A Misranking/Masquerading-Proof Mechanism for Online Reputation System

Transcription

1 A Misanking/Masqueading-Poof Mechanism fo Online Reputation System Michael Xiaoquan Zhang Sloan School of Management, MIT 1 Intoduction In e-commece based online maketplaces, infomation asymmety is a big poblem. On one hand, the buyes need to lean moe than just the pice to make decisions whethe to buy fom a paticula selle; on the othe hand, the selles need to distinguish themselves fom selles selling goods of wose quality. Without a well established mechanism to pevent this kind of moal hazad poblem, the maket tends to collapse. (Akelof, 1970) Basically, in an online maketplace, the buyes ely a lot on the eputations of the selles. The eputation can be a esult of wod-of-mouth, compaison epot on a magazine, o ating fom the maketplace itself. Fo big online entities such as Amazon.com, Dell.com, they can chage a pemium above the aveage pice of a homogeneous poduct than othe less famous selles. Reputation sustains the maket; in fact, eputation in the online maketplace context is the one and only means to povide infomation about a paticula poduct s quality. Thee is an even moe citical poblem fo online maketplace povides like ebay.com 1. Unlike Amazon.com o Dell.com, the selles in ebay ae all anonymous selles fom all ove the wold, thee is no way to find a compaison epot on a magazine o to lean about them by wod-of-mouth. When a selle tuns out to be cheating, thee is also not much can be done to him o he. Without a good eputation mechanism, the selles tend to take the fly-by-night o hit-and-un stategy. One incentive fo this eseach comes fom the (somewhat supising) empiical evidence that the faud ate is vey low among the astonomically lage numbe of tansactions. EBay attibutes the success to the ating system. Indeed, Lucking-Reiley et al (2000) found that selles eputation points on ebay have a measuable effect on auction pices, and negative atings has a bigge effect than positive ones. Anothe vey inteesting phenomenon we want to captue is the tuth-telling behavio of the buyes. Without buyes giving fai atings, the system will not post coect atings to eflect the selle s behavios, and the maket will not sustain. Some effects of unfai atings ae suveyed in Dellaocas (2001b). Vey peliminay, comments welcome. zxq@ecommece.mit.edu. 1 See Lucking-Reiley (1999) fo a suvey of online auctions. 1

2 2 Liteatue Review 2 The pape is oganized as follows. Section 2 summaizes the empiical and theoetical liteatues elated to this topic. Section 3 establishes a model to addess the game between the paties. Section 4 analyzes the equilibium of the maket. In section 5, a mechanism is poposed to dete deviation. Section 6 gives an algoithm to efine the model to be moe applicable. 2 Liteatue Review Thee ae a gowing liteatue suounding the topics elated to online eputation systems. 2.1 Empiical Many eseaches (Lucking-Reiley et. al.,2000; Standifid, 2001, House and Woodes, 2000) studied the impotance of a selle s eputation ating on the final bid pice associated with ebay auctions. They found that positive eputation atings has a mildly influence in the final bid pice, and negative eputation atings ae highly significant in detemining the final bid pice. Many empiical esults suggest that ebay s eputation system has managed to povide emakable stability in the maket given the consideable uncetainty in tansactions. (Dewan and Hsu, 2001; Resnick and Zeckhause, 2001) 2.2 Theoetical Many theoetical wok has been done about consume infomation, poduct quality, and selle eputation. Akelof (1970) is the fist one to take qualities into a equilibium analysis, in his wok, qualities ae exogenously given, and an advese selection poblem aises. In Shemalensee (1978) and Smallwood and Conlisk (1979), quality is assumed to be positively elated to the pobability of epeat puchase. Shapio (1982, 1983) ae some ealy aticles taking qualities as endogenous and analyzing the poblem as a moal hazad one. Reputation is shown to induce a pemium that compensates the selle fo the esouces expended in building up the eputation. In taditional signaling models following the line of eseach stated by Spence (1975, 1976) and Sheshinski (1976), it can be shown that when quality is exogenous, a high quality selle can signal a bette quality while it is too costly fo a low quality selle to do so 2. An advantage of teating quality as endogenous is that unde some cicumstances, selles can be motivated to choose to povide a highe quality (Salop and Stiglitz, 1977; Faell, 1986; Chan and Leland, 1982; Coope and Ross, 1985; Fishman and Simhon, 2000). Ebay is a adopting a ating system base on subjective binay atings (good/bad, paise/complaint), Rogeson (1983) shows that this simple ating system ceates an extenality fo buyes while a system based on exact evaluation of quality does not. 2 Fo example (Wolinski, 1983), (Bagwell and Riodan, 1991).

