基于可变供给量的可分离物品拍卖及其应用

本文对统一价格下可分离物品的拍卖问题进行了研究。首先,在买者报价连续、买者和卖者风险中立、卖者采取可变供给量(将供给量看成价格的函数)的策略下,设计了一个新的基于可变供给量的可分离物品统一价格拍卖机制,研究了其信息激励性和分配的有效性,给出了卖者的最佳供给策略和买者的均衡报价策略。然后,将拍卖机制推广到风险中立、风险爱好和风险厌恶三类风险买者共存的情形,并给出了相应的均衡结论,该结论与现有的一些成果相比更具一般性。最后,给出了拍卖机制在环境规划中应用。具体地,结合"十一五"期间获得的"1+8武汉城市圈"环境规划中有关污染物允许排放总量分配数据和统计申报资料,利用拍卖模型来分析和评价了免费分配方案的有效性程度,并据此给出了关于目前排污申报制度和免费分配方法的若干结论和建议。     

Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

Trial or No Trial: Supplying Costly Signals to Improve Profits*

Many software and video game firms offer free trials with limited content to help buyers assess the likely value of the goods that they may purchase. This article examines fundamental issues related to the incentives and risks for a monopoly by providing a trial. Assuming that a seller can control the mix of components in a trial, we introduce a new mechanism for buyers’ inference of using a trial. We find that a trial may enable the seller to segment the market and charge a higher price to high‐valuation buyers, but can also cause a decline in demand. Moreover, the seller forfeits partial value of a full product through providing a free trial, so the benefit is offset by this cannibalization loss. In addition to the size and content of a trial, the distribution of buyers’ prior belief also affects a trial's ability to convey information. We show that a trial can provide more information if the prior belief is more concentrated in the tails of the distribution.     

非对称情况下的多物品拍卖

本文讨论当投标人之间存在不同的预算约束时两物品的序贯增价拍卖,对于物品之间不同的关系(互补、替代或者不相干的关系),物品价值大小的不同及与预算大小之间的关系,在一个简单的完全信息模型下,我们分不同情况讨论投标人的均衡出价策略,并发现对卖方来说,先拍卖价值高的物品是弱占优的策略。     

基于信号博弈的卖方欺诈行为分析

本文主要基于信号博弈的卖方欺诈行为进行研究,假设拍卖中可能存在欺诈型和诚实型两种卖家,其中欺诈行为有概率发生在第二价格拍卖中：欺诈型卖方冒充竞拍者递交仅次于最高价的报价从而获得额外收益。两种卖家根据各自效用选择拍卖形式：第一价格或者第二价格。而竞买者将卖者的选择作为信号,更新对卖方类型的判断,然后制定报价策略。这是一个买卖方信号交叉影响的过程。考虑到拍卖过程中买方价值相关性,本文在建立模型中参考了关联价值原理。针对该模型进行分析,得出了不同情况下的买卖方策略,并且研究了买方报价、买方判断、卖方收益三者之间的关系。文中利用贝叶斯公式对双方的策略选择问题进行预测,与单纯的概率分布方法相比,更具实践价值。     

不完全信息采购环境下的供应链协调问题： 拍卖机制的应用

本文研究了不完全信息采购环境下供应链的协调问题.拍卖不仅是一种价格确定机制,它也可以作为一种供应链协调的机制.文献已经证明拍卖机制对于参与方的收益及整条供应链的有效性具有显著影响.本文研究了当市场中存在n个供应商1个买者的情形下,拍卖环境满足独立私人值(IPV)条件、且市场反需求函数为对数函数时,批发价格拍卖、目录拍卖及二部合同拍卖为各方所产生的期望收入,并且证明了批发价格拍卖和目录拍卖不能实现渠道协调,而在拥有信息中介的二部合同拍卖机制下系统可以达到渠道协调.     

Feedback Mechanisms,Judgment Bias,and Trust Formation in Online Auctions*

Online markets, like eBay, Amazon, and others rely on electronic reputation or feedback systems to curtail adverse selection and moral hazard risks and promote trust among participants in the marketplace. These systems are based on the idea that providing information about a trader's past behavior (performance on previous market transactions) allows market participants to form judgments regarding the trustworthiness of potential interlocutors in the marketplace. It is often assumed, however, that traders correctly process the data presented by these systems when updating their initial beliefs. In this article, we demonstrate that this assumption does not hold. Using a controlled laboratory experiment simulating an online auction site with 127 participants acting as buyers, we find that participants interpret seller feedback information in a biased (non‐Bayesian) fashion, overemphasizing the compositional strength (i.e., the proportion of positive ratings) of the reputational information and underemphasizing the weight (predictive validity) of the evidence as represented by the total number of transactions rated. Significantly, we also find that the degree to which buyers misweigh seller feedback information is moderated by the presentation format of the feedback system as well as attitudinal and psychological attributes of the buyer. Specifically, we find that buyers process feedback data presented in an Amazon‐like format—a format that more prominently emphasizes the strength dimension of feedback information—in a more biased (less‐Bayesian) manner than identical ratings data presented using an eBay‐like format. We further find that participants with greater institution‐based trust (i.e., structural assurance) and prior online shopping experience interpreted feedback data in a more biased (less‐Bayesian) manner. The implications of these findings for both research and practice are discussed.     

