基于Priceline的易腐品网上逆向拍卖研究
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摘要
电子商务为新的商业模式提供了广阔的天地,同时各种商业模式也丰富了电子商务的发展,由Priceline.com率先推出的B2C网上逆向拍卖模式就是其中之一。Priceline采用独特的“由你定价”交易模式,在成立的几年内已经在注册用户数量、营业收入和业内影响力等方面取得了骄人成绩,成为国际著名网站。然而,对B2C网上逆向拍卖的定量理论研究相对较少,本论文将对通过Priceline交易的顾客(买方)和商家(卖方)进行研究,重点在于买方的报价策略和卖方的保留价策略。
首先,采用不完全信息静态博弈的方法,在一定的条件下,建立卖方的模型,证明卖方均衡保留价随其成本递增,但是小于其成本;分析买方报价策略,证明买方最优报价随其估价递增,并且满足既定条件时是唯一最优报价;对卖方保留价策略和买方报价策略进行数值分析,结果验证了理论分析的正确性。
随后,研究在通过Priceline销售易腐商品的过程中,卖方如何动态设定其保留价,从而使得自己在销售期内的期望收益最大。分别从连续时间和离散时间两个角度进行研究。首先研究连续时间情形,运用最优控制的方法建立数学模型,并进行理论分析,获得了最优值和最优策略的一些性质;之后运用动态规划方法建立多阶段卖方动态设定保留价模型,得到了和连续时间模型相似的性质;数值分析进一步说明我们的结论,并和传统收益管理进行比较,得出结论。
论文还探讨基于Priceline的买方/卖方定价收益管理问题。假定顾客到达是一任意的更新过程,决策时刻为顾客到达时刻。对于每个顾客只有单个需求的情形,分别建立卖方定价和买方定价下的马氏决策过程模型,并获得最优策略的表达式。而在传统收益管理问题中,通常是卖方定价、连续时间决策、同时需要假定顾客到达是一Poisson过程。对于买方定价,证明卖方是否知道到达顾客的报价信息不影响他的收益;同时,随着剩余物品数的增加,卖方的期望收益递增,而边际收益和最优价格递减。对于卖方定价,对期望收益和最优价格得到类似的结论。之后讨论两种定价方式下卖方的期望收益之间的关系;并将结论推广到顾客需求是多重的情形。数值分析验证了所得的结论。
Electronic commerce has provided a wide field for the new business models. Meanwhile, all kinds of business models have enriched the electronic commerce's development. In the Business-to-Customer situation, one of them is reverse auctions represented by Priceline.com. As the unique business model of Name Your Own Price, Priceline has owned millions of registration users and rapid growth of business income. It mainly deals in perishable commodities and has been a famous international reverse auction website since it was operated. However, quantitative research on Priceline is relatively not rich. The dissertation aims to study customers' behavior and sellers' policies based on Priceline, mainly on customers' bidding strategies and sellers' pricing policies. The main contribution of the dissertation includes the following three aspects.
First, the dissertation studies the reserve price policies for the sellers and the bidding strategies for the customers by static game theory under incomplete information. We show under some basic assumptions that the optimal reserve price is increasing in the cost, but less than the cost for the seller. We also show that customers' bidding prices are increasing in their valuation, and the optimal bidding prices are exclusive under some condition. The results have been illustrated by numerical analysis.
Second, this dissertation studies a problem of how to dynamically set reserve prices for some goods of the seller in a period of time when customers arrive at Priceline one after another according to a non-stationary Poisson process, so that the seller can gain maximal expected revenue. We consider this problem in two aspects, one is the continuous time model, and the other is the multi-stage model. The dissertation discusses the continuous time model first. The optimal control model of the expected revenue for sellers is presented, and some theoretical results have been obtained. After that, we set up a multi-stage mathematical model with dynamic programming, and make analysis on this model. Some properties of optimal value and optimal price are obtained, which are quite similar to the ones of continuous time model. Numerical analysis are consistent with theoretical results, and the comparison of traditional revenue management with continuous time model illustrates that the closer the bidding price is to the valuation, the more dominant Priceline will be to revenue management.
Finally, we study revenue management problems with either customer-pricing or seller-pricing. Here, a seller wants to sell a given amount of items in a fixed time, customers arrive according to an arbitrary renewal process. In the customer pricing, customers bid and then the seller decides to accept or reject their bids; while in the seller pricing, the seller decides the price and then customers determine to accept or reject the price. Markov decision processes models are presented and expressions for the optimal policies are obtained. These problems differ from the traditional revenue management problems where (1) the seller sets continuously a price, and (2) customers arrive according to a Poisson process. It is shown for the customer-pricing that there is no impact on the seller whether or not he knows the customers' private information, the optimal policy is monotone in the remaining items, and the optimal value is the concave function of the remaining items. Similar results of expected revenue and optimal price strategy have been obtained. Also, the expected revenues of the seller in the two pricing cases are compared, and the models and the results are generalized to the multiple demand case. Finally, the models and the results are illustrated by numerical analysis.
