考虑属性关联的两阶段获胜者确定模型

研究了多属性逆向拍卖的获胜者确定问题。考虑属性之间的两两关联，以定义在2-可加模糊测度上的Choquet积分表达拍卖人的偏好，其中模糊测度的值由拍卖人提供的偏好信息推测得出。由于一般情况下与偏好信息一致的模糊测度取值并不唯一，考虑所有一致的评分函数提出了两阶段获胜者确定方法。首先采用线性规划挑选出在任意评分函数下可能获胜的报价，再通过混合整数规划确定一个与所有一致的评分函数的评价结果最为接近的报价排序，以得分最高者为稳健获胜报价。仿真实验表明，大量的报价为不可能获胜报价，说明了在第一阶段进行筛选的必要性。与现有方法的比较表明了该方法的有效性，且在拍卖轮数较大、报价数目较多时，该方法在计算效率上更有优势。     

The Effect of Timing on Jump Bidding in Ascending Auctions

We investigate the role of timing in ascending auctions under the premise that time is a valuable resource. Traditional models of the English auction ignore timing issues by assuming that the auction occurs instantaneously. However, when auctions are slow, as Internet auctions used for procurement often are, there are significant opportunity or monitoring costs to bidders, and the choice of the size of the jump bid becomes a strategic decision. We study the choice in the experimental laboratory by systematically varying the opportunity costs associated with fast bidding. When time is more valuable bidders respond by choosing larger jump bids. Surprisingly, the economic performance of the auction is not significantly affected. We develop a simple model of ascending auctions with impatient bidders that provides insights into the effect jump bids have on auction performance.     

基于优先权拍卖的产能分配机制研究

本文考虑一个供应商和两个独立零售商构成的供应链系统。当供应商的产能受到约束时，零售商可能会竞争有限的产能。本文提出将“优先分配权”作为一个有价值的标的物进行拍卖，按照出价高低确定优先分配顺序。本文证明了优先权拍卖机制属于共同价值模型，并提出了两类拍卖机制：事先拍卖和事后拍卖。本文证明两类优先权拍卖机制均会促使零售商提交真实的需求作为订单量，并且满足收益等价定理。而就供应商期望利润而言，事后优先权拍卖机制要高于事先优先权拍卖机制。     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.     

Identification of Standard Auction Models

This paper presents new identification results for models of first–price, second–price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data. The simplest model—symmetric independent private values—is nonparametrically identified even if only the transaction price from each auction is observed. For richer models, identification and testable restrictions may be obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders; (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder–specific covariates. While many private values (PV) models are nonparametrically identified and testable with commonly available data, identification of common values (CV) models requires stringent assumptions. Nonetheless, the PV model can be tested against the CV alternative, even when neither model is identified.     

Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions

This paper studies the nonparametric identification of the first‐price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.     

First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue

We explore the impact of private information in sealed‐bid first‐price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning‐bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.     

Estimation of a Dynamic Auction Game

This paper proposes an estimation method for a repeated auction game under the presence of capacity constraints. The estimation strategy is computationally simple as it does not require solving for the equilibrium of the game. It uses a two stage approach. In the first stage the distribution of bids conditional on state variables is estimated using data on bids, bidder characteristics, and contract characteristics. In the second stage, an expression of the expected sum of future profits based on the distribution of bids is obtained, and costs are inferred based on the first order condition of optimal bids. We apply the estimation method to repeated highway construction procurement auctions in the state of California between May 1996 and May 1999. In this market, previously won uncompleted contracts reduce the probability of winning further contracts. We quantify the effect of intertemporal constraints on bidders' costs and on bids. Due to the intertemporal effect and also to bidder asymmetry, the auction can be inefficient. Based on the estimates of costs, we quantify efficiency losses.     

基于幂效用函数的多属性英式拍卖研究

以采购问题为背景研究多属性拍卖问题,其中拍卖问题的特点是：（1）包含任意有限个属性;（2）买卖双方的效用函数均具有加性结构,且在除价格以外的单个属性上,买方的效用函数和卖方的成本函数均为一般幂函数形式。首先,设计了一种买方事先公布评分函数而卖方轮流提交投标的多属性英式拍卖机制;其次,在卖方对称的假设下分析了拍卖机制中的最优投标策略,确定了最优投标价格和最优非价格属性值;然后,分析得出了最具成本优势的卖方最终胜出的条件以及最优多属性投标;最后,计算了该拍卖机制中买方的期望收益,并求出了使其期望收益最大化的最优评分函数权重。     

Optimal Nonparametric Estimation of First‐price Auctions

This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first‐price sealed‐bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two‐step kernel‐based estimator that converges at the optimal rate.     

AUCTION DESIGN WITHOUT COMMITMENT

In anonymous platforms like the Internet, committing to honor the outcome of an auction is difficult since the seller can benefit by reauctioning the good. We argue that how information is processed within the auction mechanism is crucially important in such circumstances. In our model, the seller uses an intermediary to extract information from the buyers but is not tied to sell the good with terms that the mechanism proposes. Instead, she may reauction the good again via some other intermediary. There are no restrictions on how many times and through which mechanisms the good can be reauctioned. The buyers may also choose their outside option at any stage of the game. We argue that a sequentially rational seller can only implement a version of the English auction, in particular the popular version where bidders employ proxy bids. This is a consequence of the informational properties of the English action: it reveals just the right information for the seller to be able to commit to the mechanism.     

