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An Incentive Mechanism Designed for E-Marketplaces with Limited Inventory Yuan Liu and Jie Zhang School of Computer Engineering, Nanyang Technological University, Singapore Abstract In electronic marketplaces, reputation systems and incentive mechanisms are prevalently employed to promote the honesty of sellers and buyers. In this article, we focus on the scenario in which the inventory is in short supply, i.e. an e-marketplace with limited in- ventory (EMLI). The challenges are in two-fold: (a) for sellers who aim to maximize their profit, they may intentionally conduct dishonest transactions since the limited products are likely to be sold out regardless of their reputation; (b) for buyers who intend to gain the limited products, they may provide untruthful ratings to mislead other buyers. To address these issues, we propose an incentive mechanism to promote buyer and seller honesty for this type of e-marketplaces. Specifically, the mechanism models the honesty of buyers and sellers as scores and reputation, respectively. It then oers a higher price to the products of more honest sellers (with higher reputation) and allocates the products to more honest buyers (with higher scores). In this way, both sellers and buyers are well encouraged to be honest. Furthermore, we impose proper membership fee on new sellers to cope with the whitewashing attack. We finally theoretically analyze and empirically demonstrate the ecacy of the proposed mechanism and its nice properties. Keywords: Incentive mechanism, buyer and seller honesty, electronic marketplaces, limited inventory 1. Introduction In e-marketplaces, buyers and sellers conduct transactions through the electronic me- dia, such as the Internet. Along with the convenience that e-marketplaces bring, the lack of trust and reliability has been frequently criticized as one of the key factors that dis- courage buyers from participation. A reputation system, aggregating the ratings shared by the buyers with whom the sellers ever conducted transactions, is an eective way to help the buyers choose a reliable transaction partner (seller) (Mui et al., 2002a,b), even Preprint submitted to Electronic Commerce Research and Application November 7, 2013 *Manuscript Click here to view linked References

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Page 1: An Incentive Mechanism Designed for E-Marketplaces with ... · An Incentive Mechanism Designed for E-Marketplaces with Limited Inventory Yuan Liu and Jie Zhang Schoolof Computer Engineering,Nanyang

An Incentive Mechanism Designed for E-Marketplaces withLimited Inventory

Yuan Liu and Jie Zhang

School of Computer Engineering, Nanyang Technological University, Singapore

Abstract

In electronic marketplaces, reputation systems and incentive mechanisms are prevalentlyemployed to promote the honesty of sellers and buyers. In this article, we focus on thescenario in which the inventory is in short supply, i.e. an e-marketplace with limited in-ventory (EMLI). The challenges are in two-fold: (a) for sellers who aim to maximize theirprofit, they may intentionally conduct dishonest transactions since the limited products arelikely to be sold out regardless of their reputation; (b) for buyers who intend to gain thelimited products, they may provide untruthful ratings to mislead other buyers. To addressthese issues, we propose an incentive mechanism to promote buyer and seller honesty forthis type of e-marketplaces. Specifically, the mechanism models the honesty of buyers andsellers as scores and reputation, respectively. It then offers a higher price to the productsof more honest sellers (with higher reputation) and allocates the products to more honestbuyers (with higher scores). In this way, both sellers and buyers are well encouraged tobe honest. Furthermore, we impose proper membership fee on new sellers to cope withthe whitewashing attack. We finally theoretically analyze and empirically demonstrate theefficacy of the proposed mechanism and its nice properties.

Keywords: Incentive mechanism, buyer and seller honesty, electronic marketplaces,limited inventory

1. Introduction

In e-marketplaces, buyers and sellers conduct transactions through the electronic me-dia, such as the Internet. Along with the convenience that e-marketplaces bring, the lackof trust and reliability has been frequently criticized as one of the key factors that dis-courage buyers from participation. A reputation system, aggregating the ratings sharedby the buyers with whom the sellers ever conducted transactions, is an effective way tohelp the buyers choose a reliable transaction partner (seller) (Mui et al., 2002a,b), even

Preprint submitted to Electronic Commerce Research and Application November 7, 2013

*ManuscriptClick here to view linked References

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though the negative ratings cannot be regarded as the evidences of punishing the dishonestsellers by law (Wang and Singh, 2006). In order to be chosen by many buyers, the sellershave to maintain high reputation by delivering promised products, given that the ratingsprovided by the buyers can truthfully reflect sellers’ behavior in the transactions. Thus,reputation systems can effectively elicit seller honesty in delivering products. However,the buyers may provide untruthful ratings to promote some low quality sellers or demotesome high quality sellers. To address this issue, incentive mechanisms, e.g. (Jurca, 2007;Wang and Vassileva, 2007; Zhang and Cohen, 2007; Zhao et al., 2011; Phoomvuthisam,2011), have been designed to elicit truthful ratings from buyers so that the reputation sys-tems can work properly.

One common and implicit assumption in the reputation systems and incentive mecha-nisms is that sellers can provide a large number of products compared to buyers’ demand.However, in some realistic scenarios, the supply of sellers cannot satisfy the demand of allthe buyers. For example, the dentist booking in U.S., as a marketplace, has been observedthe phenomenon that there are more dentist bookings than the number of dentists (Collier,2009). Another example is the hotel booking system for a famous tourism area during apeak season since booking a satisfactory hotel is often difficult. Similar marketplaces alsoinclude second-hand marketplaces where some used and workable goods (e.g. textbooks)are often in short supply due to lower prices. There are two common properties of thesemarketplaces: (a) each seller has limited inventory, e.g. the number of dentists, rooms of ahotel, and used textbooks, to provide within a unit of time; (b) buyers compete with eachother so as to purchase one piece of the inventory. We define such a marketplace as ane-marketplace with limited inventory (EMLI). More generally, this concept is applicable toan e-marketplace where only a few sellers could provide promised products. In this article,for simplification and clarification, we focus on the e-marketplaces with limited inventoryin the narrow case where the supply is less than the demand and leave the general scenariofor future investigation.

New challenges are imposed on promoting buyer and seller honesty in an EMLI. Sell-ers with limited inventory, given that other sellers also hold limited inventory compared tobuyer demand, may behave maliciously in their transactions to gain more profit, by not de-livering promised products or reducing the quality of delivered products. Given that theirreputation will be decreased due to negative ratings from buyers cheated by them, the sell-ers may still be willing to increase their profit by sacrificing their reputation. Even thoughthe sellers can attract more buyers by sustaining higher reputation, they can only providethe limited inventory which disables them from benefiting as much as in the e-marketplacewhere the supply outweighs the demand. Therefore, in these e-marketplaces, reputationitself may not be effective enough to motivate sellers to behave honestly. Moreover, buyersmay also have incentives to report untruthful ratings. After a successful transaction with

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a seller, the buyer knows that the particular seller is good. If the buyer provides a truthful(positive) rating about the seller, then other buyers considering the positive rating are morelikely to conduct transactions with the good seller which reduces the buyer’s opportunityof doing business with the particular seller in the future, due to the limited inventory thatthe seller has. If the transaction is unsuccessful, reporting a truthful (negative) rating alsoreduces the buyer’s opportunity of doing business with other good sellers because otherbuyers will be less likely to do business with the bad seller but with the other good sellers,after taking the buyer’s advice. Thus, buyers may lose their chance to purchase productsbecause of providing truthful ratings. In other words, in the EMLI, providing truthful rat-ings is costly for buyers. The existing incentive mechanisms seldom consider these costsimposed on providing truthful ratings, which is demonstrated in Section 6.2.4 by applyingone representative incentive mechanism, i.e. side-payment incentive mechanism (Jurca,2007), in EMLI.

In this article, we propose an incentive mechanism to promote buyer and seller hon-esty together with a reputation system1 for e-marketplaces with limited inventory, whichovercomes the above-discussed challenges. In our mechanism, buyer honesty is measuredby a normalized proper scoring rule, making sure that a buyer can and only can gain max-imal scores by providing truthful ratings. Seller honesty is measured by the reputationsystem that aggregates ratings provided by buyers (weighted based on the buyers’ scores)such that honest sellers are able to gain high reputation. Our mechanism also consists of apricing algorithm and an allocation algorithm, making sure that: (a) the products of sellerswith higher reputation are offered with a higher price; (b) buyers with higher scores havemore opportunities to conduct transactions with more reputable sellers. Thus, both sellersand buyers can benefit from behaving honestly. In addition, to make the mechanism robustagainst the whitewashing attack where dishonest buyers or sellers may leave the market-place and rejoin using a new identity to erase their bad history, we discuss how to initializebuyer scores and seller reputation for new buyers and sellers and properly determine themembership fees for new sellers. The properties of our mechanism have been theoreti-cally analyzed in terms of individual rationality, incentive compatibility, and social wel-fare. Finally, we conduct experiments to validate the proposed mechanism, and comparethe performance of our mechanism with a classical (side-payment) incentive mechanismin e-marketplaces with unlimited and limited inventory respectively, to demonstrate thewider applicability of our mechanism.

The rest of the article is organized as follows. Section 2 summarizes the related work.In Section 3, our system environment is specified by explicitly listing the assumptions andclearly defining the concept of e-marketplaces with limited inventory. Section 4 presents

1The reputation system is included as a part of the proposed incentive mechanism.

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the proposed incentive mechanism. Section 5 is devoted to the theoretical analysis of theproperties of the proposed mechanism. In Section 6, a set of experiments are conducted toevaluate the efficacy of the proposed mechanism. Finally, Section 7 concludes the articleand discusses future research directions.

2. Related Work

The problem where buyers may provide untruthful ratings to promote or demote somesellers has been acknowledged by many researchers in the literature of trust research(Wang and Vassileva, 2007; Zhang and Cohen, 2008; Phoomvuthisam, 2011). In this sec-tion, we first summarize related work proposed in the area of incentive mechanism designto address the problem. We then discuss the limited studies about EMLI of our concern.

Several incentive mechanisms for eliciting truthful ratings from buyers have been pro-posed. Jurca proposed a side-payment incentive mechanism (Jurca, 2007) where truthfullyproviding ratings is buyers’ optimal strategy. In the mechanism, buyers would gain someamount of side payment if their ratings coincide with the refereed raters. Since buyerscould gain the maximal expected side payment through providing truthful ratings, theyhave incentives to be honest. Furthermore, Jurca and Faltings (Jurca and Faltings, 2009)developed an enhanced version of the side payment mechanism such that it can achievethe minimal cost imposed on the marketplace owner and discourage agents from conduct-ing the collusive attack where three pure collusive strategies were considered: all positiveratings, all negative ratings, and opposite ratings. The reward scheme (side-payment) wasobtained by solving a linear optimization problem, subject to certain constraints, e.g. eachhonest buyer could achieve the maximal and non-negative utility.

The credibility mechanism (Papaioannou and Stamoulis, 2010) is another type of in-centive mechanisms which punish dishonest buyers and sellers. It required both buyersand sellers to submit ratings on the performance of each other in their mutual transactions.The credibility of buyers and sellers were modeled to indicate their honesty. If the tworatings submitted for a transaction was disagreement, then both the buyer and the sellerwere punished and prevented from conducting transactions for some period which was in-versely determined by their credibility, i.e. the number of period of not allowing to conducttransactions was smaller if the agent was more credible, and vice versa. The punishmentis reasonable, because such a pair of disagreed ratings signals that one of them is lyingand the less credible agent is more likely to be the one who lies and deserves the morepunishment.