首先,采用不完全信息静态博弈的方法,在一定的条件下,建立卖方的模型,证明卖方均衡保留价随其成本递增,但是小于其成本;分析买方报价策略,证明买方最优报价随其估价递增,并且满足既定条件时是唯一最优报价;对卖方保留价策略和买方报价策略进行数值分析,结果验证了理论分析的正确性。
随后,研究在通过Priceline销售易腐商品的过程中,卖方如何动态设定其保留价,从而使得自己在销售期内的期望收益最大。分别从连续时间和离散时间两个角度进行研究。首先研究连续时间情形,运用最优控制的方法建立数学模型,并进行理论分析,获得了最优值和最优策略的一些性质;之后运用动态规划方法建立多阶段卖方动态设定保留价模型,得到了和连续时间模型相似的性质;数值分析进一步说明我们的结论,并和传统收益管理进行比较,得出结论。
论文还探讨基于Priceline的买方/卖方定价收益管理问题。假定顾客到达是一任意的更新过程,决策时刻为顾客到达时刻。对于每个顾客只有单个需求的情形,分别建立卖方定价和买方定价下的马氏决策过程模型,并获得最优策略的表达式。而在传统收益管理问题中,通常是卖方定价、连续时间决策、同时需要假定顾客到达是一Poisson过程。对于买方定价,证明卖方是否知道到达顾客的报价信息不影响他的收益;同时,随着剩余物品数的增加,卖方的期望收益递增,而边际收益和最优价格递减。对于卖方定价,对期望收益和最优价格得到类似的结论。之后讨论两种定价方式下卖方的期望收益之间的关系;并将结论推广到顾客需求是多重的情形。数值分析验证了所得的结论。
Electronic commerce has provided a wide field for the new business models. Meanwhile, all kinds of business models have enriched the electronic commerce's development. In the Business-to-Customer situation, one of them is reverse auctions represented by Priceline.com. As the unique business model of Name Your Own Price, Priceline has owned millions of registration users and rapid growth of business income. It mainly deals in perishable commodities and has been a famous international reverse auction website since it was operated. However, quantitative research on Priceline is relatively not rich. The dissertation aims to study customers' behavior and sellers' policies based on Priceline, mainly on customers' bidding strategies and sellers' pricing policies. The main contribution of the dissertation includes the following three aspects.
First, the dissertation studies the reserve price policies for the sellers and the bidding strategies for the customers by static game theory under incomplete information. We show under some basic assumptions that the optimal reserve price is increasing in the cost, but less than the cost for the seller. We also show that customers' bidding prices are increasing in their valuation, and the optimal bidding prices are exclusive under some condition. The results have been illustrated by numerical analysis.
Second, this dissertation studies a problem of how to dynamically set reserve prices for some goods of the seller in a period of time when customers arrive at Priceline one after another according to a non-stationary Poisson process, so that the seller can gain maximal expected revenue. We consider this problem in two aspects, one is the continuous time model, and the other is the multi-stage model. The dissertation discusses the continuous time model first. The optimal control model of the expected revenue for sellers is presented, and some theoretical results have been obtained. After that, we set up a multi-stage mathematical model with dynamic programming, and make analysis on this model. Some properties of optimal value and optimal price are obtained, which are quite similar to the ones of continuous time model. Numerical analysis are consistent with theoretical results, and the comparison of traditional revenue management with continuous time model illustrates that the closer the bidding price is to the valuation, the more dominant Priceline will be to revenue management.
Finally, we study revenue management problems with either customer-pricing or seller-pricing. Here, a seller wants to sell a given amount of items in a fixed time, customers arrive according to an arbitrary renewal process. In the customer pricing, customers bid and then the seller decides to accept or reject their bids; while in the seller pricing, the seller decides the price and then customers determine to accept or reject the price. Markov decision processes models are presented and expressions for the optimal policies are obtained. These problems differ from the traditional revenue management problems where (1) the seller sets continuously a price, and (2) customers arrive according to a Poisson process. It is shown for the customer-pricing that there is no impact on the seller whether or not he knows the customers' private information, the optimal policy is monotone in the remaining items, and the optimal value is the concave function of the remaining items. Similar results of expected revenue and optimal price strategy have been obtained. Also, the expected revenues of the seller in the two pricing cases are compared, and the models and the results are generalized to the multiple demand case. Finally, the models and the results are illustrated by numerical analysis.
引文
[1]陈剑,黄河.基于树型结构的在线逆向组合拍卖模型.系统工程理论方法应用,2004,13(4):310-315.
[2]陈剑,黄河.逆向组合拍卖投标者获胜概率研究.系统工程理论与实践,2005,(3):13-19.
[3]陈开周.最优化计算方法.西安:西安电子科技大学出版社,69-87.
[4]邓永录,梁之舜.随机点过程及其应用.北京:科技出版社,1992.
[5]杜黎,胡奇英.网上拍卖品数量的优化.西安电子科技大学学报,2003,30(1):120-124.
[6]杜黎,胡奇英.网上分批拍卖中的保留价比较分析.系统科学与数学,2002,22(3):343-354.
[7]杜黎,胡奇英.一类网上英式拍卖:顾客投标行为研究.管理科学学报,2006,9(3):31-38.
[8]杜黎,胡奇英等译.保尔·米格罗姆(Paul Milgrom)著,拍卖理论与实务(Putting Auction Theory to Work).北京:清华大学出版社,2006.
[9]高强,朱金福.航空收益管理中非限化估计方法研究.预测,2005,24(5):66-69.
[10]官振中,陈旭.卜祥智和史本山.易逝性高科技产品收益管理资源分配及定价策略.系统工程,2006,24(1):23-29.
[11]官振中,史本山.基于顾客选择模型易逝性产品收益管理订购和定价策略.系统工程理论与实践,2007,(9):47-53.
[12]胡奇英,刘建庸.马尔可夫决策过程引论.西安:西安电子科技大学出版社,2000.