3 3 The Model 3 Dellaocas (2001a), on the contay, shows that unless the buyes use the ight theshold paametes when they judge selle pofiles, binay eputation mechanisms will not function well. Thee ae also consideably many papes on collaboative filteing, which is basically a ecommende system that keeps tack of each subscibe s likes and dislikes and pefoms statistical analysis to match uses with simila tastes. (Resnick and Vaian, 1997; Resnick et al., 2000; Besee et al., 1998; Sawa et al., 2000; Shafe et al., 2001;) 3 The Model 3.1 The setting We pesent a game model in infinite hoizon with thee types of playes: a cente, a selle, and a goup of buyes. In this maket, the selle is selling a good (eithe a poduct o a sevice) in a competitive envionment. Thee ae many othe selles selling simila goods at multiple quality levels. In each peiod, the selle poduce unit mass of the good. Although the selle can poduce at any quality level, thee is a minimum quality q 0, below which it is illegal to poduce. Thee is also a maximum quality q m, above which the cost will ise shaply while the maginal pofit will not incease accodingly. Let the pe-peiod inteest ate be. The cente is in chage of poviding the maket place (thus obtaining accuate tansaction data), and maintaining a eputation mechanism to facilitate the tustwothiness of the tansactions. Reputation measues how a good s quality deviates fom the expected quality. The buyes can enjoy a cetain suplus by puchasing in this maket athe than in some othe makets (say, the bick-and-mota maket). They ely on the pice and the eputation system solely to make the puchase decisions. As in Shapio (1983), consume of type θ attaches benefits of U(q,θ) to a good of quality q. In Shapio s model, the buye needs to epot q in each peiod, but it is vey ambiguous fo buyes to epot a quality in numeical tems. We adopt a atio benchmak method of epoting poduct quality, the buye epots a elative feeling with espect to the expected quality: R = U(q eal,θ) U(q expected,θ) = q eal θ q expected θ = q eal q expected ; (assuming consumes utility functions ae sepaable in q and θ, and choose the units so that g(q)=q). So in each ound the eputation will just be a pue numbe, eflecting how eal quality is compaed to expected quality. A value of 1 means that the eal quality is exactly the same as expected. The maket is competitive; all selles ean ex ante zeo pofit. 3.2 The game Due to infomation asymmety, the buyes and the cente do not know the eal quality of the good befoe the buye puchase the good. Buyes ely heavily on the atings to

4 4 Equilibium 4 judge a selle s tustwothiness. When selle comes to the maket fo the fist time, she will be foced to chage p 0, whee p 0 is the pice coesponding to q 0, the minimum quality. Because a fist-time selle has no histoy, and she can only sell at the lowest possible pice, the cente will just post R 0 = 1 as the eputation. (R 0 = 1 means that the selle is selling at a quality coesponding to the expected quality). Evey selle poducing a highe quality will suffe a loss in the fist peiod, but when she establishes a eputation, she then can enjoy a pemium coesponding to the eputation of eliable quality, and the pemium of eputation will eventually compensate he so that he ex ante pofit will still be zeo. (A fai pofit in competitive maket.) The buyes won t lose if they ty the poduct, because the eal quality is at least q 0. Afte puchase, the buye (who puchased fom this selle) will lean the tue quality, and he will vote accoding to the atio benchmak ule. (Since q q 0,R 1 1). In the next ound, the selle has nothing to do but chage a pice accoding to the eputation. If the buye votes coectly, the selle can chage p(q). Although this is a competitive maket, the selle can still chage p(q) > c(q) and enjoy a ent bought about by keeping the quality. The game goes on in this manne. 4 Equilibium Suppose the selle poduces the good in quality level q fo all of the ounds, and the buyes epot tuthfully, the selle will enjoy a pemium fom the second ound on. Since the selle is expecting an ex ante zeo pofit, the pemium she enjoys will be exactly the same as he initial loss in the fist ound. 4.1 The case of complete infomation With complete infomation, the selle will chage p c (q) [Note: the supescipt c epesents competitive ] and bea the cost of c(q). Since the maket is pefectly competitive, p c (q)=c(q). Then the selle will have a net pesent value of pofit π c =[p c (q) c(q)] The case of incomplete infomation = 0. Due to the incompleteness of infomation, the selle can only get p 0 = c(q 0 ) in the fist peiod, but he cost is c(q); when q > q 0, he loss is c(q 0 ) c(q). Fom the beginning of the second peiod, she can stat to chage a pice highe than the cost, say p p (q) [Note: the supescipt p epesents pemium ]. The net pesent value fom all the p p (q) c(q) futue ounds (stating fom ound 2) will be: zeo pofit, [c(q 0 ) c(q)] + pp (q) c(q) so,. Since she expects ex ante = 0 p p (q)=c(q)+[c(q) c(q 0 )] (1)

