95% 88% 00% 738% 738% 88% 00% 740% 740% Rcall that th Ecommrc oprator also trusts a sllr with an insuranc crtificat. Thrfor, an insurd sllr can attract I transactions with an arrival rat bing quivalnt to thos rputabl sllrs. Lt T dnot th transaction s arrival rat to a sllr with an insuranc crtificat. W hav I = T 2P br. W now quantify th impact of our insuranc mchanism on th four prformanc masurs. Lt T I r, P I d, GI s, GI dnot th ramp up tim, th nw sllr drop out probability, th long trm profit gains and th avrag pr sllr transaction gains rspctivly, whn a nw sllr subscribs our insuranc. Thorm 5.. Suppos a nw sllr subscribs to our proposd insuranc mchanism, th xpctd ramp up tim and th nw sllr drop out probability ar () h E[T I r ]=d = P 2 T (`) 2 k P T (`) r h, P I d = Tw/d P T (`) Tw/d P T (`) k, whr T (`) = 2 P br d for all ` = 0,,...,T d /d, and T (`) = P ba d for all ` = T d /d,...,. Th long trm xpctd profit gains for a nw sllr who subscribs an insuranc is: G I s = I {T d <Tw} + Tw/d 2P br d h =T d /d + I {Td Tw} 2P br d h ( 2 P br T d ) k ( 2 P br T d ) k h G I s incrass in T d. Furthrmor, G I = p u GI s. Proof. Plas rfr to Appndix for drivation. r h k k 0 =0 2P br Tw ( 2P br T w ) k r h k k 0 =0 P ba (Tw T d ) ( P ba (T w T d )) k 0 P ba ( d T d ) ( P ba ( d T d )) k 0 k 0 2P br d T w/d ( k 0 P ba 2 P br )d 2P br d T w/d. (2) Rmark. Thorm 5. quantifis th impact of our insuranc mchanism on four important prformanc masurs. Bfor w discuss mor about how to slct insuranc paramtrs, i.., C I, D I, T d, T c, lt us illustrat th ffctivnss of our insuranc mchanism using som numrical xampls. Th computational complxity in valuating E[T I r ] is (P = r h) = (). Thorm 4.2 can b asily xtndd to approximat E[T I r ]. Tabl 5 prsnts numrical xampls on E[T r ], P d, G s and G undr th baslin rputation stting and th insuranc stting, whr w rfr to improvmnt as dducting ratio for E[T r ] and P d, and as improving ratio for G s and G. W us th following stting: = 20, 2 = 50, u =, T w = 80, d = 3, P br = 0., P ba = 0.03, C I = 00, D I = 00,b DI = 50, C S = 0.5, T = 0., T d = 99, T c = 3, = Whn r h = 00, w hav E[T r ]=68 and E[T I r ]=2.5. In othr words, our insuranc mchanism rducs th xpctd ramp up tim from 68 days to only 2.5 days, or ovr 87% rduction. It is intrsting to obsrv that our incntiv mchanism rducs th nw sllr drop out probability from P d = 0.2 to P I = d 0. Namly, our insuranc mchanism can guarant that nw sllrs ramp up bfor th dadlin lin T w with a high probability (vry clos to.0). In addition, our insuranc mchanism improvs long trm xpctd profit gains from G s = 76 to G I = s 485, a 95% improvmnt. This improvmnt ratio also holds for avrag pr sllr transaction gains. As r h incrass from 00 to 200, th improvmnt on th E[T r ], P d, G s, G, bcoms mor significant. W nxt stat th appropriat valus for C I, D I,b DI and T c in th following thorm. Thorm 5.2. An uppr bound for th insuranc pric C I is C I < G I s G s. If D I and b DI satisfy D I b DI C S max ln, 2, thn Pr[shipmnt cost xcdsd I ] appl. If T c d, thn all products sold by a sllr with an insuranc crtificat can b guarantd to oby th insuranc mchanism.