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.     

Valuing Dealers' Informational Advantage: A Study of Canadian Treasury Auctions

In many financial markets, dealers have the advantage of observing the orders of their customers. To quantify the economic benefit that dealers derive from this advantage, we study detailed data from Canadian Treasury auctions, where dealers observe customer bids while preparing their own bids. In this setting, dealers can use information on customer bids to learn about (i) competition, that is, the distribution of competing bids in the auction, and (ii) fundamentals, that is, the ex post value of the security being auctioned. We devise formal hypothesis tests for both sources of informational advantage. In our data, we do not find evidence that dealers are learning about fundamentals. We find that the “information about competition” contained in customer bids accounts for 13–27% of dealers' expected profits.     

考虑广告主信誉和用户体验的GSP机制研究

目前,竞标在线广告位是广大广告主宣传其产品的重要途径之一,在线广告位的拍卖已成为搜索引擎企业最主要的盈利手段之一。在国内,广告位拍卖机制的逐利本质诱发了大量的虚假广告,引发了公众的广泛争议;拥有高报价的广告主并不总是带给搜索引擎用户好的用户体验,这些问题已成为搜索引擎亟需解决的重要问题。本文提出了一种既考虑广告主信誉又考虑用户体验的可信有效竞价广告位拍卖机制,定义了在该机制下的对称纳什均衡,给出了广告主的均衡竞价策略,证明了在该均衡下的配置是有效率的。通过与单纯竞价GSP拍卖机制进行比较,我们发现用户的满意度得到了提高,这增加了搜索引擎的竞争优势。此外,本文的拍卖机制不仅有利于促进广告主提高信誉,在提高搜索引擎的长期均衡收益和拍卖效率方面也有一定的优势。通过数值模拟验证了我们的结论。     

开放式逢低买入中买家数量确定的投标决策

逢低买入是一种新型的在线动态价格机制。本文以B2B开放式逢低买入拍卖为研究对象,在买家数量确定且独立投标的条件下,将已有的针对两个价格水平下买家最优订货决策拓展到更复杂的多个价格水平的最优订货决策问题。本文提出的零售商投标决策定理,不仅满足了买家的实际需求,也提高了决策的实用性。     

多属性采购拍卖的价值函数与打分规则

在多属性采购中,采购方不仅关心交易价格,更加关注供应商的交货时间和提供的装备质量对其价值的影响。为综合评价供应商的投标,采购方在采购拍卖开始时宣布一个打分规则。本文根据装备采购实践建立多属性采购拍卖的价值函数,以此为基础构建集成了质量属性、提前期属性和价格的三元打分规则。     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

网上逢低买入拍卖形式下的买方策略

逢低买入是一种新型的基于网络的动态定价方式。这种定价方式将不同的投标人联合起来以便获得数量折扣,它的一个特点就是商品的价格随着中标人数的增加而降低。本文采用独立私有估价假设,建立了一个不完全信息的动态博弈模型来解释在逢低买入机制下的买方的投标策略问题。通过求解发现,对于买方而言,存在一个弱占优策略:投标人投低于他估价的最大被允许投标值,这表明逢低买入拍卖是一种弱激励相容的机制。     

Bidding under auctioneer default risk

In a financially turbulent economy, participants of a procurement auction should consider in their bids the event of default of the auctioneer, which may result to substantial damages for the winning bidder. We examine a sealed bid auction, with private cost values and interdependence among the beliefs of the bidders about the auctioneer׳s default risk. The probability of payment of the bid price by the auctioneer is estimated by each bidder. For a first and a second price auction, we derive equilibrium bidding strategies, which address the risk of default and optimally adjust the bid price, introducing a risk premium in the form of an additional mark-up. A numerical illustration of the proposed strategies is provided. The effect of auctioneer׳s risk of default on the procurement project cost is examined. Financial arrangements that may be used to relax or eliminate the effect of the risk of default, such as early payment methods, third party guarantees or insurance programs are discussed and evaluated in comparison with the approach of risk premium on bid price.     

IT服务外包项目工期与费用控制的 多属性英氏逆拍卖机制

工期和费用是影响IT服务外包项目成败的两个重要因素,且两者之间呈负相关的关系。在IT服务外包项目执行前,发包方与接包方需要就项目的工期和费用达成一致。通常,发包方并不完全了解外包项目的市场行情,在这种情况下,就需要一种有效的方式使发包方和接包方之间就工期和费用达成一致。本文设计了改进的英氏逆拍卖机制,针对一对多的情况设计了新的拍卖协议;针对工期和费用的多属性情况,引入多属性效用理论解决,设计了相应的效用增加函数。最后通过一个算例来演示所设计的拍卖机制对解决此类决策问题的作用。得出一些结论:所设计机制能够以拍卖方式描述费用和工期管理流程;找到了发包方和接包方的最佳增量效用,并且建议的拍卖协议是发包方和接包方获得双赢结果的机制;从不同大小的案例中可以得到完全一致的结果,这表明设计的拍卖机制的有效性和效用增加函数对协商结果的有效性。