5 5 One-Round Deviation fom Equilibium 5 Obviously, p p (q) > p c (q)=c(q) if q > q 0. The tem [c(q) c(q 0 )] epesents the pemium as etun to eputation. 5 One-Round Deviation fom Equilibium The buyes won t deviate fom voting tuthfully unde this scheme. Fo a buye, if he votes above the tue value of the quality, the pice will ise in the next ound; if he votes below the tue value of the quality, the pice will dop in the next ound. But fist, he may not buy fom the selle in the next ound, second, if the selle is undeated fo too many ounds, she will no longe exist in this competitive maket, then the buye will not enjoy the loweed pice. If all the buyes undeate the qualities of the goods in the maket, the maket will collapse soone o late. If some buyes oveate, and some buyes undeate, then the ode of the qualities will be messed up, and the eputation system will no longe be useful to buyes to make puchase decisions. 5.1 Punishment of a single-time deviation In the spiit of section 3 (whee the mechanism compensates fo the initial loss), we can deive a mechanism that discounts the futue gains if a selle deviates once fom poviding q. Suppose fom the initial peiod, the selle povides quality q till peiod t, then she deviated and povides a quality q (1) (q (1) < q), afte that, she etuns to povide quality q fo all the following ounds. The net pesent value of no deviation is [p p (q) c(q)] 1+, when deviated to povide q (1), the selle will ean p p (q) c(q (1) ) in this ound. The mechanism should discount he futue pemium afte the deviation by paying he less money than p p (q) even when she povides q fom then on. Let the discounted pice be p (1) (q), then he net pesent value is [p(1) (q) c(q)]. A deviationpeventing mechanism will make it not wothwhile to deviate, so: [p p (q) c(q (1) )] + p(1) (q) c(q) [p p (q) c(q)] 1 + ; then p (1) (q) c(q)+[c(q (1) ) c(q 0 )] p (1) (q) is smalle than p p (q), when the selle milks he eputation, she can no longe ean the same pemium of high quality, instead, although she is still poviding a highe quality q, she is punished to only chage at a pemium of q (1). (Notice the fom of p (1) (q) is exactly the same as that of p p (q) except that c(q) is eplaced by c(q (1) ) in the pemium tem.) The cente can simply choose to enfoce p (1) (q)=c(q)+[c(q (1) ) c(q 0 )] (2) in equilibium, and the stategy to deviate is weakly dominated. 5.2 What if the selle deviates again? Afte the fist deviation, the selle has aleady been punished, and can only chage a lowe pemium (offeing a elatively high quality q); if she deviates again in some

6 5 One-Round Deviation fom Equilibium 6 ound by offeing a quality q (2), she will be punished again. Adopting ou discounting mechanism and following the same line of easoning, we have: [p (1) (q) c(q (2) )]+ p (2) (q) c(q) =[p (1) (q) c(q)] 1+ ;sop (2) (q)=c(q)+[c(q (1) )+c(q (2) ) c(q) c(q 0 )]. Easy to deive that afte t times of deviation, the pice will be: p (t) (q)=c(q)+[ t i=1 (q (i) epesents the quality of the ith deviation). c(q (i) ) (t 1)c(q) c(q 0 )] (3) 5.3 What if the selle deviates to povide a highe quality than q? Suppose in one cetain ound i, the selle offes a high quality q (q > q), and still chages the pice as if offeing q. She must have incued loss in this ound, so the buyes will vote a R i > 1, this can be viewed as a good-will action to establish eputation, and should cetainly be ewaded by a futue pemium. In vigoous fomulation: (suppose she was chaging p(q) in the pevious ound) [p(q) c(q )] + p (q) c(q) = [p(q) c(q)] 1+ ;so p (q)=p(q)+[c(q ) c(q)] (4) The fomula is vey intuitive if viewed togethe with the milking case. Notice (2) can be witten as p (1) (q)=p p (q)+[c(q (1) ) c(q)], we can conclude the ule fo awading(o punishing) positive(o negative) deviations. 5.4 The law of deviation Afte the initial phase, if the selle does not deviate, she will chage a pemium pice p p (q), which she can chage till she deviates. When she deviates, she will be chaging some othe pice p (q), which she can also chage till foeve until she deviates again. So wheneve the situation meets the case that: 1. The long-tem expected quality is q; 2. Cuent pice is p(q); 3. Deviation in some ound to q ; We can have the futue equilibium pice as p (q)=p(q)+[c(q ) c(q)] (5) Adopting this mechanism, it can be ensued that in each step, the pice is competitive and eflecting a quality pemium. So no matte how the quality will change, all the futue pofits will be affected in such a way that the selle won t be bette off by deviating.