11 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Proof. Plas rfr to Appndix for drivation. Rmark. Not that th insuranc pric should b lowr than G I s G s, othrwis sllrs hav no incntiv to subscrib an insuranc. Th claring tim should b largr or qual to d in ordr to guarant all products sold by a sllr with an insuranc crtificat oby th insuranc mchanism. To guarant that th insuranc dposit covrs th shipmnt cost for rturning products with high probability, D I and b DI nd to b no lss than C S max ln, 2. W nxt formally show how to slct C I, D I, T d, T c subjct to diffrnt tradoffs. 6. Tradoffs in insuranc mchanism Hr, w formulat a mtric, th marginal profit gain improvmnt G I, to quantify sllrs incntiv in subscribing our insuranc. W formulat an optimization framwork to slct appropriat paramtrs for our insuranc mchanism, i.., C I, D I, T d, T c, which aims to maximiz G I. W prsnt an fficint mthod to locat th optimal C I, D I, T d, T c. 6.. Mtrics An Ecommrc systm oprator wants to incntiviz nw sllrs to subscrib to our insuranc. To quantify sllrs incntiv in subscribing an insuranc, w dfin marginal profit gain improvmnt by an (C I, T d, T c, D I )insuranc as G I, G I s G s C I D I + D I (T d +T c )/d. (3) Th physical maning is that whn subscribing an insuranc, a sllr pays C I + D I in total, and a rmaining dposit of D I (bcaus sllrs advrtis honstly, hnc no dposit is dductd) will b rturnd to a sllr aftr (T d + T c )/d tim slots. Th largr th valu of G I, th highr th incntiv that nw sllrs will subscrib to our insuranc Insuranc dsign to maximiz marginal profit gains improvmnt Our objctiv is to slct C I, D I, T d, T c so as to maximiz G I. Th optimization formulation is: max G I, G I (T s G s C I D I + D d +T c )/d I. C I,D I,T d,t c s.t. Eqs. (0) and (2) hold, C I 0, T d /d 2 N, T c d, T c /d 2 N, D I C S max{ln, 2 }, (5) whr Inquality (5) spcifis th minimum dposit, which is drivd in Thorm 5.2, and Inquality (4) guarants that all products sold by a sllr with an insuranc crtificat can b guarantd to oby th insuranc mchanism. Thorm 6.. Th optimal insuranc pric, insuranc claring tim and insuranc dposit satisfy C I = 0, T c = d and D I = C S max ln, 2 rspctivly. (4) Proof. Plas rfr to Appndix for drivation. Rmark. Th abov thorm implis that to maximiz G I (or maximiz sllrs incntiv to subscrib an insuranc), an Ecommrc oprator should st th insuranc pric to b zro, st th claring tim to b d, and st th insuranc dposit to b max{ln, 2 }. Thorm 6. simplifis our optimization formulation as follows: max G I, G I T s G s ( d /d+ )C S max ln, 2. T d s.t. Eqs. (0) and (2) hold, and T d /d 2 N. Th rmaining issu is to locat th optimal insuranc duration tim for th abov simplifid optimization problm. In th following thorm, w driv an uppr bound for th optimal duration tim. n Thorm 6.2. Th optimal insuranc duration tim T d satisfis T appl d d max ln 0.5 l mo, 2 u 2P br ( ) G s. ln dc S 2 2P br Proof. Plas rfr to Appndix for drivation. Rmark. With th uppr bound of T d drivd Thorm 6.2, and not that T d/d 2 N, on can asily locat th optimal ln 0.5 insuranc duration tim by xhaustiv sarch. And th complxity is (max{d, d2 u 2P br ( ) G s }). Actually, ln dc S 2 2P br this complxity is quit low,.g., for th Bay stting in Sction 7, th complxity is (693). Hnc our xhaustiv sarch mthod is quit fficint and rasonabl.
12 2 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Fig. 2. Rputation scor accumulating in th Bay systm. Tabl 6 Statistics for Bay fdback rating datast. Numbr of sllrs 4362 Total numbr of ratings 8,533,93 Maximum/Minimum on numbr of ratings pr sllr 7,00/ Man/Mdian on numbr of ratings pr sllr 490/437 Rating mtric {, 0, } 7. Exprimnts on ralworld data W conduct xprimnts using a rallif datast from Bay. W idntify that th ramp up tim in Bay is quit long (i.., 777 days on avrag), nw sllrs drop out probability is quit high, and both xpctd long trm profit gains and avrag transaction gains ar low. W slct th optimal paramtrs for our insuranc mchanism and show that our insuranc mchanism rducs th ramp up tim by 9%, improvs both xpctd long trm profit gains and avrag pr sllr transaction gains by 26.66%. It also guarants that nw sllrs ramp up bfor th dadlin T w with a high probability (vry clos to ). 