统计信息下在线反向拍卖的竞争分析

对于投标具有统计特征的在线反向拍卖问题,利用在线算法与平均情形竞争分析相结合的方法,讨论了单一定价策略的平均情形最优单一定价及其竞争性能,提出了无限可分商品在线反向拍卖的平均情形竞争分析策略,基于此策略建立了具有均匀分布特征的在线反向拍卖模型,通过对模型求解得到了采购商的竞争需要曲线。与不考虑投标的统计信息、只是利用常规的最坏情形竞争分析得到的在线反向拍卖的竞争策略进行对比分析,发现统计信息的利用提高了在线反向拍卖策略的竞争性能。     

Coasian dynamics in repeated English auctions

We extend the Coase conjecture to the case of a seller with a single object, who faces n potential buyers and holds a sequence of English auctions until the object is sold. In an independent-private-values environment in which buyers and sellers share the same discount factor, we show that the (perfect Bayesian) equilibrium path of reserve prices obeys a Coasian logic. Moreover, the equilibrium reserve path lies below that for the repeated sealed-bid, second-price auctions studied by McAfee and Vincent (in Games Econ Behav 18:246–276). Nevertheless, the open (English) and sealed-bid formats are shown to be revenue equivalent.     

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.     

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.     

Declining valuations in sequential auctions

We analyze an independent private values model where a number of objects are sold in sequential first- and second-price auctions. Bidders have unit demand and their valuation for an object is decreasing in the rank number of the auction in which it is sold. We derive efficient equilibria if prices are announced after each auction or if no information is given to bidders. We show that the sequence of prices constitutes a supermartingale. Even if we correct for the decrease in valuations for objects sold in later auctions we find that average prices are declining.Received June 2004We are grateful to Christian Groh, Wolfgang Köhler and Benny Moldovanu for helpful suggestions. Financial support from the German Science Foundation through SFB 504 and SFB/TR 15 at the University of Mannheim and the University of Bonn is gratefully acknowledged.     

Reflections about pseudo-dual prices in combinatorial auctions

Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices, a set of item prices is called market clearing or equilibrium if all the winning (losing) bids are greater (less) than or equal to the total price of the bundle items. However, the prices for individual items are not readily computed once the winner determination problem is solved. This is due to the duality gap of integer programming caused by the indivisibility of the items. In this paper, we reflect on the calculation of approximate or pseudo-dual item prices. In particular, we present a novel scheme based on the aggregation of winning bids. Our analysis is illustrated by means of numerical examples.     

Pricing and market segmentation using opaque selling mechanisms

In opaque selling certain characteristics of the product or service are hidden from the consumer until after purchase, transforming a differentiated good into somewhat of a commodity. Opaque selling has become popular in service pricing as it allows firms to sell their differentiated products at higher prices to regular brand loyal customers while simultaneously selling to non-loyal customers at discounted prices. We develop a stylized model of consumer choice that illustrates the role of opaque selling in market segmentation. We model a firm selling a product via three selling channels: a regular full information channel, an opaque posted price channel and an opaque bidding channel where consumers specify the price they are willing to pay. We illustrate the segmentation created by opaque selling as well as compare optimal revenues and prices for sellers using regular full information channels with those using opaque selling mechanisms in conjunction with regular channels. We also study the segmentation and policy changes induced by capacity constraints.     

Sets in excess demand in simple ascending auctions with unit-demand bidders

This paper analyzes the problem of selecting a set of items whose prices are to be updated in the next iteration in so called simple ascending auctions with unit-demand bidders. A family of sets called “sets in excess demand” is introduced, and the main result demonstrates that a simple ascending auction always terminates at the minimum Walrasian equilibrium prices if and only if the selection belongs to this family.     

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.     

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.     

Optimal pricing strategies under co-existence of price-takers and bargainers in a supply chain

We investigate how the co-existence of two types of customers, price-takers, and bargainers, influences the pricing decisions in a supply chain. We consider a stylized supply chain that includes one manufacturer and one retailer, and we characterize the optimal prices of the retailer and the manufacturer. We further discuss the effects of the fraction of the bargainers in the customer population and the relative bargaining power of the bargainers on these optimal prices. Our results show that, given the wholesale price, the lowest price at which the retailer is willing to sell (ie, cut-off price) increases with the relative bargaining power of the bargainers. Both posted and cut-off prices increase in the fraction of the bargainers in the customer population. Moreover, depending on the type of negotiation cost, the variations of both prices will vary. In equilibrium, both posted and cut-off prices do not monotonically increase with the fraction of the bargainers in the customer population. When the maximum reservation price of the customers is low, and/or the negotiation costs are high, and/or the relationship between the bargainer's negotiation cost and reservation price is high, the retailer may reduce both posted and cut-off prices as the fraction of the bargainers increases.     

