Comparing the Spanish and the discriminatory auction formats: A discrete model with private information

The Spanish Treasury is the only Treasury in the world that uses a hybrid system of discriminatory and uniform price auctions to sell government debt: winning bidders pay their bid price for each unit if this is lower than the weighted average price of winning bids (WAP), and pay the WAP otherwise. Following Gordy [Gordy, M., 1996. Multiple bids in a multiple-unit common-value auction. Board of Governors of the Federal Reserve System], we model the Spanish auction as a common value auction of multiple units with private information, allowing for multiple bids. Numerical analysis shows that bidders spread their bids more in the Spanish than in the discriminatory auction and bid higher for the first unit, and that the expected seller’s revenue is higher in the Spanish than in the discriminatory auction within a reasonable set of parameter values.     

Vickrey–Dutch procurement auction for multiple items

We consider a setting where there is a manufacturer who wants to procure multiple items from a set of suppliers each of whom can supply one or more of these items (bundles). We design an ascending price auction for such a setting which implements the Vickrey–Clarke–Groves outcome and truthful bidding is an ex post Nash equilibrium. Our auction maintains non-linear and non-anonymous prices throughout the auction. This auction has a simple price adjustment step and is easy to implement in practice. As offshoots of this auction, we also suggest other simple auctions (in which truthful bidding is not an equilibrium by suppliers) which may be suitable where incentives to suppliers are not a big concern. Computer simulations of our auction show that it is scalable for the multi-unit case, and has better information revelation properties than its descending auction counterpart.     

基于数据包络分析的混合多属性第二分值拍卖机制

多属性拍卖在传统价格拍卖的基础上纳入了价格和质量多个属性,已广泛应用于许多领域。本文针对输入几乎没有先验结构且投标人数量足够大的情况,在以往有关多属性拍卖研究的基础上将单个投入扩展为多个投入,将物品的多个属性(价格、完成时间、劳动力数量、质量等因素)合理划分为投入或产出,设计了运行有效的基于数据包络分析的多属性第二分值拍卖机制。与其他方法相比,数据包络分析方法可以有效解决多投入多产出问题,结合多目标规划方法,可以帮助采购方在最大化自身利益的同时,找到整体表现更好的供应商。该机制满足个人理性和激励相容,与传统第二分值拍卖机制相比,在吸引投标人的前提下能够最大化拍卖人的利益。     

Modeling and analysis of an auction-based logistics market

We consider a logistics spot market where the transportation orders from a number of firms are matched with two types of carriers through a reverse auction. In the spot market, local carriers compete with in-transit carriers that have lower costs. In order to analyze the effects of implementing a logistics spot market on these three parties: firms, local carriers, and in-transit carriers and also the effects of various system parameters, we develop a two-stage stochastic model. We first model the auction in a static setting and determine the expected auction price based on the number of carriers engaging in the auction and their cost distributions. We then develop a continuous-time Markov chain model to evaluate the performance of the system in a dynamic setting with random arrivals and possible abandonment of orders and carriers. By combining these two models, we evaluate the performance measures such as the expected auction price, price paid to the carriers, distribution of orders between local and in-transit carriers, and expected number of carriers and orders waiting at the logistics center in the long run. We present analytical and computational results related to the performance of the system and discuss operation of such a logistics spot market in Turkey.     

Non-linear anonymous pricing combinatorial auctions

In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant that has won a subset of items knows why his bid was a winning bid and that agents that have not acquired any item easily can detect why they lost. The problem in the combinatorial auction setting is that the winner determination problem is a hard integer programming problem and hence a linear pricing scheme supporting the optimal allocation might not exist.     

Optimal bidding in auctions of mixed populations of bidders

A mixed population of bidders consists of two asymmetric groups. Members of the first group are game-theoretic players, who maximize their expected profit and incorrectly believe that their opponents act similarly. The second group of bidders adopts an irrational strategy: they either choose their bids randomly following a given probability distribution, in a “naïve” form of bidding, or follow a decision-theoretic approach, maximizing their expected profit under the assumption that all other bids are random. In a sealed bid private-value procurement auction we examine the optimal strategy of a new player, who has perfect knowledge of the structure of the mixed bidder population and enters the auction. The optimal bid of the new bidder is derived when the cost and mark-up follow a uniform distribution in [0, 1]. The effect of the relative size of the group of game-theoretic bidders and the population size on the optimal bid price is established.     