Furthermore, a trust-based incentive mechanism was proposed (Zhang et al., 2012).In this mechanism, a community is organized by a buyer who selects some trusted otherbuyers to be his advisors. An honest buyer is then more likely to be selected as advisors by

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many other buyers. On the other hand, honest sellers would prefer to provide some extraprofit, i.e. lower prices or higher quality products, to the honest buyers (advisors), as theseadvisors will be helpful to reveal and propagate the trustworthiness of the honest sellerssuch that the sellers can attract more buyers to purchase their products. As a result, buyerswould have incentives to provide truthful ratings to gain the chance of obtaining the extraprofit offered by the honest sellers.

In the existing incentive mechanisms discussed above, there is a common and implicitassumption that sellers have a large number of products to sell compared to the demand ofbuyers, and sellers can gain more profit from sustaining a good reputation given truthfulratings provided by buyers. However, in an e-marketplace with limited inventory (EMLI)where the supply is in short, the sellers may not concern much about the amount of sales,thus the reputation itself may not be effective enough to motivate the sellers to be honest(Ramezani et al., 2011; Zhang, 2009). In addition, as discussed in Section 1, buyers willhave to bear additional cost for providing truthful ratings in an EMLI because of compe-tition from other buyers on the limited inventory. Considering the competition cost andthe property of an EMLI, the side-payment, credibility and trust based incentive mecha-nisms may fail to work. For the side-payment mechanism, the side-payment gained fromproviding truthful ratings is likely to be offset by the additional cost; for the credibilitymechanism, the punishment over sellers by not allowing them to participate in the market-places for some periods will decrease the already limited products served in the market-place, which is not applicable in an EMLI; for the trust-based incentive mechanism, honestsellers may lack the incentive to offer discount to honest buyers (advisors) as their limitedproducts are likely to be sold out without the help of the honest advisors in propagatingthe seller’s good reputation among their community.

The wage-based incentive mechanism (Zhao et al., 2011) for P2P file sharing reputa-tion systems, where agents report feedbacks for other agents about file download/sharingtransactions, explicitly considers the effort or cost exerted by agents, i.e. time and hard-ware resources consumed in reporting feedbacks, as part of agents’ payoffs. The authorsmodeled the process of sharing feedbacks as a reporting game between a reporter and aquerist where the payoff of the reporter contains the cost function in reporting feedbacks.The optimal wage contract (payment protocol) was designed through solving an optimiza-tion problem so as to minimize the total payment subjective to some constraints, whichis similar to (Jurca and Faltings, 2009). However, the cost caused by the competition be-tween agents is still not included in the model. Considering the competition cost in anEMLI, the result of the optimization problem may be different, since the problem strictlyrelies on the specific form of the cost function. Moreover, the competition cost in shar-ing feedbacks is difficult to explicitly and quantitatively modeled. Thus, a new incentivemechanism needs to be designed specifically for an EMLI.

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For an EMLI, the way that a seller could increase its profit is to sell every singleproduct at a higher price. In our mechanism, honest sellers are offered higher prices fortheir products than dishonest sellers. This idea of the price premium is well supportedby economics studies. Empirical evidence reveals that prices of products sold by hon-est sellers are generally higher (Mai et al., 2010; Standifird, 2001). Buyers’ purchaseintention of buying products from high reputation sellers would not be affected by theprice premium, as the risk of the buyers will be decreased by conducting transaction withthose reputable sellers (Choe et al., 2009; Houser and Wooders, 2006). A dynamic pric-ing agent (Ramezani et al., 2011) was designed to increase product prices when sellershad limited inventory, following the rule of supply and demand in economic theory. Theirpurpose is to maximize the utility of sellers. In contrast, in our work, we increase productprices to create incentives for sellers to be honest.

One of the limited studies about EMLI in the literature (Noorian et al., 2012) considersthe impact of the limited inventory provided by sellers in the design of the optimal report-ing strategy for buyers. Because the amount of products provided by sellers are limited,buyers are in competition to purchase the products and their optimal reporting strategy isto only provide truthful ratings to other honest buyers (advisors) and untruthful ratings todishonest buyers. The optimal strategy can effectively balance between the competitionamong buyers and the discovery of good sellers. It also indicates that truthful ratings inthe EMLI are challenging to be elicited from all the buyers. Our incentive mechanismproposed in this article aims to address this challenge.

3. Assumptions

For the purpose of simplicity and clarity in presenting our proposed incentive mecha-nism, we first make the following assumptions:

(a) No difference between promised products: In the e-marketplaces, the products promisedby different sellers are assumed to be identical so that buyers will experience sametransactions if the products are honestly delivered by different sellers. In other words,the different transaction results are due to difference in the seller honesty, rather thanthe difference between the products. For example, the digital products provided bydifferent retailers are indifferent for buyers as long as they have the same function-ality (Haring, 2003). The buyers in such marketplaces could experience differentlyeven if the products are identical, since some sellers behave honestly by delivering therequired products on time and others may lingeringly or never deliver. By setting thisassumption, in this article, we focus on the impact of seller honesty on the transactionresults, by neglecting the context information of the products.

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(b) No subjectivity in providing ratings: Buyers have the same evaluation criteria in pro-viding ratings. Specifically, given a transaction where sellers behave honestly, anyhonest buyer will provide a positive rating and any dishonest buyer on the other handwill provide a negative rating, and vice versa.

(c) One inventory per transaction period: Each seller can only serve one piece of productwithin a transaction period. It requires the length of the transaction period to be prop-erly determined so that the number of products provided by a seller within a period isno more than one. For example, a dentist can only make one diagnosis within an hour,and in this case, a period is an hour.

(d) Buyers are able to afford the price of the required products: The candidate buyers inour mechanism are assumed to have the capability to pay for the required products. Inother words, the budget of buyers is out of our consideration. Several techniques canguarantee the achievement of this assumption. One is to allow buyers to submit theirmaximal acceptable prices together with their request, and the system would filterout those buyers whose acceptable prices are lower than the offered price. Anothertechnique is to publicize the maximal offered price such that only buyers who canaccept the maximal offered price can be the candidate buyers. In our analysis, wehave shown that the price of a product is upper bounded.

(e) Sellers are able to deliver the promised products: Sellers in the mechanism have thecapability of conducting a satisfactory transactions. In other words, sellers can manip-ulate their behavior or control their honesty in the transactions.

Based on the assumptions, we formally define the e-marketplaces with limited inven-tory as follows.

Definition 1. The e-marketplace with limited inventory (EMLI) Given a set of sellersS each of whom provides the same product and a set of buyers B each of whom demandsone piece of the products. An e-marketplace satisfying the condition, |S| < |B|, is called ane-marketplace with limited inventory.

4. Our Incentive Mechanism

The e-marketplaces employing our mechanism runs periodically. At the beginning ofeach transaction period, sellers post the products they want to sell and buyers post the re-quests specifying the products they want to buy. The e-marketplace center gathers togetherthe sellers who sell the non-difference products and the buyers who want to buy those prod-ucts. The products are in short supply, i.e. the marketplace is an EMLI. Thus some buyerswould not be able to gain the products that they want to buy. For those non-differenceproducts, their prices will then be determined by the e-marketplace center and be allocated

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to some buyers. At the end of each transaction period, buyers who have been successfullyallocated products can provide ratings in [0, 1] for sellers from whom the buyers boughtproducts, reflecting the honesty of sellers in their transaction, i.e. the satisfactory level ofa buyer towards a seller by comparing the actually experienced transaction with what theseller promised.

Modelingbuyer

honesty

Modelingseller

honesty

Allocation

algorithm

Pricing

algorithm

Buyerhonesty is

promoted

Sellerhonesty is

promoted

Seller reputation

Buyer

ratings

Buyer

honesty+

Buyer

scoresSeller

reputation

Transactions

Figure 1: The relationships between the main components of our incentive mechanism

As the central component of the e-marketplace, our incentive mechanism is composedof a normalized proper scoring rule to model buyer honesty, a reputation model to evaluateseller honesty, a pricing algorithm, and an allocation algorithm, as shown in Figure 1.More specifically, in our incentive mechanism, we measure buyer honesty by a score andseller honesty by the reputation, which are updated after each transaction period. Buyerscore will be updated after the buyer submits a rating, according to the normalized properscoring rule. The normalized proper scoring rule makes sure that truthful ratings providedby buyers are awarded the maximum expected scores. Seller reputation is calculated by thereputation model which aggregates ratings of the seller provided by buyers. The pricingalgorithm sets higher prices for the products provided by sellers with higher reputation.The allocation algorithm ranks buyers according to their scores, and allocates products ofhonest sellers to buyers with highest scores. As a result, sellers prefer to behave honestly indelivering promised products to achieve higher prices for their products, and buyers intendto provide truthful ratings in order to receive products from honest sellers. Therefore, ourincentive mechanism can promote honesty from both buyers and sellers.

4.1. Modeling Buyer Honesty

In this section, we propose a class of normalized proper scoring rules to measurebuyer honesty, where buyers providing truthful ratings about sellers will be able to gain

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the maximum scores.Given a binary event with two outcomes e and e, p is the actual probability of the

outcome e and the actual probability of e is 1 − p. Let x be a predicted probability of theoutcome e, i.e. x predicates p. If the outcome of the event is e, then the agent havingpredicted the probability as x will be rewarded the scores S(x), whereas if the outcomehappens to be e, the agent will be rewarded S(1− x). The expected amount of the rewardedscores is calculated as E(S, x, p) = pS(x) + (1 − p)S(1 − x). The scoring function S(x) iscalled a proper scoring rule, if and only if E(S, p, p) ≥ E(S, x, p) and the equality is trueonly when x = p (Fang et al., 2010). Based on the concept of the proper scoring rule,we extend it to the normalized proper scoring rule. The reason why proper scoring rulescannot be directly used in our mechanism is that we aim to use scores to measure buyerhonesty which should be comparable, even when the scores are gained from transactionswith sellers having different honesty levels in delivering products.

Definition 2. Normalized Proper Scoring Rule S Given a proper scoring rule S, Max(p) =maxx E(S, x, p) and Min(p) = minx E(S, x, p), a normalized proper scoring rule is definedas S(x) = S(x)−Min(p)

Max(p)−Min(p) .

From Definition 2, normalized proper scoring rules are bounded in [0, 1]. It is also essen-tially observed that they inherit the properties of the proper scoring rules, that is E(S, p, p) ≥E(S, x, p), and equality is true only when x = p.

In order to further explain the definition, we give an example here. Suppose that abuyer is to predict the honesty of one seller in delivering promised products. We canadopt a quadratic scoring rule S(x) = −2x2 + 4x − 1 (Fang et al., 2010), and calculatethe maximum and minimum expected scores as: Max(p) = 2p2−2p+1 and Min(p) =min{1−2p, 2p−1}. According to Definition 2, the normalized proper scoring rule is:

S(x) =2x − (x2 + (1 − x)2) − min{1 − 2p, 2p − 1}

2p2 − 2p + 1 −min{1 − 2p, 2p − 1} . (1)

In our mechanism, the honesty of a seller s in delivering promised products is modeledby the seller’s reputation Rs, which will be introduced in detail in the next section. Thus,the probability of s being dishonest 2 is 1−Rs. At the end of the current transaction periodt, a buyer b involved in the transaction with seller s can provide a rating indicating thehonesty of the seller in the transaction. Once the rating is given, the buyer’s score towardsseller s will be updated, according to Equation (2). In consequence, the buyer’s overallscores towards all sellers will also be updated.

2The reputation of sellers is considered to be equivalent to and interchangeable with the probability ofthe sellers in providing products honestly.