[13]胡奇英.随机终止的非平稳折扣半马氏决策规划.应用数学学报,1993,16(4):566-570.
[14]李冰州,武振业和卜祥智.能力随机的海运集装箱收益管理超订模型.西南交通大学学报,2006,41(4):501-506.
[15]李为相,赵林度.基于拍卖的电子商务动态定价研究.南京工业大学学报,2005,27(4):67-70.
[16]李晓花,萧柏春.航空公司收入管理价格与舱位控制的统一分析.管理科学学报,2004,7(6):63-69.
[17]刘晓君,席酉民.拍卖理论与实务.北京:机械工业出版社,2000.
[18]罗利,彭际华.竞争环境下的民航客运收益管理动态定价模型.系统工程理论与实践,2007,(11):15-25.
[19]马俊,汪寿阳,黎建强.e-Auction网上拍卖理论与实务.科学出版社,2003.
[20]毛用才,胡奇英.随机过程.西安:西安电子科技大学出版社,1998.
[21]梅虎,朱金福和汪侠.基于博弈分析的航空收益管理定价研究.预测,2006,25(6):45-49.
[22]梅虎,朱金福和汪侠.基于旅客舱位选择的航空收益管理.系统工程,2006,24(9):11-17.
[23]王忠民,梁军民,郭立宏.拍卖理论与应用.西北大学出版社,1999.
[24]魏轶华.随机环境下的若干定价问题研究.博士学位论文,西安电子科技大学,2004年10月.
[25]魏轶华,胡奇英.顾客有最大最小保留价的连续时间收益管理.管理科学学报,2002,5(6):47-52.
[26]吴继兰,李培亮。基于供应链绩效的网上逆向拍卖模型.管理科学,2007,20(6):31-35.
[27]解学书.最优控制理论与应用.清华大学出版社,1986.
[28]张光澄.最优控制问题计算方法.成都:科技大学出版社,1991.
[29]张维迎.博弈论与信息经济学.上海:上海三联出版社,1996.
[30]Ayhan S H and Foley R D.Relationships among three assumption in revenue management.Operations Research,2004,52:804-809.
[31]Anand S K and R Aron.Group- buying on the web:a Comparison of price discovery mechanisms.Management Science,2003,49:1546-1562.
[32]Bajari P and Hortacsu A.Online Auctions:A review of empirical findings.The Journal of Economic Literature,2000.
[33]Bajari P and Hortascu A.Winner's curse,reserve prices and endogenous entry:Empirical insights from eBay auctions.Working paper,Department of Economics,Stanford University,Stanford,CA.2002.
[34]Bajari P and Summers G.Detecting Collusion in Procurernent Auctions:A Selective Survey of Recent Research.Antitrust Law Journal,2002,70:143-170.
[35]Bapna R.Online Auctions:A closer look.in Lowry,P(ed),Handbook of Electronic Commerce in Business and Society.CRC Press,2001.
[36]Bapna R,Goes P and Gupta A.A theoretical and empirical investigation of multi-item on-line auctions.Information technology and Management,2001,1:1-23.
[37]Bapna R,Goes P and Gupta A.Analysis and design of Business-to-Consumer online auctions.Management Science,2003a,49:85-101.
[38]Bapna R,Goes P and Gupta A.Replicating online Yankee auctions to analyze auctioneers' and bidders' strategies.Information Systems Research,2003b,14:244-268.
[39]Beam C and A Segev.Auctions on the Internet:A field study.Working paper,Haas School of business,University of California Berkeley.http://groups.haas.berkeley.edu/citm/publications/papers/wp-1032.pdf,1998.
[40]Belobaba P P.Air travel demand and airline seat inventory management D.Ph.D.thesis,Cambrid ge:HIT,1987.
[41] Bclobaba P P. Airline yield management: an review of seat inventory control.Transportation Science, 1987, 21: 63-73.
[42] Bertsimas D, Hawkins J and Perakis G. Optimal bidding in online auctions.Working Paper, MIT, 2001: 153.
[43] Besanko D and W L Winston. Optimal price skimming by a monopolist facing rational consumers. Management Science, 1990, 36(5): 555-567.
[44] Biais B, Hillion P and Spatt C. An empirical analysis of the limit order book and the order flow in the Paris Bourse. Journal of Finance, 1995, 50(5): 1655-1689.
[45] Brumelle S L. Allocation of airline seats between stochastically dependent demand. Transportation Science, 1990, 24: 87-116.
[46] Brumelle S L and Walczak D. Dynamic allocation of airline seat inventory with batch arrivals. Air Transport Research Group of the WCTR Society Proc. 3, Faculty of Commerce and Business Administration, University of British Columbia,Vancouver, BC. 1997.
[47] Chatwin R E. Continuous-time airline overbooking with time dependent fares and refunds. Transportation Science, 2000, 33: 182-191.
[48] Chen L and De Mello T H. Multistage stochastic programming models for airline revenue management. Working paper of Northwestern University, 2004.
[49] Chiang W C, Chen J C H and Xu X. An overview of research on revenue management: current issues and future research. Int. J. Revenue Management, 2007,1(1): 97-128.
[50] Choua F S and Parlarb M. Optimal quota allocation for a revenue-maximizing auction holder facing a random number of bidders. International Transactions in Operation Research, 2005, 12: 559-580.
