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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 inventory (EMLI). The challenges are in twofold: (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 offers 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 efficacy of the proposed mechanism and its nice properties.

In e-marketplaces, buyers and sellers conduct transactions through the electronic media, 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 discourage buyers from participation. A reputation system, aggregating the ratings shared by the buyers with whom the sellers ever conducted transactions, is an effective way to help the buyers choose a reliable transaction partner (seller) Mui et al., 2002a and Mui et al., 2002b, even though the negative ratings cannot be regarded as the evidences of punishing the dishonest sellers by law (Wang and Singh 2006). In order to be chosen by many buyers, the sellers have to maintain high reputation by delivering promised products, given that the ratings provided 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 demote some 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 and Phoomvuthisam, 2011, have been designed to elicit truthful ratings from buyers so that the reputation systems can work properly. One common and implicit assumption in the reputation systems and incentive mechanisms 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 all the buyers. For example, the dentist booking in U.S., as a marketplace, has been observed the 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 a peak season since booking a satisfactory hotel is often difficult. Similar marketplaces also include 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 these marketplaces: (a) each seller has limited inventory, e.g. the number of dentists, rooms of a hotel, and used textbooks, to provide within a unit of time; (b) buyers compete with each other so as to purchase one piece of the inventory. We define such a marketplace as an e-marketplace with limited inventory (EMLI). More generally, this concept is applicable to an 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 inventory in the narrow case where the supply is less than the demand and leave the general scenario for future investigation. New challenges are imposed on promoting buyer and seller honesty in an EMLI. Sellers with limited inventory, given that other sellers also hold limited inventory compared to buyer demand, may behave maliciously in their transactions to gain more profit, by not delivering promised products or reducing the quality of delivered products. Given that their reputation will be decreased due to negative ratings from buyers cheated by them, the sellers may still be willing to increase their profit by sacrificing their reputation. Even though the sellers can attract more buyers by sustaining higher reputation, they can only provide the limited inventory which disables them from benefiting as much as in the e-marketplace where the supply outweighs the demand. Therefore, in these e-marketplaces, reputation itself may not be effective enough to motivate sellers to behave honestly. Moreover, buyers may also have incentives to report untruthful ratings. After a successful transaction with 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 more likely to conduct transactions with the good seller which reduces the buyer’s opportunity of doing business with the particular seller in the future, due to the limited inventory that the seller has. If the transaction is unsuccessful, reporting a truthful (negative) rating also reduces the buyer’s opportunity of doing business with other good sellers because other buyers 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 products because of providing truthful ratings. In other words, in the EMLI, providing truthful ratings is costly for buyers. The existing incentive mechanisms seldom consider these costs imposed on providing truthful ratings, which is demonstrated in Section 6.2.4 by applying one 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 honesty together with a reputation system1 for e-marketplaces with limited inventory, which overcomes the above-discussed challenges. In our mechanism, buyer honesty is measured by a normalized proper scoring rule, making sure that a buyer can and only can gain maximal scores by providing truthful ratings. Seller honesty is measured by the reputation system 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 a pricing algorithm and an allocation algorithm, making sure that: (a) the products of sellers with higher reputation are offered with a higher price; (b) buyers with higher scores have more opportunities to conduct transactions with more reputable sellers. Thus, both sellers and buyers can benefit from behaving honestly. In addition, to make the mechanism robust against the whitewashing attack where dishonest buyers or sellers may leave the marketplace and rejoin using a new identity to erase their bad history, we discuss how to initialize buyer scores and seller reputation for new buyers and sellers and properly determine the membership fees for new sellers. The properties of our mechanism have been theoretically analyzed in terms of individual rationality, incentive compatibility, and social welfare. Finally, we conduct experiments to validate the proposed mechanism, and compare the performance of our mechanism with a classical (side-payment) incentive mechanism in e-marketplaces with unlimited and limited inventory respectively, to demonstrate the wider 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 and clearly defining the concept of e-marketplaces with limited inventory. Section 4 presents the proposed incentive mechanism. Section 5 is devoted to the theoretical analysis of the properties of the proposed mechanism. In Section 6, a set of experiments are conducted to evaluate the efficacy of the proposed mechanism. Finally, Section 7 concludes the article and discusses future research directions.