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More formally, we first calculate the expectation value (denoted by rsb(t) ∈ [0, 1]) of

the distribution of the ratings provided by a buyer b towards a seller s until the transactionperiod t. The buyer b’s score towards seller s is measured as:

Rsb(t) = Rs(t − 1)S(rs

b(t)) + (1 − Rs(t − 1))S(1 − rsb(t)), (2)

where S is a normalized proper scoring rule, and Rs(t−1) is the reputation of seller s up tothe previous transaction period t − 1. We also count the total number of ratings given byb towards s, denoted as Ns

b(t). By weighted average of the scores towards different sellers,the buyer b’s overall score is:

Rb(t) =

∑s∈S Rs

b(t) × Nsb(t)∑

s∈S Nsb(t)

, (3)

where S is the set of sellers whom the buyer b has done transactions with before andprovided ratings for.

Proposition 1. Given a seller s whose reputation is Rs(t−1) up to the previous transactionperiod, a buyer b who buys a product from s can achieve the maximum amount of scoresby providing truthful ratings, if (1) S is a normalized proper scoring rule, and (2) Rs(t− 1)truly reflects the honesty of s in delivering promised products.

The proof of Proposition 1 is in Appendix A.

4.2. Modeling Seller Honesty

The honesty of a seller s is modeled by aggregating the ratings provided by buyers(who have conducted transactions with s), considering the buyers’ honesty in providingthem. More formally, at the end of the transaction period t, given the expected value rs

b(t)of the distribution of a buyer b’s ratings towards the seller s, buyer b’s score Rb(t) measuredby Equation (3), and the number of transactions Ns

b(t) between buyer b and seller s, thereputation value (in [0, 1]) of seller s can be calculated as:

Rs(t) = F(Rs(t − 1),Ns

b∈B(t),Rb∈B(t − 1), rsb∈B(t)

), (4)

where B is the set of buyers whom the seller s has conducted transactions with beforeand received ratings from, and Rs(t − 1) is seller reputation at the end of the previoustransaction period t − 1. F is a reputation model which can truly measure seller honestyin delivering promised products. In this paper, we do not specify the formation of F, sinceit is application dependent and many reputation modeling approaches have already beenproposed in the literature, such as (Mui et al., 2002a; Wang and Singh, 2006).

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4.3. Pricing and Allocating Products

In our mechanism, the pricing algorithm determines the prices for the products pro-vided by sellers and the allocation algorithm assigns the limited products to some of thebuyers. We assume that buyers’ valuation of the products is a random value chosen inan interval [V∗,V∗] where V∗ and V∗ are the maximum and minimum valuation of buyerstowards the products provided by sellers, respectively. We also assume that sellers havethe same cost C of producing the non-difference products, and V∗ > C making sure thatthe products are worthy of being produced.

As we analyzed in Section 1, sellers in the EMLI generally lack of the incentive tobehave honestly even with reputation systems employed, because reputation informationabout sellers cannot impose competition among sellers in the EMLI. Sellers with rela-tively low reputation can still have the chance to do business with buyers because of thelimited available products in the markets. The consequence is that sellers will decreasethe probability of delivering the products (also reputation) to the point where buyers’ util-ity is minimized (i.e. approaches 0) and at the same time maximize their own profit. Inour mechanism, the pricing algorithm associates sellers’ profit with their behavior. Morespecifically, it offers higher prices to products of sellers with higher reputation. In this way,it creates incentives for sellers to behave honestly. At the same time, the pricing algorithmmakes sure that buyers can gain positive utility which motivates the buyers to participatein the EMLI.

In our pricing algorithm, product prices are determined by a pricing function P(Rs),where Rs is seller reputation modeled by Equation (4). The pricing function should sat-isfy some basic requirements: (a) P(Rs) > 0 for Rs ∈ (0, 1]; (b) P(0) = 0; (c) P(δ) = C;(d) dP(Rs)

dRs> 0; (e) P(R0) = R0 × C. Requirement (a) ensures that the price set for sellers

with positive reputation is still positive. In the extreme case where sellers never deliverproducts at all, the price for the sellers’ products should be set 0 as in requirement (b). Inrequirement (c), δ is a reputation value set by our mechanism so that the price of productsprovided by sellers with reputation δ is exactly equal to the cost C, and δ is called cost-price reputation. Also, the price should increase with seller reputation by satisfying re-quirement (d) (i.e. it should be a monotonically increasing function), because sellers withhigher reputation bear higher expected cost for delivering the promised products. SinceP(0) = 0 and P(δ) = C, there should exist a reputation value R0 so that P(R0) = R0 × Cas in requirement (e), according to the continuity property of the pricing function P(Rs).Thus, when a seller’s reputation Rs = R0, the seller’s profit would be P(R0) − R0C = 0.In other words, R0 is the minimum reputation that sellers can gain non-negative profit andsellers with reputation lower than R0 will not be profitable. R0 is also called zero-profitreputation. The purpose of setting the zero-profit reputation is to disappoint those sellerswho intend to take advantage of the limited inventory situation by behaving dishonestly

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since sellers with reputation lower than R0 will generally leave the market.To come up with a proper but simple pricing function, we start with a linear function for

P(Rs), however it is impossible to satisfy all the basic requirements listed above. Thus, wechoose a quadratic function in the general form P(Rs) = αR2

s +βRs +γ. Given requirement(b), we have γ = 0. Given requirements (c) and (e), we can derive α = C(1−δ)

δ(δ−R0) and β =C(δ2−R0)δ(δ−R0) . According to requirement (d), we can also derive that 2aRs + b > 0, which can

be satisfied by setting the constraint δ ≥ √R0. The pseudo code summary of the pricing

algorithm is shown in Algorithm 1.

Algorithm 1: The Pricing AlgorithmInput : S , a set of sellers offering the products;

Rs, reputation of a seller s ∈ S before the current transaction period;C, δ, R0, which are introduced above;

Output : P, the price for a seller’s product;

α =C(1−δ)δ(δ−R0) ;1

β =C(δ2−R0)δ(δ−R0) ;2

foreach s ∈ S do3

Ps = P(Rs) = αR2s + βRs;4

In addition, our pricing algorithm has two nice properties. The first property is thatbuyers’ utility is positive when R0 and δ are set so as to satisfy the conditions in Propo-sition 2 in Section 5. The second property is that buyers who conduct transactions withsellers having higher reputation will be able to gain larger utility even though the pricesare higher due to the lower risks in conducting transactions with those reputable sellers(see Proposition 4). Therefore, buyers are willing to buy products from sellers with higherreputation (see Proposition 4). Due to the first property and the fact that not all buyerscan be allocated with products (limited inventory), our allocation algorithm ensures thathonest buyers (i.e. buyers with larger scores) will have higher probabilities of being al-located with products. Due to the second property, we make sure that honest buyers willalso likely be allocated with products provided by sellers with higher reputation, so thathonest buyers will be able to gain more profit. These create incentives for buyers to behavehonestly by providing truthful ratings.

Following the two properties of the pricing algorithm, we come up with the allocationalgorithm whose pseudo code summary is shown in Algorithm 2. More specifically, thealgorithm sets an exploration factor η ∈ [0, 1]. All the available products are randomlydivided into two sets: S g taking 1 − η percentage and S r taking the other η percentage of

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Algorithm 2: The Allocation AlgorithmInput : B, buyers who want to buy products;

S , sellers offering the products;η, the exploration factor;

Output : Allocation of products to buyers;S g ← Randomly choose 1 − η percentage of S (products);1

S r ← The rest η percentage of S (products);2

Sort S g based on seller reputation in descending order;3

Sort B based on buyer scores in descending order;4

foreach s ∈ S g do5

Allocate product of s to top-ranked buyer b ∈ B;6

Remove b from B;7

foreach s ∈ S r do8

Allocate product of s to random buyer b ∈ B;9

Remove b from B;10

the products. S g will be allocated to the most honest buyers, i.e. the buyers with the largestscores. To be specific, these products are sorted according to their sellers’ reputation ina descending order. The buyers are also ranked in a descending order according to theirscores. The products are then allocated to the buyers one by one according to the orders,so that the products of sellers with higher reputation are allocated to the buyers with largerscores (see Lines 5-7 in Algorithm 2). Note that each buyer is allocated with one productin each transaction period. S r will be randomly allocated to some buyers (excluding themost honest buyers with the largest scores who have been allocated with the products inS g) (see Lines 8-10 in Algorithm 2). The parameter η provides a chance for the systemto “explore” honest buyers among the new buyers and the existing buyers who are notrecognized as being honest.

4.4. Initialization to Avoid the Whitewashing Attack

In this section, we discuss how to initialize reputation values and scores for new sellersand buyers, and at the same time avoid the whitewashing attack where buyers and sellerswith low scores and reputation values leave the marketplace and re-register as new buyersand sellers to clean their bad history, respectively.

For a new seller, since the system has no additional information to judge the seller’shonesty, initializing the reputation for the seller is tricky. If the initial reputation is set toohigh, existing sellers with lower reputation values will prefer to leave the marketplace and

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re-register as new sellers. On the other hand, if the initial reputation is set too low (e.g.lower than R0), new honest sellers will be discouraged to participate into the system be-cause their initial profit is negative according to the pricing algorithm. In our mechanism,we set the initial seller reputation as δ. New honest sellers will gain zero profit in their firsttransactions. If they act honestly in their transactions, they will be able to gain positiveprofit in their future transactions. However, existing sellers with reputation lower than δmay leave and re-enter the market. To prevent this phenomenon, we impose some amountof membership fee M = N0(M1 + M2) = N0C on new sellers, where M1 = (1 − R0)C,M2 = R0C, and N0 is the minimum number of transactions conducted by sellers so that thesystem can model the sellers’ reputation within a required confidence level σ or error rateε. The value of N0 can be determined by the Chernoff Bound Theorem (Mui et al., 2002a)as follows:

N0 =

⌈− 1

2ε2ln

(1 − σ2

)⌉(5)

where �·� is to convert a value to the closest integer that is larger than the value. Forsimplicity, the seller reputation Rs(t − 1) up to the transaction period t is denoted by Rs

by omitting the t − 1. Similarly, the buyer score is denoted by Rb. When sellers decide toleave the marketplace, the amount Mr will be returned back to the sellers, which is:

Mr =M(Rs) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩N0(M1 + M2) Rs > δ,

(Rs−R0δ−R0

)2N0M1 + N0 M2 R0 ≤ Rs ≤ δ,0 Rs < R0.

(6)

According to the proposed mechanism, the profit of the seller s in a transaction periodt can be formalized as:

Us = Us(Rs) = Ps − RsC, (7)

where Ps is the price calculated by Algorithm 1 for seller s, and C is the cost of seller sin producing the promised product. A buyer b’s utility of carrying out a transaction withseller s can be formalized as:

Usb = Ub(V s

b ,Rs) = RsVsb − Ps, (8)

where V sb is buyer b’s valuation for the product provided by seller s.

If a seller s whose actual reputation Rs ∈ (R0, δ) performs the whitewashing attack,the reputation of s is initialized to δ at the cost of M − Mr. The profit of s in the firstN0 transactions after re-entry is

∑N0t=1 Us(Rs(t)) �

∑N0t=1 P

(Rs(t)

) − N0RsC +M(Rs) − M <N0[P(δ) − RsC] +M(Rs) − M. If the seller s stays in the marketplace, the profit gained

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in the N0 transactions would be∑N0

t=1 Us(Rs(t)) = N0[P(Rs) − RsC]. Since M = N0Cand

∑N0t=1[Ur

s(Rs(t)) − Us(Rs)] < N0[M(Rs)/N0 − P(Rs)] when Rs ∈ (R0, δ), we concludethat M(Rs)/N0 − P(Rs) = [δ(δ − R0) + R0(1 − δ)](Rs − R0)(Rs − δ) < 0. It means thatsellers with reputation Rs ∈ (R0, δ) will gain smaller profit by re-entering. When Rs < R0,∑N0

t=1 Urs(Rs(t)) < N0(−RsC) ≤ 0. Thus, sellers with reputation Rs < R0 cannot gain positive

utility by re-entry. Thus, with the properly determined membership fee, the sellers whosehonesty is lower than the initial reputation value do not have the incentive to perform thewhitewashing attack. Since sellers with reputation higher than δ are obviously unwillingto perform the whitewashing attack by being initialized with lower reputation, the systemcan effectively get avoid of the whitewashing attack conducted by sellers.