[51] Chui K and R Zwick. Auctions on the Internet- A Preliminary study. Working Paper. Hongkong University of Science and Technology.http://home.ust.hk/ mkzwick/papers/auction.pdf, 1999.
[52] Curry R. Optimal airline seat allocation with fare classes nested by origins destination. Acronomics Incorporated Report. 1989.
[53] Ding M, J Eliashbcrg, J Huber and R Saini. Emotional bidders: An analytical and experimental examination of consumers' behavior in reverse auction, Working paper, 2002.
[54] Easley F R and R Tenorio. Jump Bidding strategies in Internet Auctions, Management Science, 2004, 50: 1407-1419.
[55] Elmaghraby W. The importance of ordering in sequential auctions. Management Science, 2003, 49(5). 673-682.
[56] Emiliani R and Stec D. Realizing savingsfrom on-Line reverse auctions. Supply Chain Management, 2002, 7: 12-23.
[57] Eso M. An iterative online auction for airline Seats. Technical report, IBM T J Watson Research Center, February, 2001.
[58] Feng Y Y and G Gallego. Perishable asset revenue mangement with Markovian time dependent demand intensities. Management Science, 2000, 46(7): 941-956.
[59] Feng Y Y and Xiao B C. A continuous-time yield management model with multiple price and reversible price changes. Management Science, 2000a, 46(5): 644-657.
[60] Feng Y Y and Xiao B C. A dynamic airline seat inventory control model and its optimal policy. Operations Research, 2001, 49(6):938-949.
[61] Feng Y Y and Xiao B C. Optimal policies of yield management with multiple predetermined prices. Operations Research, 2000, 48(2): 332-343.
[62] Feng Y Y and Gallego G. Optimal starting times for end-of-scason sales and optimal stopping times for promotional fares. Management Science, 1995, 41:1371-1391.
[63] Friedman L. A competitive bidding strategy. Operations Research, 1956, 4. 104-112.
[64] Gallego G and Van Ryzin G J. A multiproduct dynamic pricing problem and its applications to network yield management. Operation Research, 1997, 45(1):24-41.
[65] Gallego G and van Ryzin G J. Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Science, 1994, 40: 999-1020.
[66] Glober F, Glover R, Lorenzo J and McMillan C. The passenger mix problem in the scheduled airlines. Interfaces, 1982, 12: 73-79.
[67] Gottlieb B. Docs group-shopping work? The economics of Mercata and Mobshop.Posted on http://www.slate.lycos.com/Features/groupshop/groupshop.asp, 2000.
[68] Graham D A, R C Marshall and Jean-Francois Richard. Phantom bidding against heterogeneous bidders. Economic Letters, 1990(32): 13-17.
[69] Hann I and C Terwiesch. Measuring the frictional costs of online auctions: The case of a name-your-own-price channel. Management Science, 2003, 49(11): 1565-1581.
[70] Harstad R M. Alternative common- value auction procedures: Revenue comparisons with free entry. J. Political Econom, 1990, 98: 421-429.
[71] Kahn Research Group LLC. Group Buying and the Internet.http://www.webehavior.com/group.htm, 2000.
[72] Kannan P K and P K Kopalle. Dynamic pricing on the Internet: Importance and implications for consumer behavior.International Journal of Electronic Commerce, 2001, 5(3): 63-83.
[73] Karacsman I and van Ryzin G J. Overbooking with substitutable inventory classes. Operation Research, 2004, 52(1): 83-104.
[74] Kauffman R J and Wang B. New Buyers' Arrival under Dynamic Pricing Market Microstructure: The Case of Group- Buying Discounts on the Internet. Journal of management Information Systems, 2002a, 18: 157-188.
[75] Kauffman R J and Wang B. Bid Together, Buy together: On the Efficacy of Group-Buying Business Models in Internet-Based Selling. Handbook of Electronic Commerce in Business and Society, Boca Raton, FL: CRC Press, 2002b.
[76] Kauffman R J and Wood A C. Doing thcir bidding: An empirical examination of factors that affect a buyer's utility in Internet auctions. Forthcoming in Information Technology and Management, 2004.
[77] Kauffman R J and Wood A C. The effects of shilling on final bid prices in online auctions. Forthcoming in Electronic Commerce Research and Applications, 2005.
[78] Laffont J J, Ossard H and Vuong Q. Econometrics of First-Price Auctions. Econo-metrica, 1995, 63: 953-980.
[79] Lawrence M Ausubcl and Peter Cramton. Auctioning Many Divisible Goods.Journal of the European Economic Association, MIT Press, 2004, 2(3): 480-493.
[80] Lee T C and Hersh M. A model for dynamic airline scat inventory control with multiple seat bookings. Transportation Science, 1993, 27: 252-265.
[81] Littlcwood K. Forecasting and Control of Passengers. 12th AGIFORS SymposiumProceedings, 1972, 103-105.
[82] Lucking- Reiley D. Auctions on the Internet: what's Being Auctioned and How?Journal of Industrial Economics, 2000, 48: 227-252.
[83] Lucking- Reiley D, Bryan D, Prasad N and Reeves D. Pennies from ebay: the determinants of price in online auctions. Working paper. Vanderbilt University.Http://eller. arizona. edu/ reiley/papers/pcnnies fromEbay.pdf, 1999.
[84] Maglaras C and Meissner J. Dynamic pricing strategies for multi-product revenue management problems. Manufacturing and Service Operation Management,2006, 8: 136-148.
[85] McAfee R P and J McMillan. Auctions and Bidding. Journal of Economic Literature, 1987, XXV: 699-738.