7.. Bay datast W crawld and obtaind historical fdback ratings from Bay, th ovrall statistics ar shown in Tabl 6. This datast was obtaind in April 203. Each sllr s historical ratings in our datast starts from th first day that a sllr joind Bay to April 203. Ebay is a popular Ecommrc systm that assists customrs in onlin product purchasing, and it uss a rputation mchanism to assist buyrs to assss th trustworthinss (or rputation) of sllrs. Buyrs xprss a rating 2 {, 0, } to th sllr aftr purchasing a product. This rating indicats whthr a sllr is trustworthy or not. Ratings ar public to all buyrs and sllrs Infrring modl paramtrs W first infr th rputation thrshold r h. Rcall that r h mainly affcts th transaction s arrival rat. Mor prcisly, a sllr having a rputation scor smallr than r h attracts transactions with a rat significantly smallr than a sllr having a rputation scor highr than r h. In our data, w find out that th fraction of transactions that rsult in positiv scors is 99.43%. Namly, th transaction s arrival rat is roughly th sam as th rputation scor accumulation rat. To idntify r h, w plot th rputation scor accumulation rat in Fig. 2, whr th vrtical axis shows th rputation scor and th horizontal axis shows th avrag numbr of days to accumulat a givn numbr of rputation scor. On can obsrv that to accumulat a rputation scor of 200, it taks around 600 days on avrag, a rlativly long duration. In othr words, sllrs having rputation scor smallr than 200 attract transactions with a small rat. To incras th rputation scor from 200 to 000, it only taks around 500 days. This implis that th transaction rat is significantly largr than that corrsponds to a sllr having a rputation scor smallr than 200. W thrfor st th rputation thrshold as 200, or r h = 200. W now infr th transaction s arrival rat. W infr th transaction s arrival rat bfor a sllr ramps up ( P ba ) as th total numbr of transactions by sllrs having a rputation scor smallr than r h, dividd by th total tim to accumulat
13 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 3 Tabl 7 Optimal insuranc paramtrs for Bay. C I D I T d T c Bay days 3 days Tabl 8 Expctd ramp up tim in Bay (C I = 0, D I = b DI = , T d = 93 days and T c = 3 days). Baslin (E[T r ]) Insuranc (E[T I r ]) Improvmnt ((E[T r] E[T I r ])/E[T r]) Bay 792 days 75 days 9% Tabl 9 Nw sllr drop out probability in Bay (C I = 0, D I = b DI = , T d = 93 days and T c = 3 days). Baslin (P d ) Insuranc (P I d ) T w = yar 0 T w = 2 yars T w = 3 yars ths transactions. From our data, w obtain th following: P ba = Numbr of transactions by sllrs having r < r h Total tim to accumulat ths transactions = Namly, on avrag, bfor ramping up a sllr can attract transactions pr day. Similarly, w infr th transaction s arrival rat to a rputabl sllr as th total numbr of transactions by rputabl sllrs (i.., having a rputation scor largr than r h and th fraction of positiv scor is largr than 0.9), dividd by th total tim to accumulat ths transactions. From our data, w obtain th following: 2P br = Numbr of transactions by sllrs having r > r h Total tim to accumulat ths transactions = Namly, on avrag, a rputabl sllr attracts transactions pr day. W nxt prsnt th xprimntal rsults Exprimntal rsults W st a shipmnt dlay of d = 3 days, a shipmnt cost of C S = 0., a unit profit of u =, a transaction f of T = 0., a discounting factor of = W also us th infrrd paramtrs in Sction 7.2. W first slct th optimal insuranc paramtr for Bay. W input th paramtrs infrrd in Sction 7.2 into our optimization framwork mntiond in Sction 6. Tabl 7 prsnts th optimal insuranc paramtrs, whr C I, D I, T d, T rprsnt th optimal insuranc pric, dposit, duration tim and claring tim rspctivly. It is intrsting to obsrv that th optimal insuranc pric, duration tim, dposit and claring tim ar C I = 0, D I = , T d = 93 days and T c = 3 days rspctivly. In th following xprimnts, w st ths optimal insuranc paramtrs as dfault to show th ffctivnss of our insuranc mchanism. W xplor th ramp up tim (E[T r ]). W input th infrrd paramtrs into our modl. W obtain th xpctd ramp up tim of Bay and th xpctd ramp up tim whn a nw sllr subscribs to our proposd insuranc. Tabl 8 prsnts th xpctd ramp up tim, whr E[T r ] dnots th ramp up tim in Bay, E[T I r ] dnots th ramp up tim whn a nw sllr subscribs to an insuranc, and (E[T r ] E[T I r ])/E[T r] dnots th rduction ratio. On can obsrv that th ramp up tim in Bay is 792 days, a vry long duration. Our insuranc mchanism rducs th ramp up tim to 75 days, with a rduction of 9%. This is a significant rduction. W now xamin th nw sllr drop out probability (P d ). W vary T w (th maximum tim that a sllr is willing to wait to gt rampd up) from on yar to thr yars. Tabl 9 prsnts th nw sllr drop out probability whn a sllr subscribs to or dclins an insuranc. Considr T w = yar, i.., a sllr is willing to wait on yar to gt rampd up. In th Bay stting, th probability that h will drop out is vry clos to. Sllrs can rduc th drop out probability to if thy ar willing to wait T w = 2 yars. Howvr, th drop out probability is still high. It can b rducd to.3 0 7, if th sllr is willing to wait T w = 3 yars. Howvr a waiting tim of thr yars is too long. This implis that it is difficult for nw sllrs to continu thir businss in Bay. It is intrsting to obsrv that if a sllr subscribs to an insuranc, th drop out probability is vry clos to 0 for all T w =, 2, 3 yars. W now xplor th long trm xpctd profit gains and th avrag pr sllr transaction gains (G s and G ). W input th infrrd paramtrs into our modl. W comput G s and G I s. Tabl 0 prsnts numrical rsults on G s and G I s, whr (G I s G s )/G s and (G I G )/G dnot th improvmnt ratio. On can obsrv that a sllr in Bay can arn a long trm