For new buyers, we initialize their scores as zero. They still have the opportunity to beallocated with products because the allocation algorithm (Algorithm 2) randomly allocatesη percentage of products to buyers. Since the scores assigned to buyers are non-negativeaccording to Equation (7), any buyers who still want to buy products would never bewilling to clean their scores by re-entering the e-marketplaces.

We should note that the membership fee could incentivize sellers to keep staying inthe system, but cannot the exit problem where the agents would be dishonest in their lastseveral transactions and then permanently disappear from the system. The exit problem isa common challenge in the literature of TRS, which will be considered in future work.

4.5. An Example

To illustrate the proposed incentive mechanism well, we demonstrate it using a simpleexample. Suppose there are ten buyers b1 to b10, each of whom demands one product ineach period. There are six sellers s1 to s6, each of whom can supply one such productin each period. The system parameters are set as: C = 1, V∗ = 2, V∗ = 3, δ = 0.85,R0 = 0.6, η = 0.2, and N0 = 3 (calculated by Equation (5) where confidence level σ is 0.5and error rate ε is 0.5). After conducting a transaction, each of the buyers is required toprovide a binary rating. Among the ten buyers, the first five buyers (b1 to b5) are honest inproviding ratings, and the other five (b6 to b10) share 50% of their ratings honestly and theother 50% dishonestly (opposite to the true ratings). For sellers, the first two sellers (s1

and s2) always provide promised products and the second two sellers (s3 and s4) providepromised products at 70% (> R0, < δ), and the last two sellers provide promised productat 50% (< R0). The above described settings of buyers and sellers are clearly shown in thefirst two columns of Table 1.

Initially, the scores of buyers are set as 0 and the reputation values of sellers as δ =0.85. Each of the sellers is required to deposit M = N0C = 3 when they register into

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Table 1: The ExampleAgents Honesty Buyer Scores/ Buyer Utility/ Expected Utility

Seller Reputation Valuation Profit of Each Honesty Levelb1 1 0.95 2.37 1.13

1.03b2 1 0.95 2.65 1.41b3 1 0.95 2.47 0.97b4 1 0.95 2.68 0.86b5 1 0.95 2.35 0.79b6 0.5 0.45 2.22 1.10

0.22b7 0.5 0.45 2.22 0b8 0.5 0.45 2.60 0b9 0.5 0.45 2.46 0b10 0.5 0.45 2.47 0s1 1 0.98 – 0.24

0.24s2 1 0.98 – 0.24s3 0.7 0.69 – 0.03

0.03s4 0.7 0.69 – 0.03s5 0.5 0.49 – -0.05

-0.05s6 0.5 0.48 – -0.05

the system. We first bootstrap3 seller reputation by only allowing honest buyers (b1 to b5)to participate into the system for some periods. Suppose that seller reputation of the sixsellers becomes 0.98, 0.98, 0.69, 0.69, 0.49 and 0.48, after bootstrapping, respectively. Wethen allow dishonest buyers (b6 to b10) to participate into the system. Several periods later,we assume the score for the first five buyers is 0.95 and the other five buyers 0.45. Thebuyer score and seller reputation are recorded in the third column in Table 1.

At the beginning of the next period, each of the buyers requests a product from sell-ers. The system then runs Algorithm 1 to determine the price for sellers and executesAlgorithm 2 to allocate the products to some of the buyers. According to Algorithm 1(Ps = αR2

s + βRs, where α = 0.71 and β = 0, 58 calculated given the system parame-ters), the prices for the sellers are 1.24, 1.24, 0.73, 0.73, 0.45, and 0.44, respectively. InAlgorithm 2, the set of sellers first are randomly divided into two subsets: S r = {s3} andS g = {s1, s2, s4, s5, s6}. For S g, the sellers are sorted based on their reputation in a de-scending order (randomly break the tie), and the ranked order is assumed to be: s1, s2,

3The reason of bootstrapping the reputation of sellers is to accurately initialize the sellers’ reputationsuch that it can truthfully reflect the sellers’ honesty.

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s4, s5, s6. Meanwhile, the buyers are also sorted based on their scores in a descendingorder, and the ranked result is supposed to be: b1 to b10. The system first allocates S g

to buyers, according to the ranks. Specifically, the product provided by s1 is allocated tob1, and the product provided by s2 is allocated to b2, etc. Secondly, the system allocatesS r randomly among the buyers who have not been allocated with any product, i.e. b6 tob10, and s2 ∈ S r is allocated to one buyer, supposing b6. Assuming that the buyers havedifferent valuation towards the product, which follows a Gaussian distribution (2.5, 0.2) 4

in the interval [V∗,V∗], the valuations of the buyers are assumed to be as displayed in thefourth column of Table 1. Given this allocation, we calculate the utility of buyers andsellers according to Equations (8) and (7), which are listed as in the fifth column of Table1. In the sixth column, we calculate the average utility for each type of buyers and sellers.It shows that the average utility of honest buyers and dishonest buyers are 1.03 and 0.22,respectively. The average profit of the first two sellers is 0.24, and the second two sellers is0.03, where the profit of the four sellers are positive and increase as their honesty increases(0.24 > 0.03 > 0). Nevertheless, the average profit of the last two sellers is −0.05 (< 0),as their honesty is lower than the zero-profit reputation R0.

In this example, if a buyer, e.g. b6, leaves the system and registers under a new identity,then his score (0.45) will be initialized as 0. The allocation algorithm will then rank thebuyer at the last position so that the buyer ends up with less chance to get the productsfrom S g. For the first two sellers, if they leave, the system will return all the depositmembership fee (Mr = M) since their reputation is greater than the initial reputation(Rs > δ). However, their reputation will be initialized as δ = 0.85 which are lower thantheir current reputation values when they re-register as new sellers. Thus, they will loseprofit by reentering. For the second two sellers, their reputation is lower than the initializedreputation but larger than R0. If they leave, the system will return a part of the membershipfee Mr = 1.95 < M and they lose 1.05. When they re-register, their reputation is alsoinitialized as δ. However, the profit gained from reentering is less than N0(1−δ)C = 0.45 5

which cannot cover their loss (0.45 < 1.05) of leaving. For the last two sellers, they willlose all the membership fee when they leave. After reentering the system, the estimatedgain is still negative. Therefore, both buyers and sellers in the system have no incentivesto conduct the whitewashing attack.

4The mean of the distribution is equal to (V∗ + V∗)/2 = 2.5, and the standard deviation is 0.2.5After N0 transactions, the reputation value will truthfully reflect the honesty of the seller.

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5. Analysis of the Mechanism

In this section, we analyze the properties of the proposed incentive mechanism in termsof individual rationality, incentive compatibility, social welfare, and robustness againstvarious of collusive attacks. Moreover, the semantic meanings of parameters and the prac-ticability of the proposed mechanism are summarized

5.1. Individual RationalityIndividual rationality is a property describing an individual’s incentive to participate

in a marketplace. We show that both buyers and sellers can obtain positive utility in oursystem. In addition, the price is upper bounded for buyers and lower bounded for honestsellers, which assists both buyers and sellers in deciding whether to participate into oure-marketplaces in advance.

Proposition 2. The utility of a buyer gained in a transaction with a seller s is positive, if(a) the seller reputation satisfies Rs > R0, and (b) δ satisfies the following inequality:

δ > max{√

R0,V∗R0 − 2C +

√(V∗R0 − 2C)2 + 4C(V∗ − C)(2 − R0)

2(V∗ − C)}. (9)

The profit of a seller is positive if his reputation is greater than R0, and the profit is negativeif his reputation is less than R0, given that the inequality (9) is satisfied.

The proof of Proposition 2 is in Appendix B.1. In the proposed mechanism, the buyerscan always achieve positive utility given the two conditions being satisfied, which moti-vates them to participate into the marketplaces. The first condition requires that the buyersshould conduct transactions with sellers whose reputation is larger than R0, and the secondcondition provides a guide to set a proper δ. The interpretation of the parameters is sum-marized in Section 5.5. On the other hand, the sellers whose reputation is larger than R0

have incentives to participate into the system to achieve the positive profit. Nevertheless,those sellers whose reputation is less than R0 are discouraged to appear in the system orhave to improve their honesty to at least R0.

In addition, considering the assumptions (d) and (e) where buyers are able to afford theprice for a product and sellers are able to deliver the promised products, we now show inthe following proposition that the price for a product is upper bounded for buyers and theprice is lower bounded for honest sellers, which can assist buyers with limited budget andrational sellers to join the marketplace.

Proposition 3. The upper bound of the price for a product is CR0

, and the lower bound ofthe price for a product provided by an honest seller is C

δif the inequality (9) is satisfied,

where C is the production cost,

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The proof of Proposition 3 is in Appendix B.2. Since the prices of products are upperbounded by C

R0, the budget of buyers is required to be at least C

R0. To simplify our model

and focus on the incentive problem, we neglect the budget constraint problem by settingthe assumption (d) in Section 3. However, this upper bound indicates that this assumptionis not too strict to be satisfied. The case where some of the buyers are unable to affordthe price (< C

R0) is still valuable to be studied in the future work as discussed in Section

7. Meanwhile, the range of price for the products provided by honest sellers is betweenCδ

and CR0

where CR0> Cδ> C. Thus, the profit of honest buyers could always be positive

and they have the incentives to participate, and keep behaving honestly in the proposedincentive mechanism.

5.2. Incentive Compatibility

The incentive compatibility in our analysis is a property where each individual has theincentives to be honest, provided that others are also honest. In other words, being honestis a Nash equilibrium strategy. We show the incentive of buyers and sellers in this section,respectively.

5.2.1. Buyer incentiveProposition 4. The utility of a buyer in conducting transactions with a seller s increasesas the seller’s reputation Rs increases, if (a) Rs > R0, and (b) the inequality (9) is satisfied.

The proof of Proposition 4 is in Appendix C.1. The conditions in the proposition are thesame as those in Proposition 2, which indicates that buyers could achieve more utility byconducting transactions with sellers having higher reputation in spite of the higher pricecharged for the sellers’ products. The main reason of this phenomenon is that the higherprice of the products provided by more honest sellers is covered by the benefit that isobtained from the transaction with the honest sellers.

Proposition 5. The utility of a buyer who provides truthful ratings is no less than that ofa buyer who provides untruthful ratings.

The proof of Proposition 5 is in Appendix C.2. From the perspective of buyers, theycan obtain more utility from transactions with sellers who have higher reputation, andmeanwhile, they prefer to provide truthful ratings rather than untruthful ratings in orderto achieve the larger utility. In short, the proposed mechanism promotes buyer honesty inproviding truthful ratings.

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5.2.2. Seller incentiveProposition 6. Sellers have the incentives to improve their reputation by delivering promisedproducts.

The proof of Proposition 6 is in Appendix C.3. Therefore, from the perspective of sellers,they are profitable to be honest by delivering the promised products and building up theirreputation. In addition, rational sellers will not let their reputation become less than R0 elsetheir utility will become negative. To conclude, our mechanism promotes seller honesty indelivering promised products.