[86] Metha K and Lee B T. Efficiency comparison in electronic market mechanisms:Posted price versus auction market. WISE Conference, Charlotte, NC, 1999a.
[87] Mctha K and Lee B T. Empirical evidence of winner's curse in electronic auctions. Proceedings of the 20th International Conference on Information Systems,Charlotte, NC, 1999b.
[88] Millet I, Parcntc H D, Fizcl L J and Venkataraman R R. Metrics for managing online procurement auctions. Interfaces, 2004, 34: 171-179.
[89] Mittal V and Kamakura W A. Satisfaction, repurchase intent, and repurchase behavior: investigating the moderating effect of customer characteristics. Journal of Marketing Research, 2001, 38(1): 131-42.
[90] Ockenfels A and Roth E A. Strategic late- bidding in continuous- time second-price internet auctions. Working Paper. Germany: University of Magdeburg,2001.
[91] Paarsch H J. Deciding between common values and private value. Paradigms in Empirical Models of Auctions, Journal of Econometrics, 1992, 51: 191-215.
[92] Pinker J E, Seidmann A and Vakrat Y. Managing Online Auctions: Current Business and Research Issues. Management Science, 2003, 49: 1457-1484.
[93] Pinker J E, Seigmann A and Vakrat Y. Using transaction data for the design of sequential, multi-unit online auctions. Working Paper CIS-00-03, Simon School,University of Rochester, Rochester, NY. 2000.
[94] Roth A E and Ockenfcls A. Last minute bidding and the rules for ending second-price auctions: evidence from ebay and Amazon Auctions on the Internet. American Economic Review, 2002, 92: 1093-1103.
[95] Rothkopf M H and Harstad R M. On the role of discrete bid levels in oral auctions.Europe Journal of Operational Research, 1994a, 74: 572-581.
[96] Schwartz E and B Mendel. New auction business model helps suppliers retain price integrity.http://www.infoworld.com/cgi-bin/displayStory.pl? 991018. hnauctions.htm, 1999.
[97] Segev A, C Beam, and J Shanthikumar. Optimal design of Internet-based auctions. Inform. Tech. & Management, 2001, 2, 121-163.
[98] Sinha A R and E A Greenleaf. The impact of discrete bidding and bidder aggressiveness on sellers' strategics in open English auctions: Reserves and covert shilling. Marketing Science, 2000, 19(3): 244-265.
[99] Stidham S J. Optimal control of admission to a qucucing system. IEEE Trans.AC, 1985, 30(8): 705-713.
[100] Talluri K and van Ryzin G. The theory and practice of revenue management.New York: Kluwer Academic Publishers, 2004a.
[101] Talluri K and van Ryzin G. Revenue management under a general discrete choice model of consumer behavior. Management Science, 2004b, 50: 15-33.
[102] Vakrat Y and Seidmann A. Implications of the bidders' process on the design of online auctions. In proceedings of the 33rd Hawaii International Conference on System Sciences, R. Spraguc(ed. ), Los Alamitos, CA: IEEE Computer Society Press, CD- ROM, 2000.
[103] van Ryzin G and Vulcano G. Optimal Auctioning and Ordering in an Infinite Horizon Inventory-Pricing System. Operations Research, 2004, 52: 346-367.
[104] Vickrey W. Countcrspeculation, auctons,and sealed tenders. Journal of Finance,1961, 16: 8-37.
[105] Vulcano G, van Ryzin G J and Maglaras C. Optimal dynamic auctions for revenue management. Mangcment Science, 2002, 48(11): 1388-1407.
[106] Wang K, Wang Eric T G and Tai, C. A study of online auction sites in Taiwan:Product, auction rule, and trading type. International Journal of Information Management, 2002, 22: 127-142.
[107] Wang W, Hidvegi Z and Whinston A B. Shill bidding in English auctions.Working paper. Center for Research on E-Commerce, McComb School of Business. Austin: University of Texas, 2001.
[108] Wollmer R. An airline scat management model for a single leg route when lower fare classes book first. Operations Research, 1992, 40(1): 26-37.
[109] Wood C A. What factors drive finalprice in Internet auctions? An empirical assessment of coin transactions on eBay. Annual convention of the Institute for Operations Research and the Management Sciences. Nov. 6. Miami Beach, Fla,2001.
[110] Wurman P R. Online auction site management. Working paper,http://www.csc.ncsu.edu/faculty/wurman/Papers/Wurman-article.pdf, 2003.
[111] Zhang D and Cooper W L. Revenue management for parallel flights with customer-choice behavior. Operation Research, 2005, 53(3): 415-431.
[112] Zhao W and Zheng Y S. Optimal dynamic pricing for perishable assets with nonhomogeneous demand. Management Science, 2000, 46(3): 375-388.
[2]陈剑,黄河.逆向组合拍卖投标者获胜概率研究.系统工程理论与实践,2005,(3):13-19.
[3]陈开周.最优化计算方法.西安:西安电子科技大学出版社,69-87.
[4]邓永录,梁之舜.随机点过程及其应用.北京:科技出版社,1992.
[5]杜黎,胡奇英.网上拍卖品数量的优化.西安电子科技大学学报,2003,30(1):120-124.
[6]杜黎,胡奇英.网上分批拍卖中的保留价比较分析.系统科学与数学,2002,22(3):343-354.
[7]杜黎,胡奇英.一类网上英式拍卖:顾客投标行为研究.管理科学学报,2006,9(3):31-38.