Dynamic price dispersion in Bertrand–Edgeworth competition

This paper studies a dynamic oligopoly model of price competition under demand uncertainty. Sellers are endowed with one unit of the good and compete by posting prices in every period. Buyers each demand one unit of the good and have a common reservation price. They have full information regarding the prices posted by each firm in the market; hence, search is costless. The number of buyers coming to the market in each period is random. Demand uncertainty is said to be high if there are at least two non-zero demand states that give a seller different option values of waiting to sell. Our model features a unique symmetric Markov perfect equilibrium in which price dispersion prevails if and only if the degree of demand uncertainty is high. Several testable theoretical implications on the distribution of market prices are derived.     

Dominant strategies, superior information, and winner's curse in second-price auctions

In a general model of common-value second-price auctions with differential information, we show equivalence between the following characteristics of a bidder: (i) having a dominant strategy; (ii) possessing superior information; (iii) being immune from winner's curse. When a dominant strategy exists, it is given by the conditional expectation of the common value with respect to bidder's information field; if the dominant strategy is used, other bidders cannot make a profit. Final version November 2001     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.     

考虑线下渠道时销售商在团购网站上的最优销售策略研究

基于团购网站和销售商的典型合作模式,考虑了团购网站和线下市场的相互影响,用非线性优化理论为基础以销售商制定团购上限和团购项目定价为决策变量,考虑团购价格和最低团购数量的约束条件,建立模型优化,求解出销售商推出团购项目的最优策略。考虑到团购网站下限和团购网站销售成本以及网上销售的广告效用,分析了销售商是否应该制定团购上限,如何结合团购项目定价制定团购上限。探讨了在线低价限量销售的优势,以及顾客转移购买率和团购下限对销售商策略选择的影响。通过和单一线下渠道的最优销售策略相比较,得出销售商推出团购项目的前提条件。同时为团购网站运营商如何引导销售商推出低价团购项目提供了管理启示。     

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.     

Some inequalities related to the analysis of electricity auctions

Most balancing markets of electric power are organized as uniform-price auctions. In 2001, the balancing market of England and Wales switched to a pay-as-bid auction with the intention of reducing wholesale electricity prices. Numerical simulations of an electricity auction model have indicated that this should lead to decreased average prices. In this work we prove two inequalities which give an analytic proof of this claim in the same model.     

网络团购环境下基于电子中介的商品交易优化模型

在网络团购环境下,如何考虑顾客、商家和电子中介三方主体的利益并实现商品交易最优化,这是一个值得关注的研究问题。本文针对基于电子中介的网络团购商品交易问题,依据商家与电子中介事先商定的团购商品的交易数量区间、交易数量折扣以及顾客和商家分别提交的商品的报价和保留价,在考虑顾客、商家和电子中介三方利益最大化的前提下,构建了多目标商品交易优化模型;进一步地,将多目标优化模型转化为单目标优化模型,并给出了求解优化模型的遗传算法。最后,通过一个算例说明了本文构建的模型及其求解算法的可行性和有效性。     

A decision approach to competitive electronic sealed-bid auctions for land

Electronic markets for land are innovative techniques potentially advantageous to buyers and private sellers, the latter being interested in sealed-bid auctions assuring high levels of competition among many bidders so that coalitions and cooperative games are ruled out. Land electronic tendering requires sufficient online information for bidders such as valuation reports by prestigious surveyors. To help the bidder make his best choice, we propose a decision model for moderately pessimistic players facing tenders where competition among a great number of independent antagonists excludes the use of cooperative games and involves strict uncertainty. A worked example concerning farmland in Spain is presented.     

Endogenous budget constraints

This paper considers a model in which a single buyer seeks to buy a continuum of objects from a continuum of sellers. The sellers specify prices at which they are willing to sell their objects to the buyer, and the buyer then decides which objects to purchase. I illustrate that the buyer has an incentive to commit to a binding budget constraint before seeking offers from the sellers.