5.3. Social WelfareThe above analysis is discussed from the perspective of individuals (sellers and buy-

ers), and now we analyze the social welfare to evaluate the efficacy of the proposed mech-anism. We would only consider the social welfare created by the buyers and sellers intheir current transactions and future transactions. For the buyers without any allocatedproducts, they would cannot create loss or significant gain for the social welfare. Since theproducts are limited, some buyers will not be allocated with products in any way. Amongthese buyers, some of them who are dishonest and indicated by low score are deserved tobe punished by not being allocated with the products. Thus, the social welfare created bythem is not negative, but slightly positive by avoiding the limited products being allocatedto these dishonest buyers. The rest of these buyers may be honest often and have achievedrelative high scores, but not so high to be allocated with products. The social welfarecreated by these agents is also zero, as the products have been allocated to more honestbuyers or buyers with the same level of honesty. For this reason, we set the social value ofof all the agents who are not allocated with products as zero.

For a transaction happening between a seller s and a buyer b, the current social utilitybrought by them would be the sum of their utility. Since an honest buyer b always sharestruthful ratings to reveal the honesty of sellers, which is helpful for the system to elicitmore honest sellers, the system will obtain more future utility of the transaction conductedby the honest buyers (with a higher score). Therefore, the buyer score has the same effectas the discount rate in calculating the future social welfare, i.e. the higher the discountrate (buyer score) is, the more future social welfare could be expected. The total socialwelfare, including the future social welfare, is then equivalent to the welfare in the currenttransaction period multiplied by an additional factor 1

1−Rb. Thus, we can formalize the

social welfare of a transaction happening between seller s and buyer b as:

W(Rs,Rb) = (Us(Rs) + Ub(Rs))1

1 − Rb= Rs(V s

b −C)1

1 − Rb, (10)

where V sb is the valuation of the product provided by s, which is uniformly distributed

between V∗ and V∗.

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Proposition 7. The proposed incentive mechanism can increase the total social welfareas defined in Equation (10).

The proof of Proposition 7 is in Appendix D.1. The intuition behind this proposition isthat the social welfare will increase as both buyers and seller have the incentive to improvetheir honesty. Both the dishonest buyers and dishonest sellers are harmful for the socialwelfare. Since untruthful ratings provided by dishonest buyers will discourage sellers tobe honest and the dishonest sellers will increase the number of unsatisfactory transactions,the total utility created by the system will be decreased. In addition, as both buyers andsellers in the proposed system are motivated to behave honestly, the system will generallybecome a safer transaction platform, resulting in that more and more honest buyers andsellers will be attracted by the system in the long run.

In addition, supposing that the valuations of the products for buyers follow a certaindistribution which is independent of the buyer honesty, we are able to show that the socialwelfare achieved by our mechanism is actually no less than the free-trading marketplace.

Proposition 8. The social welfare of the proposed e-marketplace is no less than that ofthe free-trading e-marketplace.

The proof of Proposition 8 is in Appendix D.2. In this proposition, we compare the socialwelfare of the proposed system with that of the free-trading e-marketplace to show theefficiency of our mechanism. In the free-trading e-marketplace, the buyers and sellersinteract freely and have the same chance to conduct transactions. The main reason thatour mechanism can achieve higher social welfare is that we satisfy both honest buyers andsellers simultaneously, which creates higher future benefit for the system.

5.4. Robustness against Attacks

In Sections 4.4 and 4.5 we have shown that our mechanism can effectively addressthe whitewashing attack. In this section, we discuss the robustness of the mechanismagainst other general types of attacks. We consider two types of attacks: rational andirrational attacks. The agents conducting rational attacks aim to maximize their utility bybehaving dishonestly. The agents who conduct irrational attacks, on the other hand, attackthe system regardless of the cost. We first categorize the rational attacks and analyze therobustness of our mechanism against each of them. We then analyze how our mechanismwill be impacted by irrational buyers and sellers, respectively.

Rational attacks are categorized and analyzed as follows.

(a) Buyer uncoordinated attack: A buyer performs malicious behavior in order to maxi-mize his utility, without coordinating with other buyers or sellers.

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In our mechanism, buyer’s possible malicious behavior is to report untruthful ratings.Each buyer has incentive to provide truthful ratings so as to achieve a high score giventhat the seller reputation is accurate as claimed in Proposition 1. If seller reputation isnot accurate, then buyers may lose the incentive to provide ratings honestly. However,in this case, as long as the ranking of buyers in terms of their honesty is accurate,buyers are still incentivised to report honestly, since it is the order instead of the scoresused in our allocation algorithm.

(b) Seller uncoordinated attack: A seller delivers low quality products or does not deliverat all in order to maximize his utility, without coordinating with other sellers or buyers.As we analyzed in Section 5.2.2, each seller has incentive to improve his reputation sothat a higher price can be achieved for his products. If buyers report truthful ratings,then the seller can only improve his expected reputation by improving his honesty indelivering products. In other words, a rational seller has no incentive to conduct theseller uncoordinated attack.

(c) Buyer coordinated attack: A set of buyers coordinate their malicious behavior to max-imize their group utility.When buyers coordinately provide untruthful ratings to a seller such that the price ofthe products provided by the seller becomes low, the utility of the buyer group willincrease. However, the allocation is determined by the system which makes it impos-sible for the group of buyers to always conduct transactions with the attacked seller.Thus, our mechanism can effectively weaken the impact of the buyer coordinated at-tack. Nevertheless, as a large number of the buyers (even all the buyers) form a groupto attack a seller, the seller becomes non-immune to the attack. Therefore, our mech-anism can be robust against the buyer coordinated attack to an extent.

(d) Seller coordinated attack: A set of sellers form a group and cooperatively conductmalicious behavior to maximize their group utility.For an uncoordinated seller, as we analyzed, he has no incentive to misbehave. How-ever, for a group of sellers, such honesty incentive may be influenced. For example,the colluding sellers can cooperatively choose not to deliver products to a particularbuyer (discriminated buyer) but deliver promised products to all other buyers. As aresult, when the discriminated buyer truthfully provides negative ratings, the systemwill assign him a low score which mitigate the influence of the buyer’s ratings. How-ever, the allocation algorithm cannot always assign the attacked buyer to one of thecollusive sellers. As the attacked buyer will be treated fairly by other sellers out ofthe attacking group, it becomes harder for the small group of sellers to attack someparticular buyers. As the number of collusive sellers increases, the particular buyerwill be more often attacked. Then, the truthful ratings from the buyer will be signifi-cantly discounted. The group of sellers will continually attack the buyer to gain more

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profit without losing their high reputation. Finally, the buyer will lose his incentive toreport truthful ratings. Therefore, our mechanism can only be robust against the sellercoordinated attack to an extent.

(e) Buyer-seller coordinated attack: A set of buyers and a set of sellers form a group andcoordinate their behavior to maximize their group utility.Buyer-seller coordinated attack contains both buyer coordinated attack and seller co-ordinated attack. Because our proposed mechanism is only robust against buyer coor-dinated attack and seller coordinated attack to an extent, separately, our mechanism isunable to achieve perfect performance against the buyer-seller coordinated attack.

We next discuss irrational attacks. The irrational attackers are different from rationalagents, as their behavior is not motivated by the utility achieved in the mechanism. Thereasons of the irrationality of agents are complicated and hard to illustrate in a general logic(Raghunandan and Subramanian, 2012). Our analysis will focus on how the irrationalagent will impact the efficiency of our mechanism with other rational agents, where theirrational agents are separately discussed.

(a) Irrational buyers: Irrational buyers are buyers who attack the system by providinguntruthful ratings regardless of the cost. They can be newly registered or disguisedby the existing sellers, and their behavior can be in a coordinated or uncoordinatedway. When new irrational buyers enter our system, our system initializes their scoresto zero. As in Algorithm 2, the parameter η indicates the probability that buyers withlow score (including new buyers) are allocated with products. The value of η couldbe set close to 0 in a marketplace when the set of honest buyers is stable. In thatcase, the new irrational buyers will have little chance to be allocated with productsand provide ratings. However, for a newly formed marketplace, the initial value of ηneeds to be set greater than 0. In this case, new irrational buyers have a greater chanceto attack the system. In other situations, between the two extreme cases, new irrationalbuyers have some influence in the system but the impact is limited. For the existingirrational buyers, who have already earned high scores, can effectively manipulateseller reputation by providing untruthful ratings. However, after providing untruthfulratings, the attackers’ scores will decrease, and later untruthful ratings provided bythem become less influential. Thus, a bounded number of influential untruthful ratingscan be provided by an existing irrational buyer through sacrificing his score, and theseller reputation would suffer from bounded impact. Therefore, our proposed systemcan mitigate the impact of the existing irrational buyers to some extent.

(b) Irrational sellers: Irrational sellers are those who deliver low quality products or donot deliver at all. The irrational sellers can also be newly registered sellers or dis-guised by the existing sellers in a coordinated or uncoordinated way. When irrational

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sellers conduct malicious behavior, rational buyers will provide truthful negative rat-ings which can decrease the sellers’ reputation value. The decreased seller reputationcan reflect the irrational seller’s honesty. According to Proposition 5, the incentivesof buyers will not be impacted. As the existence of some number of irrational sellerscannot affect the honesty incentive of rational buyers, our system can be robust againstirrational sellers to some extent.

To conclude, the proposed mechanism is more robust against uncoordinated attacksthan coordinated attacks, and it is still robust against coordinated and irrational attacks tosome extent. In a realistic scenario, the attacks can be sophisticated and complex, and ourproposed mechanism still cannot achieve perfect robustness against all types of attacks. Inour future work, we plan to consider the various type of attacks mentioned herein, for thedesign of a robust incentive mechanism.

5.5. Parameters

According to the analysis in Sections 5.1 and 5.2, the parameters, i.e. R0, δ and η, canimpact the performance of the proposed incentive mechanism. We explain the semanticmeaning of each parameter and their possible configurations as follows:

(a) Zero-profit reputation R0: In the pricing algorithm, R0 ∈ [0, 1] represents the sellerreputation value at which sellers earn zero profit. Sellers prefer a smaller R0 to easilygain positive profit. However, buyers prefer a higher R0, since the upper bound of theprice for a product is C

R0(refer to Proposition 3), meaning that a higher R0 can decrease

the bound. In setting R0, the system should balance the preferences of sellers and buy-ers. To achieve a good balance, three main factors should be considered. The firstfactor is the risk borne by buyers and sellers. R0 should be set so that both the risksborne by buyers and sellers are balanced at the same level (the same expected marginalprofit). The second factor is the importance of buyers and sellers. The system shouldset R0 to favor the more important side (buyers or sellers) where the importance degreeis determined by the system organizers or designers. The third factor is the relation-ship between supply and demand. The system should increase R0 when the supplyincreases and decrease when the demand increases. When those factors are conflictwith each other, the system should preferably consider more significant factors.

(b) Cost-price reputation δ: In the pricing algorithm, δ ∈ [0, 1] represents the seller repu-tation value with which a seller will be assigned the price that is equal to the cost C forhis products. Sellers prefer a smaller δ, because the lower bound of the price for sell-ers is C

δ(refer to Proposition 3). However, δ cannot be too low, since buyer incentive

computability requires a lower bound for δ as in Equation (9) (refer to Proposition 4).Therefore, we can set δ equal to the right-hand side of Equation (9).