[8]杜黎,胡奇英等译.保尔·米格罗姆(Paul Milgrom)著,拍卖理论与实务(Putting Auction Theory to Work).北京:清华大学出版社,2006.
[9]高强,朱金福.航空收益管理中非限化估计方法研究.预测,2005,24(5):66-69.
[10]官振中,陈旭.卜祥智和史本山.易逝性高科技产品收益管理资源分配及定价策略.系统工程,2006,24(1):23-29.
[11]官振中,史本山.基于顾客选择模型易逝性产品收益管理订购和定价策略.系统工程理论与实践,2007,(9):47-53.
[12]胡奇英,刘建庸.马尔可夫决策过程引论.西安:西安电子科技大学出版社,2000.
[13]胡奇英.随机终止的非平稳折扣半马氏决策规划.应用数学学报,1993,16(4):566-570.
[14]李冰州,武振业和卜祥智.能力随机的海运集装箱收益管理超订模型.西南交通大学学报,2006,41(4):501-506.
[15]李为相,赵林度.基于拍卖的电子商务动态定价研究.南京工业大学学报,2005,27(4):67-70.
[16]李晓花,萧柏春.航空公司收入管理价格与舱位控制的统一分析.管理科学学报,2004,7(6):63-69.
[17]刘晓君,席酉民.拍卖理论与实务.北京:机械工业出版社,2000.
[18]罗利,彭际华.竞争环境下的民航客运收益管理动态定价模型.系统工程理论与实践,2007,(11):15-25.
[19]马俊,汪寿阳,黎建强.e-Auction网上拍卖理论与实务.科学出版社,2003.
[20]毛用才,胡奇英.随机过程.西安:西安电子科技大学出版社,1998.
[21]梅虎,朱金福和汪侠.基于博弈分析的航空收益管理定价研究.预测,2006,25(6):45-49.
[22]梅虎,朱金福和汪侠.基于旅客舱位选择的航空收益管理.系统工程,2006,24(9):11-17.
[23]王忠民,梁军民,郭立宏.拍卖理论与应用.西北大学出版社,1999.
[24]魏轶华.随机环境下的若干定价问题研究.博士学位论文,西安电子科技大学,2004年10月.
[25]魏轶华,胡奇英.顾客有最大最小保留价的连续时间收益管理.管理科学学报,2002,5(6):47-52.
[26]吴继兰,李培亮。基于供应链绩效的网上逆向拍卖模型.管理科学,2007,20(6):31-35.
[27]解学书.最优控制理论与应用.清华大学出版社,1986.
[28]张光澄.最优控制问题计算方法.成都:科技大学出版社,1991.
[29]张维迎.博弈论与信息经济学.上海:上海三联出版社,1996.
[30]Ayhan S H and Foley R D.Relationships among three assumption in revenue management.Operations Research,2004,52:804-809.
[31]Anand S K and R Aron.Group- buying on the web:a Comparison of price discovery mechanisms.Management Science,2003,49:1546-1562.
[32]Bajari P and Hortacsu A.Online Auctions:A review of empirical findings.The Journal of Economic Literature,2000.
[33]Bajari P and Hortascu A.Winner's curse,reserve prices and endogenous entry:Empirical insights from eBay auctions.Working paper,Department of Economics,Stanford University,Stanford,CA.2002.
[34]Bajari P and Summers G.Detecting Collusion in Procurernent Auctions:A Selective Survey of Recent Research.Antitrust Law Journal,2002,70:143-170.
[35]Bapna R.Online Auctions:A closer look.in Lowry,P(ed),Handbook of Electronic Commerce in Business and Society.CRC Press,2001.
[36]Bapna R,Goes P and Gupta A.A theoretical and empirical investigation of multi-item on-line auctions.Information technology and Management,2001,1:1-23.
[37]Bapna R,Goes P and Gupta A.Analysis and design of Business-to-Consumer online auctions.Management Science,2003a,49:85-101.
[38]Bapna R,Goes P and Gupta A.Replicating online Yankee auctions to analyze auctioneers' and bidders' strategies.Information Systems Research,2003b,14:244-268.
[39]Beam C and A Segev.Auctions on the Internet:A field study.Working paper,Haas School of business,University of California Berkeley.http://groups.haas.berkeley.edu/citm/publications/papers/wp-1032.pdf,1998.
[40]Belobaba P P.Air travel demand and airline seat inventory management D.Ph.D.thesis,Cambrid ge:HIT,1987.
[41] Bclobaba P P. Airline yield management: an review of seat inventory control.Transportation Science, 1987, 21: 63-73.
[42] Bertsimas D, Hawkins J and Perakis G. Optimal bidding in online auctions.Working Paper, MIT, 2001: 153.
[43] Besanko D and W L Winston. Optimal price skimming by a monopolist facing rational consumers. Management Science, 1990, 36(5): 555-567.
[44] Biais B, Hillion P and Spatt C. An empirical analysis of the limit order book and the order flow in the Paris Bourse. Journal of Finance, 1995, 50(5): 1655-1689.
[45] Brumelle S L. Allocation of airline seats between stochastically dependent demand. Transportation Science, 1990, 24: 87-116.
[46] Brumelle S L and Walczak D. Dynamic allocation of airline seat inventory with batch arrivals. Air Transport Research Group of the WCTR Society Proc. 3, Faculty of Commerce and Business Administration, University of British Columbia,Vancouver, BC. 1997.