7 6 Selle Masqueading Multi-Round Deviation fom Equilibium In the pevious deivation of moe-than-once deviation, we have an implicit assumption that the selle will eventually poduct quality q, no matte she deviates to poduce a lowe quality q L o a highe quality q H, ou mechanism will always make sue that she will be punished o compensated in the long un. howeve, one possibility of deviation is that she deviates to some quality then neve poduce q again. In this case, we can easily show that she won t be bette off following this kind of stategy. Suppose she deviates to offe q L fo all the following ounds: each time she deviates, she will be punished by discounting all he futue pices. Since the pice is bounded below by p(q 0 ), she will each that point eventually. As long as she wants to sustain the business, she needs to offe q till infinity when she eaches the pice p(q 0 ), othewise, he pice will dop below p(q 0 ), and no one will eve buy fom he. Ty to oscillate the quality won t make he bette off, because each compensation and punishment is made to affect all he futue benefits. Fom the beginning of any ound, she faces a fai pice decided by (5): p (q)=p(q)+[c(q ) c(q)], and when she deviates, she will have anothe fai pice in the beginning of the next ound. 6 Selle Masqueading Given the pevious mechanism, the selle can enjoy a pofit compensating he loss in the initial peiod of eputation establishment. The selle won t have incentives to deviate by offeing low quality in some ounds, o to oscillate between peiods. Thee is still one way fo the selle to ean a positive pofit by cheating. She can simply buy fom heself in one cetain ound, and vote a vey high value (o bibe some buyes to vote a vey high value fo he). The maximum she can get though this pocess would be he poducing q 0 3 in all ounds and voting as if eceived q m in the masqueading ound. Since she is poducing q 0 in all the ounds, he one-time vote will let he enjoy a futue pemium. Applying (5), we have p (q 0 )=p(q 0 )+[c(q m ) c(q 0 )] = c(q 0 )+[c(q m ) c(q 0 )] 4, and the gain fom cheating will be [c(q m ) c(q 0 )]. Thee is one way to dete selle masqueading, the cente can chage a tansaction fee fom the selle. The tansaction fee will be a makup above the competitive pice, since the buyes enjoy all the suplus in this maket, so if the tansaction fee is not too high, they will still be willing to pay above the competitive pice. If a selle masqueades, she has to pay fo the tansaction fee heself, while if a selle is honest, she does not incu this cost. Let the cente announce a pecentage tansaction fee ate δ, when a deal is made at a pice p, the cente will chage δ p. The aim of this tansaction fee ate is to make the selle not pofitable by masqueading. So the cost of δ p 0 should exceed the gain of [c(q m ) c(q 0 )]. Soδ p 0 [c(q m ) c(q 0 )]. Using the fact that p 0 = c(q 0 ), we have δ c(q m) c(q 0 ) c(q 0 ) = ( c(q m) 1) (6) c(q 0 ) 3 thee is no meaning to poduce a highe quality, as we have showed that she has to keep poducing it in the long un. In fact, it makes no diffeence fo he to choose any quality as the mechanism ensuesex ante zeo pofit and fai pice whatsoeve. 4 The cente just takes the vote at the face value, and calculate a new pice fo the next ound.