生产能力无限时逢低买入与固定价格机制的比较

逢低买入是一种新型的基于网络的动态价格机制,它通过联合单个消费者形成规模来获得价格折扣。作为双向拍卖的一种变体,逢低买入的适用条件是亟待研究的问题。本文通过研究存在规模效应的前提下,当商家能够完全满足消费者的需求时,采用逢低买入拍卖所能获得的收益情况,证明了在这种情况下逢低买入将会绝对优于固定价格机制,从而表明逢低买入适用于这种环境。     

带佣金率和保留价的一级和二级价格拍卖

本文通过引入佣金率和保留价,分别讨论了一级和二级价格密封式拍卖,得到以下结论:(1)两种密封式拍卖的均衡报价随佣金率的提高而减少;(2)一级价格密封式拍卖的均衡报价随保留价的增加而增加,而二级价格密封式拍卖的均衡报价随保留价的增加而减少;(3)一级价格密封式拍卖的投标者预期收益与佣金率和保留价均呈反向变动,而二级价格密封式拍卖的投标者预期收益独立于佣金率和保留价;(4)收益等价定理仍然成立;(5)在两种密封式拍卖中,当佣金率增加时,卖方的预期收益减少,拍卖行的预期收益以及卖方和拍卖行的总预期收益可能增加也可能减少;(6)在两种密封式拍卖中,当保留价增加时,卖方的预期收益、拍卖行的预期收益以及卖方和拍卖行的总预期收益可能增加也可能减少;(7)给出了卖方的最优保留价的表达式;(8)把本文的结论与以前相应的研究工作做了比较。     

Nonexclusive Competition in the Market for Lemons

A seller can trade an endowment of a perfectly divisible good, the quality of which she privately knows. Buyers compete by offering menus of nonexclusive contracts, so that the seller can privately trade with several buyers. In this setting, we show that an equilibrium exists under mild conditions and that aggregate equilibrium allocations are generically unique. Although the good for sale is divisible, in equilibrium the seller ends up trading her whole endowment or not trading at all. Trades take place at a price equal to the expected quality of the good, conditional on the seller being ready to trade at that price. Our model thus provides a novel strategic foundation for Akerlof's (1970) results. It also contrasts with competitive screening models in which contracts are assumed to be exclusive, as in Rothschild and Stiglitz (1976). Latent contracts that are issued but not traded in equilibrium play an important role in our analysis.     

Transparency in Buyer‐Determined Auctions: Should Quality be Private or Public?

We study buyer‐determined procurement auctions where both price and non‐price characteristics of bidders matter for being awarded a contract. Although, in scoring auctions bidders perfectly know how price and non‐price attributes determine the awarding of the contract, this remains uncertain in buyer‐determined auctions where the buyer is free to choose once all bids have been submitted. We analyze the impact of information bidders have with respect to the buyer's awarding decision. As we show theoretically whether it is in the buyer's interest to conceal the impact of non‐price characteristics depends on how important the quality aspects of the procured good are to the buyer: The more important quality aspects are, the more interesting concealment becomes. In a counterfactual analysis using data from a large European procurement platform, we analyze the reduction of non‐price information available to the bidders. Confirming our hypothesis, for auction categories where bidders’ non‐price characteristics strongly influence buyers’ decisions concealment of non‐price information leads to an increase in buyers’ surplus of up to 15% due to higher competitive pressure and lower bids. Conversely, for categories where bidders’ non‐price characteristics are of little importance concealment of non‐price information leads to a decrease in buyers’ surplus of up to 6%.     

Competition and Coordination in Online Marketplaces

Online marketplaces, such as those operated by Amazon, have seen rapid growth in recent years. These marketplaces serve as an intermediary, matching buyers with sellers, whereas control of the good is left to the seller. In some cases, e.g., the Amazon marketplace system, the firm that owns and manages the marketplace system will also sell competing products through the marketplace system. This creates a new form of channel conflict, which is a focus of this article. We consider a setting in which a marketplace firm operates an online marketplace through which retailers can sell their products directly to consumers. We consider a single retailer, who currently sells its product only through its own website, but who may choose to contract with Amazon to sell its product through the marketplace system. Selling the product through the marketplace expands the available market for the retailer, but comes at some expense, e.g., a fixed participation fee or a revenue sharing requirement. Thus, a key question for the retailer is whether she should choose to sell through the marketplace system, and if so, at what price. We analyze the optimal decisions for both the retailer and the marketplace firm and characterize the system equilibrium.     

