Encyclopedia of Wireless Networks

Living Edition
| Editors: Xuemin (Sherman) Shen, Xiaodong Lin, Kuan Zhang

Auction

  • Yanjiao ChenEmail author
  • Qian Zhang
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-32903-1_27-1
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Synonyms

Definitions

Auction is a concept from microeconomics, referring to the practice of buying and selling goods through the process of bidding. Auction participants include buyers, sellers, and the auctioneer, and the role of the auctioneer may be assumed by the seller, especially if there is a single seller. An auction mechanism is a series of rules specifying how an auction is conducted. The three most important components of an auction mechanism are the determination of the winners, the allocation of items, and the payment.

Historical Background

Auction is deemed as an effective way to assign items to buyers who value them the most. According to different numbers of participants, auctions can be categorized into three settings.
  • Forward auction. One seller, who also acts as the auctioneer, and multiple buyers.

  • Reverse auction. One buyer, who also acts as the auctioneer, and multiple sellers.

  • Double auction. Multiple buyers, multiple sellers, and a third-party auctioneer.

In the forward auction, if there is a single piece of item, there are four standard auction mechanisms.
  • English auctions or open ascending-bid auctions. Buyers openly bid against each other by iteratively raising their bids to be higher than the current highest bid. The auction terminates when no buyer offers a higher bid, and the buyer with the highest bid wins the item and pays the corresponding price.

  • Dutch auctions or open descending-bid auctions. The auctioneer starts with a high bid and then lowers the bid until some buyer accepts and pays the corresponding price.

  • First-price sealed-bid auctions. Buyers bid simultaneously without knowing each other’s bids, i.e., sealed bids. The buyer with the highest bid wins the item and pays the corresponding price. Different from the English auction, buyers can only submit their bids once and cannot adjust the bids according to other buyer’s bids.

  • Second-price sealed-bid auctions. This type of auction is identical to the first-price sealed-bid auctions, with the exception that the winner pays the second-highest bid.

These four types of auctions can be easily extended to reverse auctions and to accommodate multiunit items, and there have been many variants and extensions of these standard auction mechanisms. Besides, there are several other more advanced auction mechanisms.
  • Combinatorial auctions. Combinatorial auctions allow buyers to bid on combinations of items, such that the bid on a combination may not equal the sum of bids on individual items in the combination. For example, a buyer bids $1 on item A and $2 on item B, but may bid $2.5 on the combination {A, B} if A and B are substitutes, or bid $4 on the combination {A, B} if A and B are complements to each other.

  • All-pay auctions. Normally, nonwinning buyers or sellers will not pay in auctions. All-pay auctions exert a compulsory payment on every participant and may be used to model entry fees or other costs in the process of auctions.

  • VCG auctions (Vickrey, 1961; Clarke, 1971; Groves, 1973). Vickrey-Clarke-Groves (VCG) auction mechanism tries to maximize social welfare with feasible allocations that satisfy the constraints of the auction (e.g., total number of auctioned items). Take forward auction as an example. The auctioneer finds one optimal feasible allocation A that maximizes the total bids of all winning buyers (usually through brute force). The payment of a winning buyer i with bid bi is calculated as follows. The auctioneer removes buyer i and finds the optimal feasible allocation \(\widetilde {A}^{*}\) among the rest of the buyers. Then, buyer i will be charged the price of \(\sum _{j \ne i} b_j(\widetilde {A}^{*})-\sum _{j \ne i} b_j(A^*)\), i.e., the difference of the utility of other buyers when buyer i participates in the auction or not. The VCG mechanism can achieve truthfulness and social welfare maximization, but its major drawback is high computational complexity, since it is often NP-hard to find the optimal feasible allocation.

  • McAfee auctions (McAfee, 1992). The McAfee auction mechanism is developed for single-unit or multiunit double auctions. Take the single-unit auction, for instance. Based on their bids, the auctioneer sorts the sellers in a non-descending order and the buyers in a non-ascending order. The auctioneer finds k, the last profitable pair of seller and buyer, i.e., the bid of the k-th buyer is higher than that of the k-th seller, but the bid of the (k + 1)-th buyer is lower than that of the (k + 1)-th seller. The first (k − 1) sellers win, and each receives the payment of the bid of the k-th seller; the first (k − 1) buyer win and each pays the bid of the k-th buyer.

Since auction participants are selfish and rational individuals who will adopt the optimal bidding strategy to gain the highest utility, game theory can be applied to analyze auctions. An auction is economic robust if the following three properties are satisfied.
  • Individual rationality. A buyer or a seller is individually rational in the sense that they will not participate in the auction if the obtained utility is less than the utility of no participation. An auction mechanism is individually rational, if all sellers and buyers achieve nonnegative utility. This usually means that any seller is paid more than its bid, and any buyer pays less than its bid.

  • Truthfulness or strategy-proofness. The buyers and sellers have the motivation to manipulate their bids to maximize their own utilities. Being truthful means that a seller or a buyer will submit a bid that equals their true valuation for the item. A truthful auction mechanism guarantees that a buyer or a seller cannot get a higher payoff by misreporting their true valuations; thus they will have no incentive to be untruthful.

  • Budget balance. Budget balance is often considered in the double auction. It means that the auctioneer maintains nonnegative budget. In other words, the payment that the auctioneer receives from all buyers is no less than the payment given to all sellers. For regulators, budget balance is often enough to motivate them to host spectrum auctions. The profit-oriented auctioneers, however, may aim at revenue maximization.