[47] Chatwin R E. Continuous-time airline overbooking with time dependent fares and refunds. Transportation Science, 2000, 33: 182-191.
[48] Chen L and De Mello T H. Multistage stochastic programming models for airline revenue management. Working paper of Northwestern University, 2004.
[49] Chiang W C, Chen J C H and Xu X. An overview of research on revenue management: current issues and future research. Int. J. Revenue Management, 2007,1(1): 97-128.
[50] Choua F S and Parlarb M. Optimal quota allocation for a revenue-maximizing auction holder facing a random number of bidders. International Transactions in Operation Research, 2005, 12: 559-580.
[51] Chui K and R Zwick. Auctions on the Internet- A Preliminary study. Working Paper. Hongkong University of Science and Technology.http://home.ust.hk/ mkzwick/papers/auction.pdf, 1999.
[52] Curry R. Optimal airline seat allocation with fare classes nested by origins destination. Acronomics Incorporated Report. 1989.
[53] Ding M, J Eliashbcrg, J Huber and R Saini. Emotional bidders: An analytical and experimental examination of consumers' behavior in reverse auction, Working paper, 2002.
[54] Easley F R and R Tenorio. Jump Bidding strategies in Internet Auctions, Management Science, 2004, 50: 1407-1419.
[55] Elmaghraby W. The importance of ordering in sequential auctions. Management Science, 2003, 49(5). 673-682.
[56] Emiliani R and Stec D. Realizing savingsfrom on-Line reverse auctions. Supply Chain Management, 2002, 7: 12-23.
[57] Eso M. An iterative online auction for airline Seats. Technical report, IBM T J Watson Research Center, February, 2001.
[58] Feng Y Y and G Gallego. Perishable asset revenue mangement with Markovian time dependent demand intensities. Management Science, 2000, 46(7): 941-956.
[59] Feng Y Y and Xiao B C. A continuous-time yield management model with multiple price and reversible price changes. Management Science, 2000a, 46(5): 644-657.
[60] Feng Y Y and Xiao B C. A dynamic airline seat inventory control model and its optimal policy. Operations Research, 2001, 49(6):938-949.
[61] Feng Y Y and Xiao B C. Optimal policies of yield management with multiple predetermined prices. Operations Research, 2000, 48(2): 332-343.
[62] Feng Y Y and Gallego G. Optimal starting times for end-of-scason sales and optimal stopping times for promotional fares. Management Science, 1995, 41:1371-1391.
[63] Friedman L. A competitive bidding strategy. Operations Research, 1956, 4. 104-112.
[64] Gallego G and Van Ryzin G J. A multiproduct dynamic pricing problem and its applications to network yield management. Operation Research, 1997, 45(1):24-41.
[65] Gallego G and van Ryzin G J. Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Science, 1994, 40: 999-1020.
[66] Glober F, Glover R, Lorenzo J and McMillan C. The passenger mix problem in the scheduled airlines. Interfaces, 1982, 12: 73-79.
[67] Gottlieb B. Docs group-shopping work? The economics of Mercata and Mobshop.Posted on http://www.slate.lycos.com/Features/groupshop/groupshop.asp, 2000.
[68] Graham D A, R C Marshall and Jean-Francois Richard. Phantom bidding against heterogeneous bidders. Economic Letters, 1990(32): 13-17.
[69] Hann I and C Terwiesch. Measuring the frictional costs of online auctions: The case of a name-your-own-price channel. Management Science, 2003, 49(11): 1565-1581.
[70] Harstad R M. Alternative common- value auction procedures: Revenue comparisons with free entry. J. Political Econom, 1990, 98: 421-429.
[71] Kahn Research Group LLC. Group Buying and the Internet.http://www.webehavior.com/group.htm, 2000.
[72] Kannan P K and P K Kopalle. Dynamic pricing on the Internet: Importance and implications for consumer behavior.International Journal of Electronic Commerce, 2001, 5(3): 63-83.
[73] Karacsman I and van Ryzin G J. Overbooking with substitutable inventory classes. Operation Research, 2004, 52(1): 83-104.
[74] Kauffman R J and Wang B. New Buyers' Arrival under Dynamic Pricing Market Microstructure: The Case of Group- Buying Discounts on the Internet. Journal of management Information Systems, 2002a, 18: 157-188.
[75] Kauffman R J and Wang B. Bid Together, Buy together: On the Efficacy of Group-Buying Business Models in Internet-Based Selling. Handbook of Electronic Commerce in Business and Society, Boca Raton, FL: CRC Press, 2002b.
[76] Kauffman R J and Wood A C. Doing thcir bidding: An empirical examination of factors that affect a buyer's utility in Internet auctions. Forthcoming in Information Technology and Management, 2004.
[77] Kauffman R J and Wood A C. The effects of shilling on final bid prices in online auctions. Forthcoming in Electronic Commerce Research and Applications, 2005.
[78] Laffont J J, Ossard H and Vuong Q. Econometrics of First-Price Auctions. Econo-metrica, 1995, 63: 953-980.
[79] Lawrence M Ausubcl and Peter Cramton. Auctioning Many Divisible Goods.Journal of the European Economic Association, MIT Press, 2004, 2(3): 480-493.
[80] Lee T C and Hersh M. A model for dynamic airline scat inventory control with multiple seat bookings. Transportation Science, 1993, 27: 252-265.
[81] Littlcwood K. Forecasting and Control of Passengers. 12th AGIFORS SymposiumProceedings, 1972, 103-105.