车辆牌照拍卖模型

提出多个相同物品(如车辆牌照)同时密封拍卖的模型，给出对称均衡竞标策略；证明了该拍卖方式与第一价格密封连续拍卖产生相同的预期收益；对估价为均匀分布的拍卖预期收益进行了研究。     

Dual mechanism for an online retailer

While posted price and auction have typically been seen as alternatives to each other, we observe Web stores selling a product at a posted price and simultaneously running auctions for the identical product, a phenomenon that has not been studied fully. In this article, we study a dual mechanism, where an online retailer combines the two conventional mechanisms (posted price and auction) for multiple units of a product. We demonstrate that the dual mechanism can be used to achieve market segmentation when customers discount the expected utility of auctions. We characterize the customer’s decision rule and formulate a retailer’s profit function under the dual mechanism. Finally, we compare the performance of three selling mechanisms (posted price, auction, and dual) through computational experiments.     

国债招标拍卖的最优机制:数量与价格歧视

过去已有相当多的文献讨论国债拍卖,米勒和弗雷德曼认为统一价格比歧视价格拍卖有比较优势.研究国债拍卖最优分配方式的选择问题,采用最优机制设计方法分析国债拍卖活动,内生地得到最优拍卖机制.然而结果表明,如果使用价格歧视及数量歧视(定量分配),那么政府的销售收益会得到改善,这是一个最优拍卖机制,不同于米勒和弗雷德曼的观点.     

两种记分函数下多属性拍卖投标均衡策略

以拍卖人期望收益最大化为机制设计目标,讨论两种不同偏好的记分函数条件下,最高得分密封投标拍卖和连续完全信息多属性英式拍卖中,卖者的最优投标策略和买者的最优拍卖设计问题,主要结论是:1)无论选择哪种拍卖方式和记分函数,拍卖人均有动机隐瞒自己的真实偏好,除非竞价人是同质的或参与人数足够多.2)竞价人最优属性策略qi*与拍卖...     

A double-sided multiunit combinatorial auction for substitutes: Theory and algorithms

Combinatorial exchanges have existed for a long time in securities markets. In these auctions buyers and sellers can place orders on combinations, or bundles of different securities. These orders are conjunctive: they are matched only if the full bundle is available. On business-to-business (B2B) exchanges, buyers have the choice to receive the same product with different attributes; for instance the same product can be produced by different sellers. A buyer indicates his preference by submitting a disjunctive order, where he specifies the quantity he wants of each particular good and what limit price he is willing to pay for each good, thus providing a subjective valuation of each attribute. Only the goods with the best prices will be traded. This article considers a doubled-sided multiunit combinatorial auction for substitutes, that is, a uniform price auction where buyers and sellers place both types of orders, conjunctive (AND orders) and disjunctive (XOR orders). We show that linear competitive prices exist. We also propose an algorithm to clear the market, which is particularly efficient when the number of traders is large, and the goods are divisible.     

网上分批拍卖中的保留价比较分析

本文以Onsale网上拍卖公司的拍卖方式为背景,研究了在给定拍卖时间长度与拍卖总供给量的条件下,将拍卖品分若干批拍卖这一问题.建立了其马尔可夫决策过程模型,分别在公开保留价与不公开保留价的两种情况下,研究了每批拍卖品数量的最优问题,并证明了网上拍卖中商家不公开保留价时获得的最大期望利润多于公开时的最大期望利润.     

Hats,auctions and derandomization

We investigate derandomizations of digital good randomized auctions. We propose a general derandomization method which can be used to show that for every random auction there exists a deterministic auction having asymptotically the same revenue. In addition, we construct an explicit optimal deterministic auction for bi‐valued auctions. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 478–493, 2015     

多物品拍卖的捆绑销售策略

拍卖商在拍卖多个不同物品的过程中,面临着是捆绑拍卖还是分开拍卖的问题.本文讨论在第二价格密封拍卖(维克里拍卖)方式下,拍卖商拍卖多个不同物品时,其所采取的最优策略(捆绑拍卖或是分开拍卖)与投标人的数量以及投标人对物品的估价的关系.     

Estimating intermediate price transitions in online auctions

This paper discusses a statistical model regarding intermediate price transitions of online auctions. The objective was to characterize the stochastic process by which prices of online auctions evolve and to estimate conditional intermediate price transition probabilities given current price, elapsed auction time, number of competing auctions, and calendar time. Conditions to ensure monotone price transitions in the current price and number of competing auctions are discussed and empirically validated. In particular, we show that over discrete periods, the intermediate price transitions are increasing in the current price, decreasing in the number of ongoing auctions at a diminishing rate, and decreasing over time. These results provide managerial insight into the effect of how online auctions are released and overlap. The proposed model is based on the framework of generalized linear models using a zero‐inflated gamma distribution. Empirical analysis and parameter estimation is based on data from eBay auctions conducted by Dell. Copyright © 2011 John Wiley & Sons, Ltd.     