14 4 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Tabl 0 Long trm profit gains and avrag pr sllr transaction gains in Bay (C I = 0, D I = b DI = , T d = 93 days and T c = 3 days, T w = 3 yars). Baslin (G s ) Insuranc (G I s ) Improvmnt ( GI s Gs ) Baslin (G ) Insuranc (G I ) Improvmnt ( GI G ) Gs % % G profit gain of G s = 6452 on avrag. It can b improvd to G I s = 872 on avrag, if a nw sllr subscribs to our insuranc. Th long trm profit gains is improvd by (G I s G s )/G s = 26.66%. This improvmnt ratio also holds for avrag pr sllr transaction gains G. 8. Rlatd work Rsarch on rputation systms [4] for intrnt srvics has bn quit activ. Many aspcts of rputation systms hav bn studid, i.., rputation mtric formulation and calculation [8 0], attacks and dfns tchniqus for rputation systms [,6,2,3], and ffctivnss of rputation systms [4]. A survy can b found in [5]. Rputation mtric formulation and calculation hav bn studid xtnsivly. Two most rprsntativ rputation calculating modls ar Baylik rputation modls [8] and transitiv trust basd modls []. Th Baylik rputation modl computs th rputation scor by summarizing xplicit human fdbacks (or ratings) [6,8,7,8]. Th transitiv trust basd modl [,9,0,9,2] assums that if usr A trusts usr B and usr B trusts usr C, thn usr A trusts usr C. Mor prcisly, ach usr is rprsntd by a nod in a graph, and th wightd dirctd link from A to B quantifis th dgr that usr A trusts usr B. For this modl, many algorithms wr dvlopd to comput an ovrall rputation scor for ach usr [,9,0,9,2]. Ths works providd thortical foundations for rputation computing. Our work is diffrnt from thm in that w bring out th ramp up tim problm in Baylik rputation systms, which has not bn studid bfor. W us Bay data to show that th ramp up tim is critical to th ffctivnss of Baylik Ecommrc systms. Our rsults uncovr many practical insights to nrich th thortical rsarch on rputation formulation and calculation. Svral works hav xplord attack and dfns tchniqus for rputation systms. On typ of potntial attacks is that usrs may not giv honst fdbacks. Prprdiction mthod basd mchanisms wr proposd to licit honst fdbacks [20 22]. Anothr typ of potntial attacks is rputation inflation, or slfpromotion. Many works hav bn don to addrss this issu [,6,2,3]. A survy on attack and dfns tchniqus for rputation systms can b found in [6]. Not that ths dfns tchniqus may rsult in a long ramp up tim or low profit gains for sllrs. This may discourag nw sllrs to join an Ecommrc systm. Our work uncovrs an important factor, i.., ramp up tim, in which many dfns tchniqus nd to b awar of. This will improv th practical usag of dfns tchniqus. Th most closly rlatd works ar [7,4,5,23], which studid ffctivnss of Baylik rputation mchanisms. Authors in [7] drivd th minimum transaction f to avoid ballot stuffing (i.., fak positiv fdbacks). Author in [4] proposd to us buyr frindship rlationship to filtr out unfair ratings. In [4], th author xplord th impact of buyrs biass (i.., lnincy or criticality) in xprss fdback ratings on sllrs in advrtising product quality. In [23], authors studid th impact of ngativ fdbacks by buyrs. Our work diffrs from thirs in that w bring out a nw problm of ramp up tim, which is critical to th ffctivnss of Baylik rputation mchanisms. W idntify ky factors that influnc th ramp up tim and w propos an insuranc mchanism to rduc th ramp up tim. 9. Conclusion This is th first papr which rvals th ramp up tim problm in Baylik rputation mchanisms. Via thortical analysis and xprimnts using data from Bay, w showd that th ramp up tim is critical to th ffctivnss of Baylik rputation systms. W formulatd four prformanc masurs to xplor th ramp up tim problm: () nw sllr ramp up tim, (2) nw sllr drop out probability, (3) long trm profit gains for sllrs and (4) avrag pr sllr transaction gains for Ecommrc oprators. W dvlopd a stochastic modl to idntify ky factors which influnc th abov four prformanc masurs. W applid our modl to study a datast from Bay. W discovrd that th Bay systm suffrs a long ramp up tim, a high nw sllr drop out probability, low profit gains and low avrag pr sllr transaction gains. W dsignd a novl insuranc mchanism to improv th abov four prformanc masurs. W formulatd an optimization framwork to slct appropriat paramtrs for our insuranc mchanism so as to incntiviz nw sllrs to subscrib th insuranc. W conductd xprimnts on a datast from Bay to show that our insuranc mchanism rducs th ramp up tim by 9%, improvs both long trm profit gains and avrag pr sllr transaction gains by 26.66%. It also guarantd that nw sllrs drop out with a small probability (vry clos to 0). Furthrmor, it can rduc th risk that a buyr purchass a product from an untrustworthy sllr. Acknowldgmnt Th rsarch work of John C.S. Lui was supportd in part by th GRF #452.