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(c) Exploration factor η: In the allocation algorithm, η ∈ (0, 1) represents the percentageof products that are randomly allocated among buyers (including new buyers). First,η should be positive, due to the following two reasons: (a) η provides a chance fornew buyers to be allocated with products and allows the system to discover honestbuyers from those newcomers; (b) a positive η can also allow buyers with low scoresto gain high scores by providing truthful ratings, instead of having to whitewash theirscores by reentering the system. In addition, η determines the strength of incentiveprovided for the existing buyers. A lower η means that a larger proportion of productswill be allocated to honesty buyers, which provides higher incentives for the existinghonest buyers to report truthful ratings. Therefore, in order to set a proper η, thesystem should balance between the existing honest buyers and new buyers, as well asdishonest buyers. For a newly formed e-marketplaces, η should be set relatively highto attract and discover more new honest buyers. While for a stable system with fewnewcomers, η should be set as a smaller value (greater than 0).

5.6. PracticabilityThe proposed incentive mechanism is a centralized system to promote buyer and seller

honesty for e-marketplaces with limited inventory. The price of products is determinedby the pricing algorithm considering the sellers’ reputation, and the matching betweenproducts and buyers is implemented by the allocation algorithm based on the buyers’ score.We argue that our incentive mechanism is practical in reality, in the following aspects:

• The proposed mechanism is consistent with the general phenomenon in the realworld and the design of many existing (incentive) mechanisms. Firstly, the idea ofproviding price premium to honest sellers is well supported in the literature. It isgenerally observed that the price of products provided by sellers with higher repu-tation is also higher in many empirical studies of e-marketplaces (Choe et al., 2009;Mai et al., 2010). In this sense, our pricing algorithm is a natural realization andextension of this observed phenomenon.

Secondly, our mechanism allocates limited products to honest buyers so that dishon-est buyers have less chance to conduct transactions, which has the similar spirit withseveral existing incentive mechanisms. More specifically, for the honest buyers,they can gain more utility which is similar to the side-payment incentive mechanismwhere the extra side-payment will be rewarded to honest buyers (Jurca, 2007); forthe dishonest buyers, the probability of conducting transactions is decreased, whichis similar to the credibility mechanism where these dishonest buyers will not beallowed to conduct transactions for a period of time (Papaioannou and Stamoulis,2010). Moreover, the effect of the pricing and allocation algorithms has certain sim-ilarity with the double auction mechanism where sellers “ask” by specifying the cost

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in producing the products and buyers “bid” by providing their valuation towards theproducts. The double auction mechanism, based on the costs and valuations, de-termines which pairs of buyers and sellers are able to conduct transitions and howmuch money the buyer or seller should pay or be paid, respectively, such that theproducts are purchased by the desirable buyers. In our mechanism we model thereputation of sellers and scores of buyers. The reputation and scores are then takeninto account to dertermine the allocation of the limited products and their prices.Through the allocation algorithm, the products provided by the sellers with highestreputation are allocated to buyers with highest scores (desired buyers) at the pricedetermined by the pricing algorithm. In fact, we will investigate an auction-baseddesign of our incentive mechanism in future work as explained in Section 7.

Thirdly, the centralized design is common among the existing incentive mecha-nisms, such as Trunit (Kerr and Cohen, 2010), trust-based mechanism (Dash et al.,2004), the incentive mechanism in (Zhang et al., 2012), etc.

• As proved in Section 5.1, both buyers and sellers have incentives to participate intoour system. In our mechanism, the honest sellers are rewarded with higher prices fortheir products and honest buyers gain the limited products provided by the honestsellers. In this case, honest buyers and sellers will be motivated to participate intoour system. Since the existence of these buyers and sellers, more buyers and sellerswill participate too. Moreover, the incentives for buyers and sellers will motivatedishonest buyers and sellers change their behavior so as to achieve more benefit.Thus, we realize a virtuous circle in the proposed system where more and morebuyers and sellers will join our system and they are also motivated to become moreand more honest.

• The social welfare of our system is increasing and no less than the free-tradinge-marketplace (proved in Proposition 10). The allocation algorithm tries to matchproducts from honest sellers to honest buyers in the proposed mechanism. The socialwelfare also includes the future profit of the system by considering the honesty ofbuyers and sellers in transactions. Once buyers and seller have incentives to improvetheir honesty, the social welfare can be absolutely increased due to the increase ofsatisfactory transaction ratio. The way of bringing the honest sellers and buyers ina transaction further increases the future benefit of the system, making the socialwelfare of our system is no less than the free-trading e-marketplace. In order tofurther improve the social welfare, the valuations of products for buyers will beconsidered in the allocation algorithm in our future work. Since the valuation isprivate information, it may be necessary to apply the auction theory to incentivize

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buyers to bid on their true valuation (Klemperer, 1999), which will be an importantresearch direction to optimize the social welfare.

6. Experimental Evaluation

In this section, we carry out a set of experiments to evaluate the proposed incentivemechanism. We first conduct experiments in both static and dynamic settings to validatethe incentives created by our proposed mechanism. In the static setting, there is no newseller or new buyer participating in the marketplace during the experiment. While in thedynamic setting, some new sellers and buyers join the marketplace periodically. Secondly,we show that our mechanism discourages sellers from conducting the whitewashing at-tack, by initializing the reputation of a new seller as δ and applying the membership feedesigned in Section 4.4. Finally, our mechanism is compared with the side-payment mech-anism (Jurca, 2007), in marketplaces with unlimited and limited inventory, respectively.The side-payment mechanism and other mechanisms are commonly facing the new chal-lenges discussed in Section 2 when they are applied in EMLI. In our comparison, we aimto intuitively show these challenges. Moreover, the side-payment mechanism is a repre-sentative mechanism among the existing incentive mechanism. Therefore, we choose tocompare our mechanism with the side-payment mechanism.

6.1. Experimental Settings

We simulate an e-marketplace environment involving sellers and buyers conductingtransactions. The total number of (same) products provided by the sellers is less than thatof the buyers’ demand, i.e. a market with the limited inventory. We set R0 = 0.6, δ = 0.85(satisfying Proposition 4), the cost in producing promised product C = 1, the minimalvaluation of buyers towards the product V∗ = 2, the maximal valuation of buyers towardsthe product V∗ = 2.5, and allocation exploration factor η = 0.1. A set of simulations withvarious settings have been implemented, and the results are similar, so we only show theresults of one specific setting as described above.

In our simulation, if a seller behaves honestly in one transaction, the seller woulddeliver a quality product. Otherwise, the seller delivers a product with 50% quality. Theseller reputation model used in the experiments is

Rs(t) = λRs(t − 1) + (1 − λ)∑

b∈B Nsb(t) × Rb(t − 1) × rs

b(t)∑b∈B Ns

b(t) × Rb(t − 1), (11)

where λ = 0.5 is the learning rate, Nsb the number of ratings provided by buyer b for seller

s and rsb(t) the expected value of the ratings provided by buyer b for seller s. For a buyer, if

he behaves honestly, then he provides 1 for sellers who deliver quality products and 0.5 for

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sellers who deliver products with 50% quality. If the buyer is dishonest then he provides1 for sellers who deliver products with 50% quality and 0.5 for those who have deliveredquality products.

6.2. Experimental ResultsThe experimental results in static and dynamic scenarios are shown in the Sections 6.2.1

and 6.2.2, respectively. In Section 6.2.3, the robustness of our mechanism against thewhitewashing attack is demonstrated. Finally, we show the comparison results in Sec-tion 6.2.4.

6.2.1. Static scenarioIn the static setting, we show that the proposed incentive mechanism can promote

honesty from both buyers and sellers. In the beginning of our simulation, we bootstrap oursystem by only allowing 80 honest buyers who are labeled by buyer identities (ID) from 1to 80, and 40 sellers labeled by seller identities (ID) from 1 to 40, to conduct transactionsin the first 1000 transactions. Among the 40 sellers, there are five types of honesty indelivering products and each type includes 8 sellers, i.e the sellers labeled by ID from 1 to8 deliver quality products at 100% and the sellers labeled by ID from 9-16 deliver qualityproduct at 90%, etc. The reputation and profit of the sellers is shown in Figure 2.

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Figure 2: The relationship between probability of sellers in behaving honestly and (a) seller reputation, (b)average seller profit in selling one product during the bootstrapping stage

In Figure 2, the probability of sellers in delivering quality products is displayed usingthe left y axis in both Figures 2(a) and 2(b). We observe that seller reputation reflects theirprobability of honest delivery in Figure 2(a). Seller average profit in selling one productalso follows the same trend with the probability of honest delivery as shown in Figure 2(b).During the bootstrapping stage, all sellers are assigned relatively accurate reputation, andsellers with higher reputations can gain more profit in selling products.

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After the bootstrapping, we run another 9000 transaction periods, where another 320(dishonest) buyers labeled by buyer ID from 81 to 400 are join the system. These 320buyers have five types of honesty in providing ratings and each type includes 80 buyers,i.e. the buyers labeled by ID from 81 to 160 provide truthful ratings at 90%, and the buyerslabeled from 161 to 240 deliver truthful at 80%, etc. The reputation and profit of the sellers(seller ID from 1 to 40) is shown in Figures 3 and the score and utility of buyers (buyer IDfrom 1 to 400) is shown in 4 show the experimental results.

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Figure 3: The relationship between probability of sellers in behaving honestly and (a) seller reputation, (b)average seller profit in the static setting

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Figure 4: The relationship between probability of buyers in behaving honestly and (a) buyer scores, (b)buyer total utility in the static setting

In Figure 3, we show how seller reputation and profit change with respect to theirprobability in delivering quality products. We observe in Figure 3(a) that seller reputationfollows the same trend as the probability of honest delivery. But it is slightly influenced by

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untruthful ratings compared with that during the bootstrapping stage. The average profitin selling one product also follows the same trend. The sellers with higher honesty areable to gain more profit, as shown in Figure 3(b). Therefore, Figure 3 shows that sellershave the incentive to deliver quality products. In Figure 4, we show the relationshipsbetween buyer scores, total utility and the probability of honest ratings. We observe thatthe expected buyer score decreases as the buyer probability of honest ratings reduces asshown in Figure 4(a). In addition, the fluctuation of the score increases, since buyerswith lower scores have less opportunities to be allocated the products of honest sellerswhich results in a high fluctuation. In Figure 4(b), we observe that the total utility of ahonest buyer is grater than a dishonest buyer. Many dishonest buyers cannot gain muchutility because they do not have any chance to do business with sellers, according to ourallocation algorithm (Algorithm 2).

Moreover, in Figure 4(b), we can observe that honest buyers (those buyers whose hon-esty is 1) have much higher chance to conduct transactions than dishonest buyers (honestyis less than 1), since the utility of dishonest buyers is close to zero indicating that the dis-honest buyers are rarely allocated with products. Indicated in Equation (10), the socialwelfare is higher as the buyer score increases in transactions between buyers and sellers.Thus, our mechanism can achieve an improved social welfare by allocating most productsto honest buyers.

6.2.2. Dynamic scenarioIn the dynamic setting, we allow new buyers and sellers to join the marketplace during

the simulation. In order to maintain our system being a EMLI, we allow 1 new seller and10 new buyers to participate into our system at the same time. After the bootstrappingstage, we let 5 new sellers and 50 new buyers participate into the system in every 100transaction periods, where the honesty of the the new sellers have two types (deliveringquality products at 100% and 60%) and the honesty of the buyers have five types (provid-ing truthful ratings at 100%, 90%, 80%, 70%, 60%). After 400 transaction periods, 20new sellers and 200 new buyers participate into our system. The new sellers are labeledby ID from 40 to 60. Specifically, the sellers labeled by seller ID from 41 to 50 deliverquality products at 100% and the other sellers labeled by ID from 51 to 60 deliver qualityproducts at 60%. The new buyers are labeled by buyer ID from 401 to 600 and amongevery 50 buyers each type of buyers takes for 10. For example in the first 50 buyers from401 to 450, the buyers labeled by 401 to 410 deliver quality products at 100%, and thebuyers labeled by 411 to 420 delivery quality products at 90%, etc. The buyer honesty andseller honesty are displayed by using the left y axis in Figure 5 and Figure 6. After sucha dynamic process, we simulate another 1000 transaction periods in the static setting toobserve seller profit and reputation. We obtain the results as shown in Figure 5 and Figure

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6.