On the incentive properties of multi-item auctions

In a market of indivisible objects where a buyer consumes at most one object, the buyer-optimal auction is a multi-item generalization of Vickrey's second-price auction. If the optimal auction is formulated as a strategic game, it is well-known that it satisfies good incentive properties, i.e., the honest strategy profile is a Nash equilibrium, a unique perfect equilibrium and a dominant strategy equilibrium. For each of the three incentive properties, it is shown that the optimal auction is aunique auction satisfying the property. The uniqueness results are derived in a general setting with budget constraints and non-linear utilities.I would like to thank three anonymous referees for detailed comments and constructive suggestions. I would also like to thank Edward J. Green and John G. Riley for their valuable comments and advice on earlier drafts of this paper. I am solely responsible for any errors.     

Using bid data for the management of sequential,multi-unit,online auctions with uniformly distributed bidder valuations

Internet auctions for consumers’ goods are an increasingly popular selling venue. We have observed that many sellers, instead of offering their entire inventory in a single auction, split it into sequential auctions of smaller lots, thereby reducing the negative market impact of larger lots. Information technology also makes it possible to collect and analyze detailed bid data from online auctions. In this paper, we develop and test a new model of sequential online auctions to explore the potential benefits of using real bid data from earlier auctions to improve the management of future auctions. Assuming a typical truth-revealing auction model, we quantify the effect of the lot size on the closing price and derive a closed-form solution for the problem of allocating inventory across multiple auctions when bidder valuation distributions are known. We also develop a decision methodology for allocating inventory across multiple auctions that dynamically incorporates the results of previous auctions as feedback into the management of subsequent auctions, and updating the lot size and number of auctions. We demonstrate how information signals from previous auctions can be used to update the auctioneer’s beliefs about the customers’ valuation distribution, and then to significantly increase the seller’s profit potential. We use several examples to reveal the benefits of using detailed transaction data for the management of sequential, multi-unit, online auctions and we demonstrate how these benefits are influenced by the inventory holding costs, the number of bidders, and the dispersion of consumers’ valuations.     

Selecting optimal selling format of a product in B2C online auctions with boundedly rational customers

The advancement of Internet technology has enabled new formats for selling products in the B2C online auctions. At present, on the major online auction sites, there exist three popular selling formats, namely, the posted price, pure auction and buy-price auction formats. It is an important decision problem for a firm to select the most profitable format to sell its products through the Internet. The customer behavior is of course a crucial element of the decision process. To the best of our knowledge, most models available today assume that customers are perfectly rational. To better understand the decision process, in this paper, we incorporate the concept of bounded rationality into consideration. We first present a “behavior choice function” to characterize the behavior of the customers with bounded rationality. Then corresponding to each selling format, we construct a revenue model based on the bounded rationality for analysis. Finally, we conduct some elaborate computational experiments to investigate the performance of each revenue model for developing new managerial insights. Our computational results clearly demonstrate how the bounded rationality of customer behavior affects the choice of a preferable selling format for a B2C firm in an online auction.     

Multi-criteria auctions without full comparability of bids

The emergence of auction mechanisms that support bids characterized by several attributes is one of the most recent evolutions within auction theory. These mechanisms, referred to as multi-attribute, multiple issue or multi-dimensional auctions, are at the intersection between multi-criteria decision and auction theories. The purpose of this paper is to introduce multi-criteria auctions the originality of which is not to require full comparability between bids. We claim that this distinctive feature is of great interest, especially in procurement situations. Furthermore, the existence of potential incomparability between multi-dimensional offers will permit us to manage different bidding niches coexisting within the same bidding space. A theoretical framework based on a general preference structure will be introduced and then referenced to existing approaches such as multi-attribute auctions or new ones such as dominance based multi-criteria auctions or butterfly auctions.     

Short communication: DEA based auctions simulations

In this paper we use simulations to numerically evaluate the Hybrid DEA – Second Score Auction. In a procurement setting, the winner of the Hybrid auction by design receives payment at the most equal to the Second Score auction. It is therefore superior to the traditional Second Score scheme from the point of view of a principal interested in acquiring an item at the minimum price without losing in quality. For a set of parameters we quantify the size of the improvements and show that the improvement depends intimately on the regularity imposed on the underlying cost function. In the least structured case of a variable returns to scale technology, the hybrid auction only improved the outcome for a small percentage of cases. For other technologies with constant returns to scale, the gains are considerably higher and payments are lowered in a large percentage of cases. We also show that the number of the participating agents, the concavity of the principal value functions, and the number of quality dimensions impact the expected payment.