In this article, we have proposed an incentive mechanism to promote seller and buyer honesty in the e-marketplaces with limited inventory (EMLI). More specifically, a pricing algorithm is proposed to set high prices for products provided by honest sellers which motivates sellers to be honest, and an allocation algorithm is proposed to allocate quality products to honest buyers, motivating buyers to be honest. Theoretical and empirical evaluations have been conducted to confirm the efficacy of the proposed mechanism. The contributions of this article are summarized as follows. Firstly, we analyze a special e-marketplace, i.e. the EMLI, where the demand outweighs the supply. The new challenges 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 sacrifice the chance of successfully purchasing products from honest sellers otherwise. The simulation results have validated that the side-payment mechanism cannot work properly in this environment. Secondly, an incentive mechanism for the EMLI has been proposed, considering these new challenges. In our mechanism, sellers have incentive to improve their reputation (or honesty) since a higher reputation value can bring a higher price for the products supplied by them. On the other hand, buyer honesty in providing ratings is modeled and buyers can benefit a higher chance to do transactions with honest sellers from their truthfully reporting. Theoretical analysis and experimental results have shown the efficacy of the proposed incentive mechanism. Moreover, The whitewashing attack is well addressed by designing the membership fee and robustness against other various attacks is discussed. Finally, we have shown that the proposed mechanism can work in both e-marketplaces with unlimited and limited inventory. Based on the learnt knowledge, an ideal incentive mechanism for e-marketplace should satisfy the following properties: (a) The seller reputation should motivate the sellers to honestly deliver products even when the sellers have limited inventory on hand. (b) The buyers providing truthful ratings should always achieve higher utility than providing untruthful ratings. (c) The existing buyers or sellers prefer to keep sustaining in the system, instead of performing the whitewashing attack. (d) The mechanism could robust against irrational/collusive buyers and sellers. For future research, we will relax some of the assumptions listed in Section 3. For example, by relaxing the assumption (b), we will consider the subjectivity of buyers in providing ratings. The subjectivity problem has been well recognized in the literature Jøsang et al., 2007 and Rosaci et al., 2012 and some existing trust and reputation models can effectively cope with this problem, such as PeerTrust (Xiong and Ling 2004) and our coalition formation based reputation system (Liu and Zhang 2011). We will look into the integration of those approaches with our incentive mechanism. Moreover, the returning rate of buyers and sellers is also an potential factor to be considered in designing the incentive mechanisms for e-marketplaces with limited inventory, where the agents would discriminately behave dishonestly against agents with low returning ratio. What’s more, designing the incentive for new producers to join the e-marketplaces with limited inventory is also an interesting direction for the study of EMLI. We also plan to design an auction based incentive mechanism for the EMLI to further increase the social welfare. Given that the social welfare of the proposed mechanism is not maximized (even though no less than the free-trading marketplace), it is possible to improve it by allowing buyers to bid their valuations towards products and sellers to reveal their costs in producing the products (Zhou and Zheng 2009). Meanwhile, we could relax the assumption (d) by allowing the buyers to report their budget. The auction based mechanism will adapt accordingly to consider the buyer budget information, e.g. by not allocating 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 from matching 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 show high robustness against some attacks but not every attack. For example, the side-payment mechanism (Jurca 2007) is highly robust against collusive attacks; the trust-based mechanism (Zhang et al. 2012) is highly robust against constant attacks. Thus we will identify the significant factors which impact the robustness of incentive mechanisms, towards the design of a more robust incentive mechanism for the EMLI. In addition, some trust models, e.g. (Zhang and Cohen 2008), that can effectively detect untruthful ratings may be employed to improve the robustness of the incentive mechanism. Ideally, in the future incentive mechanisms, the strategy of being honest will be the dominant strategy such that the agents have the incentive to be honest regardless of the strategy taken by others.