关键词拍卖中最优保留价的研究

研究了近年来在搜索引擎上广泛采用的一种广告形式——关键词拍卖.在关键词拍卖中如何设定每个关键词的保留价是搜索引擎在实践中向理论界提出的一个难题.通过建立一个可分单物品的拍卖模型来描述这种广告服务的销售机制,进而利用最优机制理论推导出每个关键词最优保留价所满足的方程.这一结果是对Riley和Samuelson关于最优机制研究中一个经典结论的推广,并可直接用于实践.     

佣金收取对拍卖结果的影响

在引入佣金提成的独立私人价值模型及关联价值模型中,讨论第一价格和第二价格拍 卖,发现佣金比例k 的大小对投标人的出价策略、卖方和拍卖行的期望收益都有影响. k 越大, 买方出价越谨慎,卖方的期望收益更少,拍卖行的期望收益却更大. 虽然买方会随着k 的增大 出价更谨慎,但均衡期望收益却与k 无关. 在独立私人价值模型中,当引入佣金时,收益等价 性仍然成立. 这对拍卖实践提供了建议:投标人(买方) 对于佣金比例高低的担忧是多余的     

考虑佣金的关联价值拍卖模型

在标准的只考虑买卖双方的拍卖模型中引入第三方,拍卖公司.拍卖公司提供服务要收取一定的佣金,佣金费用由买家支付,支付额占成交价的比例为k.文章发现,佣金比例k的大小对买卖双方均有一定影响:买方的出价策略变得谨慎但是其均衡期望收益却与k无关;卖方的期望收益受到影响而降低.事实上,拍卖公司的佣金就是来自于卖方的期望收益中.文中就第一价格与第二价格机制在关联价值模型上讨论佣金问题,得到的结果有较普遍的意义.     

拍卖中的串通出价

本文在扩展的独立私有价值模型下,考虑第二价格和第一价格拍卖机制下的串通出价行为和卖方对串通出价的反映。第二价格串通出价机制和第一价格串通出价机制分别为在这两种拍卖机制下的激励相容、有效的直接显示串通出价机制。我们发现卖方若知道有串通行为,可以提高保留价来减少损失。由于卖方一般情况下不太可能确定是否存在串通行为及参与串通的人数k,但可以确定给定保留价时串通人数的'最优反应',在第二价格串通出价机制下,给定串通人数,增加保留价可以提高卖方的期望收益,对于确定的保留价,串通人数的增加会减少卖方的期望收益。从而存在这样的纳什均衡:所有的投标人串通,即,k=N,而卖方宣布与之相应的保留价r (N)。当然,并不是所有的串通出价对投标人都是有利可图的,在第一价格拍卖机制下,若卖方可以调整保留价,只有当参与竞投的人很多时,串通出价才有利可图。     

三类风险投标者共存下的一级价格拍卖

许多拍卖文献在研究投标者的投标策略时,假设所有投标者要么是风险中性的,要么是风险规避的.但是,在实际投标中,可能风险中性、风险规避和风险爱好的投标者同时存在.针对1级价格密封式拍卖,假设3类风险投标者共存,通过引入"风险指标"度量3类风险投标者的风险态度,给出了投标者的对称均衡投标策略,推广了经典的独立私人估价模型;此外,说明各类风险偏好的投标者的"风险指标"不仅对自己的报价有正向影响,而且对其他风险偏好的投标者的报价有交叉影响.     

多物品网上拍卖的最优设计

考虑网上拍卖与传统拍卖相比的特性,包括竞标者随机到达,末尾抢标效应,拍卖平台的存在和收费,以及多物品多批次,系统地研究多物品网上拍卖中的一些重要问题.结果表明,竞标者估值离差越大的商品越适合通过拍卖来进行销售,但前提是网络用户基础必须要达到一定规模;在统一分析框架下,分别求解了卖者最优的公开保留价格和隐藏保留价格,并证...     

在线拍卖中的“托”出价研究

本文分析了独立的私人估价环境下最优保留价格与竞买人数之间的关系,纠正了最优保留价格与竞买人数无关的传统观点.在此基础上,讨论了卖者可能递交"托"出价的条件以及拍卖中只剩下一个竞买人时卖者的最优"托"出价.     

两类拍卖的收益等价性和均衡投标价格排序

以收益等价原理为基础,在独立私人估价模型假设下将四类基本拍卖形式与两类全支付拍卖形式进行对比研究.依据买者的均衡期望收益、卖者的均衡期望收益和均衡期望报价这三个指标,给出了排序关系.得出了报价虽然不同,但不同拍卖形式中买卖双方期望收益等价的结论.并将收益等价原理用于均衡策略的求解.     