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Figure 5: The relationship between probability of sellers in behaving honestly and (a) seller reputation, (b)average seller profit in the dynamic setting

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Figure 6: The relationship between probability of buyers in behaving honestly and (a) buyer score, (b) buyertotal utility in the dynamic setting

Figure 5 shows seller reputation and profit in selling one product (60 sellers in total).We observe that new honest sellers still gain the same reputation and profit as the honestsellers who previously exist in the system. These results are shown in Figures 5(a) and5(b), respectively. It means that honest sellers can always gain higher reputation and moreprofit no matter when they join our e-marketplace. In addition, more honest buyers gainhigher scores and more utility, as shown in Figures 6(a) and 6(b). Therefore the incentivesof buyers and sellers in behaving honestly are still maintained when new sellers and buyersdynamically join into our e-marketplace. In other words, for honest sellers or buyers, re-gardless of whether they are new or exiting ones, they always have incentives to be honest

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in our proposed system. To conclude, our incentive mechanism ensures the sustainabil-ity of the e-marketplace by allowing new sellers and new buyers to participate into oure-marketplace, and our mechanism still works well in such a dynamic environment.

6.2.3. Evaluation against the whitewashing attackIn this simulation, we consider three sellers s1, s2 and s3 with actual reputation R1 = 1,

R2 = 0.7 and R3 = 0.55, respectively. The total profit of each seller is recorded. We runthe simulation for 10 times and show the average results in Figure 7 (a)-(c). The profit lossof the sellers with different reputation is shown in Figure 7 (d).

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Figure 7: Re-entry scenario: (a) sellers’ total profit without re-entry and without membership fee, (b) sell-ers’ total profit with re-entry but without membership fee, (c) sellers’ total profit with re-entry and withmembership fee, (d) profit loss of sellers if they preform re-entry by comparing case (c) with case (a).

In Figure 7 (a), we observe that s1 gains positive profit. Seller s2 also gains positiveprofit which is less than that of s1, and s3 gains negative profit. It shows that sellers withreputation less than R0 = 0.5 has the incentive to leave the marketplace due to the negativeprofit. In Figure 7(b), we simulate how the mechanism performs without membership fee.

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We find that sellers s2 and s3, whose reputation is less than initial reputation δ = 0.85,have the incentive to exit and re-participate again to gain temporarily higher profit, bycomparing the two lines Rep=0.7 and Rep=0.5 in Figure 7(b) with that in 7(a) (as theprofit of the two sellers increases a bit after the reentry point.). When membership feeis applied, as shown in Figure 7(c), all the three sellers will loss profit if they leave andre-enter the marketplace, by comparing them with Figure 7(a). Figure 7 (d) captures theprofit loss of sellers with different reputation if they perform re-entry in the proposedmechanism. We can observe that the profit loss follows a quadratic function with the peak0 at δ = 0.85. Thus, all the sellers would always gain non-positive profit by performingreentry. To conclude, with the membership fee, sellers do not have the incentive for re-entry.

6.2.4. Comparison resultsIn this section, we compare the effectiveness of the proposed mechanism and one rep-

resentative mechanism, i.e. the side-payment mechanism (Jurca, 2007), in e-marketplaceswith unlimited inventory (EMUI) and limited inventory (EMLI), respectively. The settingsfor the EMLI is similar to that described in Section 6.1. In the EMUI, each seller can sup-ply 20 products within a period6 where the products from honest sellers can satisfy thedemand. The sellers and buyers are divided into two groups: the first half always behaveshonestly (100%) and the second half behave honestly at 60%. We run the two market-places for 10 times and show the average results. The profit of sellers and the utility ofbuyers in the EMUI and EMLI are presented in Figure 8 and Figure 9, respectively.

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Figure 8: The incentive comparison between our mechanism and the side-payment mechanism (a) sellerincentive, (b) buyer incentive in EMUI

6In the experiment for the EMUI, a period is 1/20 of that for EMLI.

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Figure 9: The incentive comparison between our mechanism and the side-payment mechanism (a) sellerincentive, (b) buyer incentive in the EMLI

In EMUI, the profit of honest sellers are higher than the dishonest sellers when ap-plying our mechanism and the side-payment mechanism as shown in Figure 8(a), whichmeans that the sellers have the incentive to be honest when they can supply unlimitedinventory in the marketplace. In the side-payment mechanism the honest sellers can sellmore products and in our mechanism the honest sellers can sell their products at a higherprice, which is the source of their incentive. In Figure 8(b), we can observe that the honestbuyers can obtain more utility than dishonest buyers, which is similar to the side-paymentincentive mechanism where the extra side-payment will be rewarded to honest buyers.The extra side-payment offered to honest buyers is the cost that the system owners haveto bear. This in fact limits the applicability of the side-payment mechanism. Neverthe-less the incentives for buyers to be honest sustain in both systems. In our mechanism,the utility of honest buyers is slightly higher than dishonest buyers. In EMUI, inventoryis unlimited, and every buyer is able to obtain products. In our mechanism, the prod-ucts from honest sellers is more likely to be allocated to buyers at a higher price whichweaken the advantage of these honest buyers. Therefore, in EMUI, our mechanism, thesame as the side-payment mechanism, can promote honesty from buyers and sellers, butthe side-payment mechanism provides stronger incentive for buyers. Note that the strongerincentive provided by the side-payment mechanism bears cost to the marketplace operatorbecause the marketplace has to pay additional side-payment to honest buyers. In contrast,the marketplace operating our mechanism does not need to pay any additional money tohonest buyers, achieving the nice property of budget balance.

In EMLI where each seller has limited inventory, the sellers in the side-payment mech-anism can only achieve more utility by acting dishonestly. In our mechanism, the limitedproducts provided by honest sellers can be sold at higher prices, which incentives sellers

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to be honest. For buyers, in the side-payment mechanism, the utility of honest buyers isalmost the same as that of dishonest buyers. Even though honest buyers can gain moreside-payment, the truthful ratings provided by them can increase the competition for theproducts provided by honest sellers which nearly offsets the achieved higher side-payment.Comparatively, buyers in our mechanism can achieve larger utility by being honest.

By comparing the results in Figure 8 and Figure 9, we can conclude 1) the proposedmechanism can work in both the two types of e-marketplaces, especially in the EMLI, and2) the side-payment mechanism may fail to work in the EMLI.

7. Conclusion and Future Research

In this article, we have proposed an incentive mechanism to promote seller and buyerhonesty in the e-marketplaces with limited inventory (EMLI). More specifically, a pric-ing algorithm is proposed to set high prices for products provided by honest sellers whichmotivates sellers to be honest, and an allocation algorithm is proposed to allocate qual-ity products to honest buyers, motivating buyers to be honest. Theoretical and empiricalevaluations have been conducted to confirm the efficacy of the proposed mechanism.

The contributions of this article are summarized as follows. Firstly, we analyze a spe-cial e-marketplace, i.e. the EMLI, where the demand outweighs the supply. The newchallenges of promoting honesty in such marketplaces are presented. More specifically,sellers are reluctant to improve their reputation due to the limited inventory. Meanwhile,buyers also lack incentives to unveil their truthful ratings, otherwise, they will sacrificethe chance of successfully purchasing products from honest sellers otherwise. The sim-ulation results have validated that the side-payment mechanism cannot work properly inthis environment. Secondly, an incentive mechanism for the EMLI has been proposed,considering these new challenges. In our mechanism, sellers have incentive to improvetheir reputation (or honesty) since a higher reputation value can bring a higher price forthe products supplied by them. On the other hand, buyer honesty in providing ratingsis modeled and buyers can benefit a higher chance to do transactions with honest sellersfrom their truthfully reporting. Theoretical analysis and experimental results have shownthe efficacy of the proposed incentive mechanism. Moreover, The whitewashing attackis well addressed by designing the membership fee and robustness against other variousattacks is discussed. Finally, we have shown that the proposed mechanism can work inboth e-marketplaces with unlimited and limited inventory.

Based on the learnt knowledge, an ideal incentive mechanism for e-marketplace shouldsatisfy the following properties: (a) The seller reputation should motivate the sellers tohonestly deliver products even when the sellers have limited inventory on hand. (b) Thebuyers providing truthful ratings should always achieve higher utility than providing un-truthful ratings. (c) The existing buyers or sellers prefer to keep sustaining in the system,

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instead of performing the whitewashing attack. (d) The mechanism could robust againstirrational/collusive buyers and sellers.

For future research, we will relax some of the assumptions listed in Section 3. Forexample, by relaxing the assumption (b), we will consider the subjectivity of buyers inproviding ratings. The subjectivity problem has been well recognized in the literature(Jøsang et al., 2007; Rosaci et al., 2012) and some existing trust and reputation modelscan effectively cope with this problem, such as PeerTrust (Xiong and Ling, 2004) and ourcoalition formation based reputation system (Liu and Zhang, 2011). We will look into theintegration of those approaches with our incentive mechanism. Moreover, the returningrate of buyers and sellers is also an potential factor to be considered in designing theincentive mechanisms for e-marketplaces with limited inventory, where the agents woulddiscriminately behave dishonestly against agents with low returning ratio. What’s more,designing the incentive for new producers to join the e-marketplaces with limited inventoryis also an interesting direction for the study of EMLI.

We also plan to design an auction based incentive mechanism for the EMLI to furtherincrease the social welfare. Given that the social welfare of the proposed mechanism isnot maximized (even though no less than the free-trading marketplace), it is possible toimprove it by allowing buyers to bid their valuations towards products and sellers to re-veal their costs in producing the products (Zhou and Zheng, 2009). Meanwhile, we couldrelax the assumption (d) by allowing the buyers to report their budget. The auction basedmechanism will adapt accordingly to consider the buyer budget information, e.g. by notallocating a product to a buyer whose budget is smaller than the price of the product.In the auction based incentive mechanism, the system could achieve positive profit frommatching transaction partners, which will provide the incentive for the system to run.

Furthermore, we will improve the robustness of the incentive mechanism for the EMLI,based on the robustness evaluation and comparison of different incentive mechanisms(Liu and Zhang, 2013). We have observed that the existing incentive mechanisms showhigh robustness against some attacks but not every attack. For example, the side-paymentmechanism (Jurca, 2007) is highly robust against collusive attacks; the trust-based mech-anism (Zhang et al., 2012) is highly robust against constant attacks. Thus we will identifythe significant factors which impact the robustness of incentive mechanisms, towards thedesign of a more robust incentive mechanism for the EMLI. In addition, some trust mod-els, e.g. (Zhang and Cohen, 2008), that can effectively detect untruthful ratings may beemployed to improve the robustness of the incentive mechanism. Ideally, in the futureincentive mechanisms, the strategy of being honest will be the dominant strategy such thatthe agents have the incentive to be honest regardless of the strategy taken by others.