15 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 5 Appndix Proof of Thorm 4.. Not that ach nw sllr advrtiss product quality honstly. In this scnario, ach transaction rsults in on positiv fdback. Rcall our rputation updating rul spcifid in Eq. (2), w hav that th rputation scor at tim slot quals th numbr of transactions arriving within tim slot 0 to tim slot. Rcall th dfinition of T r in Eq. (4), w hav that T r /d 2 N. With ths obsrvations and by som basic probability argumnts, w hav E[T r ]= d Pr[T r = d] =d Pr[T r /d = ] = = = = d Pr[T r /d ] =d ( Pr[T r /d appl ( )]) = = = d ( Pr[r( ) r h ]) = d = Pr " 2 # N(`) r h. P 2 Not that P N(`) is a random variabl which follows a Poisson distribution with paramtr P ba ( )d. W hav P E[T r ]=d = ( k=r h P ba ( )d ( P ba ( )d) k ). Evaluating th first ordr drivativ on E[T r ] with rspct to r h and P ba rspctivly, on can asily obtain th monotonous proprty of E[T r ]. Proof of Thorm 4.2. First w can asily hav b E[Tr ] E[T r ] = P P d = + r an uppr bound for th probability h P ba ( )d ( P ba ( )d) k P rh P ba ( )d ( P ba ( )d) k. W nxt driv. Actually, this probability is quivalnt to Pr[N( ) appl r h ], whr N( ) follows a Poisson distribution with paramtr P ba d( ). Lt us rstrict our attntion to th that satisfis r h < P ba d( ), which yilds > r h P ba +. Using a Chrnoff bound [24] argumnt, w hav d Pr[N( ) appl r h ] appl P ba d( ) ( P ba d( )) r h /(r h ) r h. For simplicity, lt x = P ba d( ) r h x >. Thn w hav Pr[N( ) appl r h ] appl (r h )x (x) r h = (r h )(x ln x ).. Straightforwardly, Now w show that for any c 2 [ 0.5, ], w hav that x ln x cx holds for all x ( c) 3. W aim to show that ( c)x ln x 0. For simplicity, lt y = ( c)x. Thn w hav ( c)x ln x = y ln y = (ln y)2 (ln y)2 (ln y)2 y ln y + ln( c) + ln y + ln y + ln( c) = + ln( c). To mak + ln( c) 0, p w only nd ln y 2 ln( c). Not that c > 0.5, hnc 2 ln( c) >. Thrfor it is sufficint to mak ln y 2 ln( c), which yilds x ( c) 3. Hnc, givn c 2 [ 0.5, ], for all x ( c) 3 w hav Pr[N( ) appl r h ] appl (r h )cx. Thn w hav b E[Tr ] E[T r ] = P d Pr[N( ) appl = + r h ] appl P d = + (r h )cx = P d = + (r h )c Pbad( ) P r h = d = + c P ba d( ) = c P ba d /( c P bad ). To mak c P ba d /( c P bad ) appl, w only nd (ln( c P bad ) + ln )/(c P ba d). Not that x ( c) 3 is quivalnt to P ba d( ) ( r h c) 3, which yilds that r h ( c) 3 r P ba +. Hnc w nd h ( c) 3. In summary, w nd d P ba > max{(ln( c P bad ) + d ln )/(c P ba d), r h ( c) 3 }. Stting c P ba = 0.8 w complt this proof. d Proof of Thorm 4.3. Applying similar drivation as Thorm 4., w hav that th rputation scor at tim slot quals th numbr of transactions arriving within tim slot 0 to. Not that T w /d 2 N. Rcall th dfinition in Eq. (4) w hav h that T r > T w if and only if r(t w /d) <r h. Using som basic probability argumnts, w hav P d = Pr[r(T w /d) <r h ]= PT i w/d Pr N( ) <r h. P Tw/d Not that N( ) is a random variabl which follows a Poisson distribution with paramtr P ba T w. W hav " h T # w/d h P d = Pr N( ) = k = ( P ba Tw P ba T w ) k. Evaluating th first