[82] Lucking- Reiley D. Auctions on the Internet: what's Being Auctioned and How?Journal of Industrial Economics, 2000, 48: 227-252.
[83] Lucking- Reiley D, Bryan D, Prasad N and Reeves D. Pennies from ebay: the determinants of price in online auctions. Working paper. Vanderbilt University.Http://eller. arizona. edu/ reiley/papers/pcnnies fromEbay.pdf, 1999.
[84] Maglaras C and Meissner J. Dynamic pricing strategies for multi-product revenue management problems. Manufacturing and Service Operation Management,2006, 8: 136-148.
[85] McAfee R P and J McMillan. Auctions and Bidding. Journal of Economic Literature, 1987, XXV: 699-738.
[86] Metha K and Lee B T. Efficiency comparison in electronic market mechanisms:Posted price versus auction market. WISE Conference, Charlotte, NC, 1999a.
[87] Mctha K and Lee B T. Empirical evidence of winner's curse in electronic auctions. Proceedings of the 20th International Conference on Information Systems,Charlotte, NC, 1999b.
[88] Millet I, Parcntc H D, Fizcl L J and Venkataraman R R. Metrics for managing online procurement auctions. Interfaces, 2004, 34: 171-179.
[89] Mittal V and Kamakura W A. Satisfaction, repurchase intent, and repurchase behavior: investigating the moderating effect of customer characteristics. Journal of Marketing Research, 2001, 38(1): 131-42.
[90] Ockenfels A and Roth E A. Strategic late- bidding in continuous- time second-price internet auctions. Working Paper. Germany: University of Magdeburg,2001.
[91] Paarsch H J. Deciding between common values and private value. Paradigms in Empirical Models of Auctions, Journal of Econometrics, 1992, 51: 191-215.
[92] Pinker J E, Seidmann A and Vakrat Y. Managing Online Auctions: Current Business and Research Issues. Management Science, 2003, 49: 1457-1484.
[93] Pinker J E, Seigmann A and Vakrat Y. Using transaction data for the design of sequential, multi-unit online auctions. Working Paper CIS-00-03, Simon School,University of Rochester, Rochester, NY. 2000.
[94] Roth A E and Ockenfcls A. Last minute bidding and the rules for ending second-price auctions: evidence from ebay and Amazon Auctions on the Internet. American Economic Review, 2002, 92: 1093-1103.
[95] Rothkopf M H and Harstad R M. On the role of discrete bid levels in oral auctions.Europe Journal of Operational Research, 1994a, 74: 572-581.
[96] Schwartz E and B Mendel. New auction business model helps suppliers retain price integrity.http://www.infoworld.com/cgi-bin/displayStory.pl? 991018. hnauctions.htm, 1999.
[97] Segev A, C Beam, and J Shanthikumar. Optimal design of Internet-based auctions. Inform. Tech. & Management, 2001, 2, 121-163.
[98] Sinha A R and E A Greenleaf. The impact of discrete bidding and bidder aggressiveness on sellers' strategics in open English auctions: Reserves and covert shilling. Marketing Science, 2000, 19(3): 244-265.
[99] Stidham S J. Optimal control of admission to a qucucing system. IEEE Trans.AC, 1985, 30(8): 705-713.
[100] Talluri K and van Ryzin G. The theory and practice of revenue management.New York: Kluwer Academic Publishers, 2004a.
[101] Talluri K and van Ryzin G. Revenue management under a general discrete choice model of consumer behavior. Management Science, 2004b, 50: 15-33.
[102] Vakrat Y and Seidmann A. Implications of the bidders' process on the design of online auctions. In proceedings of the 33rd Hawaii International Conference on System Sciences, R. Spraguc(ed. ), Los Alamitos, CA: IEEE Computer Society Press, CD- ROM, 2000.
[103] van Ryzin G and Vulcano G. Optimal Auctioning and Ordering in an Infinite Horizon Inventory-Pricing System. Operations Research, 2004, 52: 346-367.
[104] Vickrey W. Countcrspeculation, auctons,and sealed tenders. Journal of Finance,1961, 16: 8-37.
[105] Vulcano G, van Ryzin G J and Maglaras C. Optimal dynamic auctions for revenue management. Mangcment Science, 2002, 48(11): 1388-1407.
[106] Wang K, Wang Eric T G and Tai, C. A study of online auction sites in Taiwan:Product, auction rule, and trading type. International Journal of Information Management, 2002, 22: 127-142.
[107] Wang W, Hidvegi Z and Whinston A B. Shill bidding in English auctions.Working paper. Center for Research on E-Commerce, McComb School of Business. Austin: University of Texas, 2001.
[108] Wollmer R. An airline scat management model for a single leg route when lower fare classes book first. Operations Research, 1992, 40(1): 26-37.
[109] Wood C A. What factors drive finalprice in Internet auctions? An empirical assessment of coin transactions on eBay. Annual convention of the Institute for Operations Research and the Management Sciences. Nov. 6. Miami Beach, Fla,2001.
[110] Wurman P R. Online auction site management. Working paper,http://www.csc.ncsu.edu/faculty/wurman/Papers/Wurman-article.pdf, 2003.
[111] Zhang D and Cooper W L. Revenue management for parallel flights with customer-choice behavior. Operation Research, 2005, 53(3): 415-431.
[112] Zhao W and Zheng Y S. Optimal dynamic pricing for perishable assets with nonhomogeneous demand. Management Science, 2000, 46(3): 375-388.