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Appendix A. Proofs of Proposition 1

Measured by Equation (2), the amount of scores that buyer b can achieve by providingratings towards seller s is Rs(t − 1)S(rs

b(t)) + (1 − Rs(t − 1))S(1 − rsb(t)). Based on the

properties of the normalized proper scoring rule S, buyer b’s score is in fact equivalent toE(S, rs

b(t),Rs(t−1)), where rsb(t) is the expectation of the distribution of the ratings provided

by buyer b towards seller s. Given the condition that the ratings provided by buyer btowards seller s are truthful, rs

b(t) can thus truly reflect the honesty of seller s in deliveringpromised products, that is rs

b(t) = Rs(t − 1). Then, we have that E(S,Rs(t − 1),Rs(t − 1)) ≥E(S, rs

b(t),Rs(t − 1)) and the equality is true only when rsb(t) = Rs(t − 1). In another word,

when rsb(t) = Rs(t − 1), E(S, rs

b(t),Rs(t − 1)) achieves the maximum value, i.e. the buyer bachieves the maximum score.

Measured by Eq. (2), the amount of scores that buyer b can achieve by providingratings towards seller s is Rs(t − 1)S′(rs

b(t)) + (1 − Rs(t − 1))S′(1 − rsb(t)). Based on the

properties of the normalized proper scoring rule S′, buyer b’s score is in fact equivalent

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to E(S′, rsb(t),Rs(t − 1)), where rs

b(t) is the expectation of the distribution of the ratingsprovided by buyer b towards seller s. Given the condition that the ratings provided bybuyer b towards seller s are truthful, rs

b(t) can thus truly reflect the honesty of seller s indelivering promised products, that is rs

b(t) = Rs(t − 1). From the properties of S′, we alsoknow that E(S′Rs(t−1),Rs(t−1)) ≥ E(S′, rs

b(t),Rs(t−1)) and the equality is true only whenrs

b(t) = Rs(t − 1). In another words, when rsb(t) = Rs(t − 1), E(S′, rs

b(t),Rs(t − 1)) achievesthe maximal value, i.e. the buyer b achieves the maximal score. Proposition 1 holds.

Appendix B. Proofs of Individual Rationality

Appendix B.1. Proof of Proposition 2

We first prove the rationality of buyers. According to Algorithm 1, the price of theproduct provided by seller s is calculated by the quadratic function: Ps = αR2

s − βRs.Then, the utility function of buyer b who is allocated the product is calculated as:

Ub(V sb ,Rs) = RsV s

b − Ps ≥ RsV∗ − Ps

= Ub(V∗,Rs)= RsV∗ − C(1−δ)

δ(δ−R0) R2s − C(δ2−R0)

δ(δ−R0) Rs

=V∗δ(δ−R0)−C(δ2−R0)

δ(δ−R0) Rs − C(1−δ)δ(δ−R0)R

2s .

(B.1)

We find the derivative of Ub(V∗,Rs) with respect to Rs as:

dUb(V∗,Rs)dRs

=V∗δ(δ−R0)−C(δ2−R0)

δ(δ−R0) − 2 C(1−δ)δ(δ−R0)Rs

>V∗δ(δ−R0)−C(δ2−R0)

δ(δ2−R0) − 2 C(1−δ)δ(δ−R0)

=V∗δ(δ−R0)−C(δ2−R0)−2C(1−δ)

δ(δ−R0)

=(V∗−C)δ2+(2C−V∗R0)δ+(CR0−2C)

δ(δ−R0) .

(B.2)

It could be observed that the numerator of the right-hand side of Equality (B.2), (V∗ −C)δ2 + (2C − V∗R0)δ + (CR0 − 2C) is greater than 0 when δ = 1, and less than 0 whenδ = R0. Since the numerator is a continuous quadratic function of variable δ and V∗ −C >

0, we can claim that there exits δ0 =V∗R0−2C+

√(V∗R0−2C)2+4C(V∗−C)(2−R0)

2(V∗−C) ∈ (R0, 1) ensuring

(V∗ − C)δ2 + (2C − V∗R0)δ + (CR0 − 2C) > 0. Therefore, if δ > max{ √R0, δ0}, thendUb(V∗,Rs)

dRs> 0 for Rs ∈ [R0, 1]. In addition, Ub(V∗,R0) = R0V∗ − P(R0) = R0(V∗ − C) > 0,

due to requirement (e) for P(R) and V∗ > C. Therefore, we can conclude that buyingproducts from sellers with reputation larger than R0 will bring positive utility for buyers.

In Algorithm 2, 1 − η percentage of products are allocated to buyers according to theirhonesty levels, i.e. the products of the sellers with the highest reputation are allocated tothe buyer who have highest score, and the other η percentage of the products are randomly

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allocated among the remaining buyers. In this way, In this way, the expected reputation ofsellers who conduct transaction with more honest buyers will be higher, which results inhigher expected buyer utility.

Next, we prove the rationality of sellers. According to Equation (7) and Algorithm 1,the profit of a seller s can be presented as:

Us =C(1−δ)δ(δ−R0)R

2s +

C(δ2−R0)δ(δ−R0) Rs − RsC

=C(1−δ)δ(δ−R0)R

2s +

R0C(δ−1)δ(δ−R0) Rs

=C(1−δ)δ(δ−R0)Rs(Rs − R0).

(B.3)

If the seller’s reputation Rs is greater than R0, the utility of the seller s will be positive, andvice versa, since δ < 1 and δ >

√R0 > R0 according to Proposition 2.

Appendix B.2. Proof of Proposition 3

We first prove that the price of a product for buyers is upper bounded. As the pricefor a product provided by a seller is determined by the function P(Rs) = αR2

s + βRs. Themaximum price is Pmax

b = α + β due to the fact that α = C(1−δ)δ(δ−R0) > 0, and β = C(δ2−R0)

δ(δ−R0) > 0

when the inequality (9) is satisfied. Since δ >√

R0, we have:

Pmaxb = α + β =

C(1+δ2−δ−R0)δ(δ−R0)

=C(1−δ)2+C(δ−R0)

δ(δ−R0) =C(1−δ)2

δ(δ−R0) +Cδ

<C(1−δ)2

δ(δ−δ2) +Cδ=

C(1−δ)+Cδδ2

= Cδ2.

(B.4)

According to the inequality (9), δ2 > R0. Therefore, we have Cδ2< C

R0, i.e. the price is

upper bounded by CR0

.Next, we prove that the price for honest sellers is lower bounded. For an honest seller

(Rs = 1), the price for his product is determined by Algorithm 1. Thus Pmins = P(1) = α+β.

Since δ >√

R0 > δ2, we have:

Pmins = α + β =

C(1+δ2−δ−R0)δ(δ−R0)

=C(1−δ)2+C(δ−R0)

δ(δ−R0) > Cδ,

(B.5)

which means that the price for the products provided by the honest sellers is always greaterthan C

δ. In other words, the price of the products provided by an honest seller is lower

bounded by Cδ.

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Appendix C. Proofs of Incentive Compatibility

Appendix C.1. Proof of Proposition 4According to the proof of Proposition 2, we know that the first order derivation of the

buyer utility function ispositive when Rs > R0, due to requirement (e) for P(Rs) and V∗ > C. Therefore, we can

conclude that buying products from sellers with higher reputation will bring larger utilityfor buyers.

Appendix C.2. Proof of Proposition 5The behavior of providing ratings directly determines buyer scores. According to

Proposition 1, buyers would gain the maximum amount of score by providing truthfulratings, given that the scoring rule is a normalized proper scoring rule. Thus, for two buy-ers b and b, who normally provide truthful and untruthful ratings for sellers, respectively,we have Rb > Rb. We analyze the utility that the two buyers can gain in the following threepossible cases. We denote the score of the buyer who is the last one receiving a productfrom a seller in S g as Rg. In the first case, both the two buyers’ score are greater than Rg

(Rb > Rb > Rg). Then, the buyers b and b will be allocated with products from two sellerss and s, and Rs ≥ Rs based on Algorithm 2. According to Proposition 2, we have Us

b ≥ Usb,

i.e. b can gain more utility than b. In the second case, one of the two buyers’s score isgreater than Rg and the other is less than Rg (Rb > Rg > Rb). Then, the chance for b tobe allocated with a product is low but b will be definitely be allocated with a product withpositive utility, thus E(Ub) > E(Ub). In the third case, both of the two buyers’ score is lessthan Rg (Rb > Rg > Rb), and both buyers will be randomly allocated with products withE(Ub) = E(Ub). To conclude, we have shown that Ub ≥ Ub′ for all the three possible cases.Therefore, the buyers prefer to provide truthful ratings rather than untruthful ratings.

Appendix C.3. Proof of Proposition 6For a seller with the reputation Rs, we have the seller utility function as Us(Rs) =

C(1−δ)δ(δ−R0)Rs(Rs − R0) (refer to Equation (B.3)). The derivation of the seller utility Us(R) withrespect to the seller reputation Rs is:

dUs(Rs)dRs

=C(1 − δ)δ(δ − R0)

(2Rs − R0). (C.1)

Since a rational seller existing in our system should sustain a reputation value which isgreater than R0 (refer to Proposition 2), we have dUs(Rs)

dRs> 0. By improving reputation, the

seller can increase his utility of selling the products at higher prices. Therefore, sellershave the incentive to improve their reputation. Moreover, since buyers are more willing toprovide truthful ratings (refer to Proposition 5), sellers can only improve their reputationby behaving honestly, i.e. delivering promised products.

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Appendix D. Proofs of the Social Welfare

Appendix D.1. Proof of Proposition 7

According to Equation (10), the total social welfare can increase if the social welfareincreases in each transaction. The first order derivation of the W with respect to Rs and Rb

can be calculated as:

dW(Rs,Rb)dRs

= (V sb − C)

11 − Rb

> 0, (D.1)

and

dW(Rs,Rb)dRb

= Rs(Vsb − C)

1(1 − Rb)2

> 0. (D.2)

Thus, the social welfare gets improved if seller s and buyer b increase their reputation andscores, respectively. According to Proposition 5 and Proposition 6, both sellers and buyershave incentive to improve their honesty. Therefore, the total social welfare of the systemwill be increased.

Appendix D.2. Proof of Proposition 8

We denote the expected social welfare of our system and a free-trading e-marketplacein a transaction as w1 and w2. Given that the valuation of products for buyers and thehonesty of buyers are independent, we calculate the expected value of the social welfareas described in Equation 10 as:

E(W(Rs,Rb)

)= E

(Rs(Vb − C)

11 − Rb

)= E(Vb −C) × E(

Rs

1 − Rb). (D.3)

where E(·) denotes the expected value of a variable.According to our allocation algorithm, the products are divided into two parts. The first

part of products (taking for 1−η) are allocated to buyers with highest scores and the secondpart of products (taking for η) are randomly allocated among buyers. Then we obtain thatw1 = (1−η)wg+ηwr, where wg is the expected social welfare in the first part of transactionsand wr is the expected social welfare in the second part of transactions. We can concludethat wr = w2 due to the fact that the second part of products are allocated in the sameway as in the free-trading marketplace. To compare wg and w2, we further describe wg andw2 as wg = Eg(Vb − C) × Eg( Rs

1−Rb) and w2 = E2(Vb − C) × E2( Rs

1−Rb. Considering that the

proposed allocation algorithm is independent of the buyers’ valuations and the valuationsare independent of the honesty, we can conclude that Eg(Vb − C) = E2(Vb −C). Thus, weonly need to compare Eg( Rs

1−Rb) and E2( Rs

1−Rb).

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Since the products are randomly allocated to buyers in the free-trading e-marketplace,then E2( Rs

1−Rb) = E2(Rs)E2( 1

1−Rb). According to the proposed allocation, the products pro-

vided by sellers with higher reputation will be allocated to buyers with higher scores. Inthis case, Eg( Rs

1−Rb) will achieve its maximum value which is no less than E2(Rs)E2( 1

1−Rb).

Thus, we derive that wg ≥ w2. Therefore, w2 ≥ w1. To conclude, the social welfare of theproposed system is no less than the free-trading e-marketplace.

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