ordr drivativ on P d with rspct to r h, T w and proprty of P d. c P ba rspctivly, on can asily obtain th monotonous Proof of Thorm 4.4. By th linarity of xpctation w hav G s = P E un( ) = P ue[n( )]. W nxt driv E[N( )]. Lt L( ) 2 {rputabl, avrag} dnot th labl of a sllr in tim slot. By th basic rul of conditional xpctation w hav E[N( )] = Pr[L( ) = rputabl]e[n( ) L( ) = rputabl]+ Pr[L( ) = avrag]e[n( ) L( ) = avrag]. A rputabl sllr attracts transactions with rat 2P br. Not that th lngth of a tim slot is d. W can thn hav E[N( ) L( ) = rputabl] = 2 P br d for all = 0,,...,. An avrag sllr attracts transactions with rat P ba. Hnc
16 6 H. i, J.C.S. Lui / Prformanc Evaluation ( ) w hav E[N( ) L( ) = avrag] = P ba d for all = 0,,...,T w /d, and E[N( ) L( ) = avrag] = 0, for all = T w /d,...,. Th last statmnt follows th fact that a sllr drops out if h dos not arn a rputabl labl bfor th dadlin T w. Givn a tim slot, a sllr is labld as avrag at this tim hslot if and only if r( ) <r h. Using som basic P i probability argumnts, w hav Pr[L( ) = avrag] =Pr[r( ) <r h ]=Pr N(`) P <r h. Not that N(`) is a random variabl which follows a Poisson distribution with paramtr P ba d. W hav " # h h Pr[L( ) = avrag] = Pr N(`) = k = P ba ( d P ba d) k. Thn it follows that Pr[L( ) = rputabl] = rputabl] = P rh, for all = 0,,...,, and Pr[L( ) = P rh P ba Tw ( P ba Tw) k for all = T w /d,...,. Combin thm all w hav E[N( )] =I { <T w/d} h h + I { <T w/d} P ba d ( P ba d) k P ba d ( P ba d) k P ba d ( P ba d) k P ba d. Thn with som basic probability argumnts w hav Tw/d h G s = P ba ( d P ba d) k 2P br d + =Tw/d + Tw/d = 2 P br d h h This proof is thn complt. P ba d ( P ba d) k P ba Tw ( P ba T w ) k P ba d 2P br d T w/d + 2P br d + I { T w/d} Tw/d h h h P ba Tw ( P ba T w ) k ( P ba Tw P ba T w ) k 2P br d P ba ( d P ba d) k ( P ba 2 P br )d. Proof of Thorm 5.. W first driv E[T I] r and P I d. Not that sllrs advrtis honstly. This mans that all transactions rsult in positiv fdbacks. This implis that th insuranc crtificat xpirs at th nd of th duration tim. Not that N(`), th numbr of transactions at tim slot ` = 0,,..., bfor a sllr ramps up, follows a Poisson distribution, and w dnot its paramtr by T (`). Applying Eq. (), w hav T (`) = 2 P br d for all ` = 0,,...,T d /d, and T (`) = P ba d for all ` = T d /d,...,. Thn with a similar drivation as Thorm 4. w obtain th xpctd ramp up tim E[T I r ]. Furthrmor, with a similar drivation as Thorm 4.3 w obtain P I d. Lt us now driv long trm profit gains (G I s ) and avrag pr sllr transaction gains (GI ). W driv G s first. Not that E[N( )] = Pr[L( ) = rputabl]e[n( ) L( ) = rputabl]+ Pr[L( ) = avrag]e[n( ) L( ) = avrag]. Lt us considr th first cas that T d T w. Rcall that an insurd sllr attracts transactions with rat 2 P br. Hnc w hav E[N( )] = 2 P br d for all = 0,,...,T w /d. Not that a sllr drops out if h dos not arn a rputabl labl bfor th dadlin T w. W can thn hav that for all = T w /d,..., it holds that E[N( )] = 2 P br d if L( ) = rputabl, othrwis E[N( )] =0. Givn any 2 {T w /d,...,}, w hav that