8 7 Model Refinement 8 The tansaction cost ate can be small when quality dispesion is small, o when the pe-peiod inteest ate is small. In the case that thee is no quality uncetainty, when q m = q 0, the tansaction cost can be 0. Fo most of the goods sold online, the selling-cycle is shot, anging fom seveal hous to seveal days. Take annual inteest ate as 5%, the can be vey small. Fo a good with selling-cycle of 1 week, is This leaves a vey lage leeway fo quality dispesion: with a 10% tansaction fee ate, we can dete selle masqueading in a maket whee costs of poducing high quality goods ae 10, 000 times highe than that of poducing low quality ones. 7 Model Refinement Poweful though the model to dete selle-deviation, it equies the cente to have additional knowledge of the selle s cost function. In equation (1), the futue pice is updated with the knowledge of the costs of both the expected quality and the eceived quality. Since the mechanism is only looking fo a "fai" justification of the selle s deviation fom poviding the expected quality, we can futhe develop an algoithm to implement the mechanism without the pesence of costs. In the following algoithm, we assume a pice-quality schedule is always available to the cente. 5 The cente keeps tack of the eal quality q s fom pevious peiods to estimate an expected quality fo the next peiod. The teatment is equivalent to that of the case that the selle announces a pojected quality fo the next peiod, and the cente takes the face value of the announcement as the expected quality. The mechanism will ensue any mis-epot o mis-estimation will be coected in the futue ounds. Any mismatch between the expected quality and the ealized quality will be eflected in a cumulative value we call good-will. Wheneve the selle povides a highe-than-expected quality, she is building up good-will, the cente will compensate he, though the mechanism, in the infinite hoizon. 7.1 The Algoithm In eality, usually we don t have the infomation of the cost of a given quality fo a cetain poduct. But in a competitive maket, the pice-quality schedule is often clea. Fo a given quality q, we can find the pice p(q) fom the schedule. When a poduct is expected to be of quality q, then the expected pice should be p = p(q). If, instead, the poduct is chaged at p = p(q ), the diffeence between p and p is the loss (in the case of p <p) o the gain (in the case of p >p) of the selle, so should be compensated(o punished) in the futue ounds. The algoithm then calculates a cumulative "good-will" value afte each deviation and add it to all futue pices to eflect the compensation o punishment. Instead of using a fixed expected quality to detemine the futue pices, we update the expected quality heuistically with the expected quality of last peiod and the eceived eal quality fom last ound. 5 Fo example, the cente can always check the pice in the bick-and-mota maket.

9 7 Model Refinement 9 Table 6-1: The Algoithm of Goodwill Hunting [Initialization] Set Initial Goodwill GW 1 = 0 Set Initial Expected Quality E(Q 1 )=q 0 Set Initial Reputation R 1 = q 0 [Iteation] (t=1...t) Post Reputation R t Tanact and Receive Pice P(R t ) Get Feedback F t Lean Tue quality Q t = F t R t Discepancy P = P(Q t ) P(R t ) Adjust Goodwill to eflect GW t+1 = GW t + P compensation/punishment Adjust Expected quality E(Q t=1 )=α E(Q t )+(1 α) Q t fo next peiod Adjust Reputation to eflect R t+1 = P 1 (P[E(Q t+1 )] + GW t ) compensation/punishment 7.2 Justifications of the algoithm The cente could compensate (o punish) the selle in the immediate finite hoizon, say T peiods. But this will make the eputation too biased fom the eal quality. In the case of compensation, the immediate T buyes would bea a too high cost of paying the selle without eally enjoying a wothwhile bette quality; in the case of punishment, the immediate T buyes would enjoy a vey high suplus, stange stategies such as buying fom tash selles will aise, and this will futhe affect selles behavio and tend to induce deviation to a wose quality to encouage futue sales. In the algoithm, the fom of E(Q t+1 ) is a function of Q t and E(Q t ). Thee ae two exteme ways of estimating E(Q t+1) : 1. As the deivation in section 5,we take the quality in ound 1 as the ultimate quality in the infinite hoizon, (this is the same as teating all the quality fluctuations as deviation fom some selle-announced quality). Then the update ule P[R i+1 ]=P[E(Q i+1 )+GW i ] is only changing in GW i, when good-will is small 6, a deviation can not be eflected in the eputation vey pomptly. In the case of selle stating to povide vey high quality goods in consecutive ounds, it will take a long time (many peiods) to actually build the good-will value high enough to eflect the change; in the case of selle stating to milk the quality fo many ounds, it will also take a long time fo the pice to eflect the change in quality. 2. Nonetheless, the cente can simply set the expected quality as the eal quality fom last ound. This way, when a selle deviates, the eputation in the next 6 if is vey small, which is often the case, then GW i is bound to be vey small.

10 7 Model Refinement 10 ound will immediately show the change, this is undesiable in a maket that a selle s quality fluctuates too often in both positive and negative diections. So the fom of E(Q t+1 ) should be elated to the chaacteistics of paticula makets. When the selles tend to deviate towad one diection, (i.e. building o milking goodwill fo consecutive ounds), we should set E(Q t+1 ) close to case 2, and let α be close to 0 7. On the othe hand, when the selles tend to fluctuate the quality a lot, we need to set α to be close to 1. This will aveage out the peaks of fluctuation, and gives a elatively stable expectation of the quality. 7 α = 0 is the case of E(Q t+1 )=Q t.

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