关键词拍卖中基于广义第一价格的投标价格决策分析

在关键词拍卖中,由于广告商不能保证对关键词的估价是最优投标价格,因此如何选取最优的关键词投标价格一直是广告商急于解决的问题。基于与Friedman投标模型假设条件等价的关键词拍卖投标假设条件,计算了各个关键词广告位置的胜标概率,并在广义第一价格拍卖机制下建立了关键词投标价格决策模型。该模型可以使广告商选取最优的关键词投标价格。最后通过仿真验证了该模型的有效性。     

在线逆向拍卖期权和单方支付契约下的供应链协调机制分析

根据报童模型和信息揭示原理建立了在线逆向拍卖期权和单方支付契约下生产商、销售商和系统的利润模型。通过对模型的优化得到两种电子佣金制度下的最优期权订购量。比较最优期权订购量和系统最优生产容量,分析了不同电子佣金制度及期权和单方支付契约类型下供应链协调特征。得到以下结论:对于具有单季节随机市场需求特征产品的期权和单方支付契约拍卖中,若生产商执行单方支付,系统不能被协调。若销售商执行单方支付,系统的协凋与电子佣金的制度有关;在赢得契约生产商支付电子佣金的制度下,最利于系统的协调和利润的分配。     

Behavior in Multi‐Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.     

Optimal Reserve Prices in Name‐Your‐Own‐Price Auctions with Bidding and Channel Options

Few papers have explored the optimal reserve prices in the name‐your‐own‐price (NYOP) channel with bidding options in a multiple channel environment. In this paper, we investigate a double‐bid business model in which the consumers can bid twice in the NYOP channel, and compare it with the single‐bid case. We also study the impact of adding a retailer‐own list‐price channel on the optimal reserve prices. This paper focuses on achieving some basic understanding on the potential gain of adding a second bid option to a single‐bid system and on the potential benefits of adding a list‐price channel by the NYOP retailer. We show that a double‐bid scenario can outperform a single‐bid scenario in both single‐channel and dual‐channel situations. The optimal reserve price in the double‐bid scenario is no less than that in the single‐bid case. Furthermore, the addition of a retailer‐own list‐price channel could push up the reserve prices in both single‐bid and double‐bid scenarios.     

On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First‐Price Auctions

We establish the existence of pure strategy equilibria in monotone bidding functions in first‐price auctions with asymmetric bidders, interdependent values, and affiliated one‐dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second‐price auctions.     

网上拍卖销售与逆向拍卖采购下的库存管理

以电子商务为背景研究网上拍卖销售与逆向拍卖采购下的库存管理。在该问题中,零售商一方面利用网上拍卖销售产品,另一方面利用逆向拍卖进行采购。对于单阶段情形,证明网上拍卖下零售商的期望收益函数是采购量的严格递增的凹函数,从而得到零售商的最优采购策略和供应商的最优投标策略。对于多阶段情形,利用马尔可夫决策过程理论建立该问题的最优控制模型,得到零售商的最优采购策略和供应商的贝叶斯-纳什均衡投标策略均与基本库存策略相类似。     

电商平台扣点率影响下的双渠道供应链协调定价研究

电商平台通常对入驻企业征收技术服务费、推广费用和促销活动费用等,这部分费用占销售额的比例即电商平台扣点率成为影响入驻企业定价的重要因素。有鉴于此,本文研究了电商平台扣点率影响下的双渠道供应链协调定价问题。首先构建了追求供应链整体利润最大化的集中式定价模型,得出最优线上、线下渠道销售价格,分析了扣点率影响下的价格、销量与利润变化,逐步确定了扣点率的决策范围。然后以分散式决策下企业最优利润为基准设计基于Shapley值的协调定价方案以确定最优线下渠道批发价格,给出了协调后的最优定价,最后使用Mathematica 11软件进行了数值分析与仿真。这一研究对解释电商平台扣点率影响下的双渠道供应链协调定价机制与相关指标的变化,实现企业和电商平台的良性互动具有重要意义。     

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。     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

Ranked Items Auctions and Online Advertisement

We study auctions for a set of commonly‐ranked items where each buyer has unit demand. This setting has promising applications in areas such as keyword auctions in the search engine advertising industry, the sale of quality‐ranked raw materials, etc. An auction mechanism suitable for this setting is the simultaneous pooled auction (SPA), where each bidder simultaneously submits a single bid and is allocated an object based on the rank of his bid among all the bids. We study how to improve the seller's expected revenue by enforcing a reserve price in an SPA. We find that the use of an appropriate reserve price may significantly increase the seller's revenue, especially when the number of items for sale is relatively large compared to the number of participating bidders. One inherent problem in the SPA is that some bidders may incur ex post losses; that is, they pay more than what they value the received objects. We propose a tailored VCG mechanism that generates the same expected revenue as the SPA does, while bidders do not incur any ex post loss. We also discuss the potential applications of this research to keyword auctions.