Apart from economic robustness, there are several other concerns in the design of auction mechanisms.
  • Social welfare. Generally speaking, social welfare is the utility of all auction participants, including the buyers, the sellers, and the auctioneer. As the payment merely transfers utility among auction participants, it does not contribute to the social welfare. Therefore, the social welfare can be calculated as the difference between the total true valuation of winning buyers and the total true valuation of winning sellers. In a truthful auction, the social welfare is simply the total bid of winning buyers minus the total bid of winning sellers.

  • Collusions. Auction participants may collude to rig the auction and gain a higher utility. For example, buyers may form collusions to bid against other buyers but not the buyers in the collusion, resulting in a favorable allocation and a lower payment. The seller may collude with the auctioneer to insert dummy bids to gain a higher payment. The practice of collusion in auctions has been revealed by many empirical studies, calling for effective countermeasures.

  • Privacy-preserving. The bid of a buyer may be sensitive and private information that should be shielded from the non-trustworthy auctioneer and other rival bidders. For example, in a truthful auction, a buyer’s bid is its true valuation, which may be closely related to its profit of winning the spectrum. The disclosure of sensitive information will render unbalanced advantage to the informed entities and cause economic damage to those whose information is divulged. Therefore, privacy-preserving auction mechanism design is gaining more and more attention.

Key Applications

The most successful application of auctions in wireless networks is dynamic spectrum allocation. Spectrum is an indispensable resource for wireless communications. To address the underutilization problem resulted from static spectrum allocation, it is proposed to dynamically redistribute spectrum through auctions. Different from traditional goods, spectrum features interference-constrained spatial reuse, i.e., the same channel can be reused by multiple non-interfering buyers whose transmission ranges do not overlap. Therefore, the objective of spectrum auctions is to realize spectrum reusability while achieving economic robustness or social welfare maximization. The interference relationship of buyers is usually represented by the interference graph, an undirected graph constructed based on the transmission range of the spectrum and geographic information of the buyers. A typical interference graph can be denoted as G = (V, E), in which the set of nodes V represents the set of buyers and the set of edges E represents interference relationship. If two buyers interfere with each other, there is an edge between them; otherwise, there is no edge between them.

The following are some typical spectrum auction mechanisms.
  • Forward spectrum auction (Zhou et al., 2008; Jia et al., 2009). The single spectrum owner with M channels acts as the auctioneer, and each buyer can demand more than one channels. After sorting the buyers according to their bids in a non-ascending order, the auctioneer will sequentially check each buyer. If the buyer’s demand di is fewer than the available channels M − ei, in which ei is the number of channels allocated to the buyer’s interfering neighbors, the buyer will become a winner. A winning buyer will pay according to the critical value, which is the lowest value that the buyer has to bid in order to win.

  • Double spectrum auction (Zhou and Zheng, 2009). Assume that each buyer demands one channel and each seller owns one channel. The third-party auctioneer first divides buyers into groups, each of which only contains non-interfering buyers. The group bid is determined by the group size and the minimum bid in the group. Regarding each buyer group as a virtual buyer, the auctioneer can execute the McAfee auction mechanism to determine the spectrum allocation and the payment.

  • Heterogeneous spectrum auction (Feng et al., 2012; Chen et al., 2014). The difference between homogeneous and heterogeneous spectrum auctions is that heterogeneous spectrum auction groups non-interfering buyers on a per-channel basis, since the interference relationship of buyers on different channels is different.

  • Combinatorial spectrum auction (Zheng et al., 2015). Motivated by the fact that channels of contiguous frequency are easier to operate, combinatorial spectrum auction allows buyers to bid on combinations of channels. To realize spatial reuse, the same channel in the combinations of two non-interfering buyers is represented by two different virtual channels. Then, buyers are sorted in the non-ascending order according to the ratio of the bid to the combination size. The auctioneer then sequentially checks each buyer and selects winners as those whose demanded combination does not contain any channel that has already been allocated. A winning buyer will also pay its critical value, as in the forward spectrum auction.

  • Online spectrum auction (Wang et al., 2010). Online spectrum auctions involve the temporal dynamics of spectrum demand and supply and require buyers to specify their requested time slots. At each time slot, the auctioneer collects bids from the arriving buyers and examines the availability of channels. Given the current buyers, the auctioneer will first conduct a screening process to remove the buyers whose bids are lower than the estimated future value of the channel. Then, the auctioneer can determine spectrum allocation among the remaining buyers using the double spectrum auction mechanism.

Apart from spectrum distribution, auction has been applied to other scenarios in wireless networks.
  • Power allocation. Auctions can enable wireless users to cooperate in distributed power allocation to improve the overall network performance (Liu et al., 2013).

  • Crowdsensing. Mobile crowdsensing platforms can adopt auctions to incentivize the participation and high-quality works from crowd workers (Luo et al., 2017).

  • Mobile data offloading. Wireless service providers can use auctions to employ Wi-Fi or femtocell access points for data offloading (Iosifidis et al., 2015).

  • Video streaming. Auctions can be used to motivate nearby wireless users to cooperate in video downloading and sharing, thus improving wireless video streaming performance (Han et al., 2009).

Cross-References

References

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceWuhan UniversityWuhanPeople’s Republic of China
  2. 2.Department of Computer Science and EngineeringHong Kong University of Science and TechnologyHong KongPeople’s Republic of China

Section editors and affiliations

  • Jianwei Huang
    • 1
  • Yuan Luo
  1. 1.Department of Information EngineeringThe Chinese University of Hong Kong, StainHong KongChina