Modeling Reputation as a Time‐Series: Evaluating the Risk of Purchase Decisions on eBay*

Reputation systems based on buyer feedback play an important role in today's online markets. In this article, we provide a rigorous methodology to establish a relationship between a seller's feedback history and risk of default. We validate this method against eBay's reputation system, using a dataset of terminated users (Not‐A‐Registered‐User or NARU) and the feedback left for them by buyers. By treating feedback rating data as a function of time, we characterize the tendency of change in seller feedback ratings in order to predict the behavior of a seller. We find that NARU sellers have significantly more negative feedback in their final weeks. Applying functional principal component analysis and classification tree methods, we find that when projecting the feedback data to an appropriate space, NARU and non‐NARU sellers can be distinguished at better than 92% accuracy. We use this to provide a quantitative mechanism for evaluating the risk of trading with a seller who has less than perfect feedback, and offer advice on how much a buyer should offer to pay, given an asking price on a commodity item and a seller's feedback history.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

Managing Risks in Multiple Online Auctions: An Options Approach*

The scenario of established business sellers utilizing online auction markets to reach consumers and sell new products is becoming increasingly common. We propose a class of risk management tools, loosely based on the concept of financial options that can be employed by such sellers. While conceptually similar to options in financial markets, we empirically demonstrate that option instruments within auction markets cannot be developed employing similar methodologies, because the fundamental tenets of extant option pricing models do not hold within online auction markets. We provide a framework to analyze the value proposition of options to potential sellers, option‐holder behavior implications on auction processes, and seller strategies to write and price options that maximize potential revenues. We then develop an approach that enables a seller to assess the demand for options under different option price and volume scenarios. We compare option prices derived from our approach with those derived from the Black‐Scholes model ( Black & Scholes, 1973 ) and discuss the implications of the price differences. Experiments based on actual auction data suggest that options can provide significant benefits under a variety of option‐holder behavioral patterns.     

Reputation and Mechanism Choice in Procurement Auctions: An Experiment

We experimentally study the role of reputation in procurement using two common mechanisms: price‐based and buyer‐determined auctions. While buyers are bound to buy from the lowest bidder in price‐based auctions, they can choose between bidders in buyer‐determined auctions. Only the latter buyers can consider the reputation of bidders. We find that bidders supply higher quality in buyer‐determined auctions leading to higher market efficiencies in these auctions. Accordingly, buyers prefer the buyer‐determined auction over the price‐based auction, while only half of the bidders do so. A more detailed analysis of buyers' and bidders' behavior and profits provides insights into their mechanism choice.     

Toward a Strategic Foundation for Rational Expectations Equilibrium

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double‐auction equilibrium is almost efficient and almost fully aggregates the agents' information.     

一类网上英式拍卖：顾客投标行为研究

网上拍卖作为一种新型营销手段正在越演越烈,在电子商务中举足轻重.网上拍卖结合传统拍卖与IT技术,有其独特性,文章以eBay为背景,研究一类有代理的网上英式拍卖,其中顾客逐个到达,卖方可以设置保留价也可以不设置保留价.具体分析了此类网上拍卖的动态进程.基此,在对顾客的到达过程与估价分布函数不作具体假设的一般情形下,证明了对于个人价值独立模型,顾客一到达就报价且报实价为占优战略.进而,将此与文献中关于关联价值模型下的均衡投标策略进行了比较分析,并解释了网上拍卖实践中的一些现象.     

Managing the Revenue of Sales Platforms: Insights into Service Fees

Online sales platforms have grown substantially in recent years. These platforms assist sellers to conduct sales, and in return, collect service fees from sellers. We study the fee policies by considering a fee‐setting platform, on which a seller may conduct a sale with a reserve price to a group of potential buyers: the seller retains the object for sale if the final trading price is below the reserve price. The platform may charge two types of fees as in current practice: a reserve fee as a function of the seller's reserve price and a final value fee as a function of the sale's final trading price. We derive the optimality condition for fee policies, and show that the platform can use either just a final value fee or just a reserve fee to achieve optimality. In the former case, the optimal final value fee charged by the platform is independent of the number of buyers. In the latter case, the optimal reserve fee is often a decreasing, instead of increasing, function of the seller's reserve price. An increasing reserve fee may make the seller reluctant to use a positive reserve price and hurt the platform's revenue. In general, the optimal fees are nonlinear functions, but in reality, linear fees are commonly used because of their simplicity for implementation. We show that a linear fee policy is indeed optimal in the case that the seller's valuation follows a power distribution. In other cases, our numerical analysis suggests close‐to‐optimal performance of the linear policy.     

信息不对称下可分公共物品的拍卖研究

在卖者面对两个风险厌恶的信息不对称知情投标者和一个风险中性的不知情投标者的假设下,研究可分公共物品的拍卖机制设计问题。通过最大化卖者的期望收入,同时满足所有投标者的理性参与约束与知情投标者的激励相容约束,建立了最优机制设计模型;给出了知情投标者的激励相容约束成立的充要条件,并用来简化了卖者的期望收入最大化问题。当不考虑随机性的卖方期望收入最大化问题时,利用Kuhn-Tucker条件进行求解,得到对每个知情投标者都存在一个临界值。当且仅当所报告的估价大于该值时,知情投标者可分配到一定数量拍品;同时,投标者报告的估值越高,就越能获得更多数量的拍品。研究结果对股票或债券发行的机制设计有参考价值,这是因为它们可看做可分的具有公共价值的商品。