Pr[L( ) = rputabl] = Pr[L( ) = avrag] = Pr[r(T w /d) <r h ] " T # w/d h = Pr N(`) <r h = ( 2P br Tw 2P br T w ) k. P rh Hnc E[N( )] =I { <T w/d} 2P br d + I { T w/d} 2P br Tw ( 2P br Tw) k 2P br d. Thn it follows that Tw/d G I = h s 2P br d + ( 2P br Tw 2P br T w ) k 2P br d = 2 P br d h =Tw/d 2P br Tw ( 2P br T w ) k 2P br d T w/d. Now lt us considr th cas that T d < T w. First, w can asily hav that E[N( )] = 2 P br d holds for all = 0,,...,T d /d. Now considr 2 {T d /d,...,t w /d }. W hav E[N( ) L( ) = rputabl] = 2 P br d and 2P br d
17 H. i, J.C.S. Lui / Prformanc Evaluation ( ) 7 E[N( ) L( ) = avrag] = P ba d. Furthrmor, Pr[L( ) = avrag] =Pr[r( ) <r h ]=Pr = Pr " Td /d N(`) + " h Td /d = Pr h = " # N(`) <r h N(`) <r h # `=T d /d # rh k Pr N(`) = k ( 2 P br T d ) k k 0 =0 r h k k 0 =0 " `=T d /d N(`) = k 0 # P ba ( d T d ) ( P ba ( d T d )) k 0 Now considr 2 {T w /d,...,}. For this cas w can driv Pr[L( ) = avrag] as Pr[L( ) = avrag] =Pr[r(T w /d) <r h ] Combin thm all w hav T d G I = /d s + + =Tw/d Tw/d = 2 P br d + h = Tw/d 2P br d + h =T d /d Tw/d h h =T d /d =T d /d h ( 2 P br T d ) k r h k k 0 =0 k 0 =0 k 0 P ba (Tw T d ) ( P ba (T w T d )) k 0 h ( 2 P br T d ) k r h k P ba ( d T d ) ( P ba ( d T d )) k 0 k 0 k 0 =0 ( 2 P br T d ) k r h k P ba (Tw T d ) ( P ba (T w T d )) k 0 k 0 2P br d ( 2 P br T d ) k ( 2 P br T d ) k ( 2 P br T d ) k r h k k 0 =0 r h k k 0 =0 r h k k 0 =0 k 0 P ba ( d T d ) ( P ba ( d T d )) k 0 k 0 P ba (Tw T d ) ( P ba (T w T d )) k 0 k 0 P ba ( d T d ) ( P ba ( d T d )) k 0 k 0.. P ba d 2P br d T w/d ( P ba 2 P br )d. 2P br d This proof is thn complt. Proof of Thorm 5.2. W want to driv th rasonabl pric that an ECommrc oprator can charg for th insuranc. Th marginal long trm profit gain of an insurd sllr is G I s C I. Not that th marginal long trm profit gain without insuranc is G s. Thus sllrs hav th incntiv to buy an insuranc if th marginal profit gain corrsponds to buying an insuranc is largr than th marginal profit gain without insuranc, i.., G I s C I > G s, which yilds C I < G I s G s. Not that sllrs advrtis honstly. Lt N 0 (T d ) dnot th total numbr of products sold in insuranc duration tim. It is asy to s that N 0 (T d ) follows a Poisson distribution with paramtr. Th worst cas is that all buyrs hold th product till th last minut of th claring tim T c and thn rturn it. Using a Chrnoff bound [24] argumnt, on can asily bound th shipmnt cost (at th worst cas) as Pr[N 0 (T d )C S N 0 C S ] appl ( 2 P br T d ) N0 /N 0N0. Stting N 0 = max{ln, 2 } w hav Pr[N 0 (T d )C S N 0 C S ] appl. Th claring tim follows th shipmnt dlay d. Proof of Thorm 6.. Obsrv that C I, D I and T c ar not paramtrs in dtrmining G I s drivd in Eq. (2). Hnc, xamining Eq. (3), on can obsrv that G I dcrass in C I, D I and T c rspctivly. This proof is thn complt. Proof of Thorm 6.2. Lt T d dnot th optimal valu of T d. Obsrv that for ach givn T d, it is possibl to b optimal if th valu of G I is no lss than zro. In othr words, T d should satisfy G I s G s ( T d /d+ )C S max ln 2P br T d, 2 2P br T d 0.
18 8 H. i, J.C.S. Lui / Prformanc Evaluation ( ) Not that max{ln 2P br T, d 2 2P br T } d 2 2P br T d. Thn it follows that G I s G s ( T d /d+ )C S 2 2P br T d 0, G I s G s ( T d /d+ )C S 2 2P br T d. Obsrv that G I appl u 2P br s, which yilds u 2 P br G s ( G s u 2 P br T d + )C S 2 2P br T, d ( C S 2 2P br T d /d+ )T d. Obsrv that to mak that T d appl d &max ( ln 0.5 ln T d /d+, w only nd T 2 d /d + ln 0.5, which yilds that T ln 0.5 ln d d ln u 2 P br, 2 dc S 2 G s 2P br )' = d max ( ln 0.5 ln, & u 2 P br 2 dc S 2 G s 2P br '). d. Thn it follows This proof is thn complt. Rfrncs [] Amazon. [2] Bay. [3] Taobao. [4] P. Rsnick, K. Kuwabara, R. Zckhausr, E. Fridman, Rputation systms, Commun. ACM 43 (2) (2000) [5] C. Dllarocas, Analyzing th conomic fficincy of Baylik onlin rputation rporting mchanisms, in: Proc. of ACM EC, 200. [6] K. Hoffman, D. Zag, C. NitaRotaru, A survy of attack and dfns tchniqus for rputation systms, ACM Comput. Surv. 42 () (2009) : :3. [7] R. Bhattacharj, A. Gol, Avoiding ballot stuffing in Baylik rputation systms, in: Proc. of P2PECON, [8] D. Housr, J. Woodrs, Rputation in auctions: Thory, and vidnc from Bay, J. Econ. Manag. Stratgy 5 (2) (2006). [9] S.D. Kamvar, M.T. Schlossr, H. GarciaMolina, Th Eigntrust algorithm for rputation managmnt in P2P ntworks, in: Proc. of WWW, [0] P. Rsnick, R. Sami, Sybilproof transitiv trust protocols, in: Proc. of ACM EC, [] A. Chng, E. Fridman, Sybilproof rputation mchanisms, in: Proc. of P2PECON, [2] H. Yu, M. Kaminsky, P.B. Gibbons, A. Flaxman, SybilGuard: Dfnding against sybil attacks via social ntworks, in: Proc. of ACM SIGCOMM, [3] B. Viswanath, M. Mondal, K.P. Gummadi, A. Mislov, A. Post, Canal: Scaling social ntworkbasd sybil tolranc schms, in: Proc. of ACM EuroSys, 202. [4] C. Dllarocas, Immunizing onlin rputation rporting systms against unfair ratings and discriminatory bhavior, in: Proc. ACM EC, [5] A. Jøsang, R. Ismail, C. Boyd, A survy of trust and rputation systms for onlin srvic provision, Dcis. Support Syst. 43 (2) (2007). [6] S. Buchggr, J.Y. L Boudc, A robust rputation systm for prtopr and mobil adhoc ntworks, in: Proc. of P2PECON, [7] A. Singh, L. Liu, Trustm: anonymous managmnt of trust rlationships in dcntralizd P2P systms, in: Proc. of P2P, [8] R. Zhou, K. Hwang, Powrtrust: A robust and scalabl rputation systm for trustd prtopr computing, IEEE Trans. Paralll Distrib. Syst. 8 (4) (2007) [9] R. Dlaviz, N. Andrad, J. Pouwls, D. Epma, Sybilrs: A sybilrsilint flowbasd dcntralizd rputation mchanism, in: Proc. of IEEE ICDCS, 202. [20] R. Jurca, B. Faltings, Minimum paymnts that rward honst rputation fdback, in: Proc. of ACM EC, [2] R. Jurca, B. Faltings, Collusionrsistant, incntivcompatibl fdback paymnts, in: Proc. of ACM EC, [22] N. Millr, P. Rsnick, R. Zckhausr, Eliciting informativ fdback: Th prprdiction mthod, Manag. Sci. 5 (9) (2005) [23] T. Khopkar,. Li, P. Rsnick, Slfslction, slipping, salvaging, slacking, and stoning: Th impacts of ngativ fdback at Bay, in: Proc. of ACM EC, [24] M. Mitznmachr, E. Upfal, Probability and Computing, Cambridg Univrsity Prss, Hong i rcivd his B.Eng. dgr from th School of Computr Scinc and Tchnology at Th Univrsity of Scinc and Tchnology of China (USTC) in 200. H is now a Ph.D. candidat in th Dpartmnt of Computr Scinc and Enginring at Th Chins Univrsity of Hong Kong (CUHK). His advisor is John C.S. Lui. His rsarch intrsts includ ntwork conomics, data analytics, stochastic modling, crowdsourcing and onlin social ntworks. John C.S. Lui is currntly th ChohMing Li Profssor in th Dpartmnt of Computr Scinc and Enginring at Th Chins Univrsity of Hong Kong (CUHK). H rcivd his Ph.D. in Computr Scinc from UCLA. Aftr his graduation, h joind th IBM Almadn Rsarch Laboratory/San Jos Laboratory and participatd in rsarch and dvlopmnt projcts on fil systms and paralll I/O architcturs. H latr joind th Dpartmnt of Computr Scinc and Enginring at CUHK. His currnt rsarch intrsts ar in Intrnt, ntwork scincs, machin larning on larg data analytics, ntwork/systm scurity, ntwork conomics, larg scal distributd systms and prformanc valuation thory. John rcivd various dpartmntal taching awards and th CUHK VicChancllor s Exmplary Taching Award. John also rcivd th CUHK Faculty of Enginring Rsarch Excllnc Award (20 202), h is a corcipint of th bst papr award in th IFIP WG 7.3 Prformanc 2005, IEEE/IFIP NOMS 2006, and SIMPLE 203. H is an lctd mmbr of th IFIP WG 7.3, Fllow of ACM, Fllow of IEEE, Snior Rsarch Fllow of th Crouchr Foundation.
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