基于博弈论的多属性拍卖模型与机制研究
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摘要
随着经济的发展和网络的普及,多属性拍卖以其能最大限度地满足拍卖人的多样化需求,充分发挥竞拍人各自的竞争优势从而提高拍卖双方的收益这一突出优点,展现出广阔的应用前景,特别是在采购中,反向在线多属性拍卖更具有优势。然而,现有多属性拍卖模型存在模型简单化、参数值固定从而不适合现实的网上多属性拍卖客观需要的问题,成为阻碍网上多属性拍卖在现实中广泛应用的瓶颈之一,不利于网上政府采购和B2B交易的快速发展,此问题亟待研究并解决。
本论文针对目前急需对网上多属性拍卖进行研究的现实需要,采用理论分析的研究方法,依据对多属性拍卖国内外研究现状的分析,结合现实客观情况,找出现有学者Che、Branco和David设计的经典模型的不足,进一步完善了多属性拍卖模型,相对提高了多属性拍卖模型对现实情况的适用性。
然后在本文建立的拍卖数学模型基础之上,主要针对第一得分密封拍卖和多属性英式拍卖这两种多属性拍卖机制,制定了竞拍人的投标策略,给出了竞拍人质量属性和价格属性的最优配置结构化的计算公式以及竞拍人的期望收益计算公式。再根据竞拍人的投标策略计算出拍卖人的期望收益,从而推导出拍卖人的最优评分函数设计策略,给出评分函数中各属性权重计算的公式。
最后,经过博弈分析得出第一得分密封拍卖与多属性荷式拍卖期望收益相等以及多属性英式拍卖与第二得分密封拍卖期望收益相等,再通过数学证明得出第一得分密封拍卖与多属性英式拍卖期望收益相等,从而得出了基于本文建立的多属性拍卖模型,拍卖人在上述四种多属性拍卖机制中期望收益是相等的这一结论。另外,在对四种多属性拍卖机制分析的同时,对影响多属性拍卖结果的影响因素进行了详细分析,如属性个数、竞拍人数、最小加分幅度等因素。
With economic development and popularization of Internet, multi-attribute auction shows broad prospects. Because multi-attribute auction has an outstanding advantage to satisfy the diverse needs of auctioneers to the last degree and give full play to bidders’competitive advantages, it can increase their mutual benefit. Especially in procurement, adoption of multi-attribute reverse auction on the net has more advantages. However, the existing models of multi-attribute auction are simple and their parameter values are fixed so that they can not suit the need of implementing multi-attribute auction on the internet. The problem will hinder the wide use of multi-attribute auction and the rapid development online government procurement and B2B transactions. The above problem urgently needs to be solved.
Firstly this thesis focuses on the current urgent need to research online multi-attribute auction, takes the method of theoretical analysis, based the domestic and foreign research status of the multi-attribute auction, combined with the reality, and finds out the shortcomings of existing classic model designed by Che, Branco and David. The model of multi-attribute auction is perfected and the model applicability is improved.
Then based on the mathematical auction model in this paper, mainly for the first score-sealed bid auction mechanism and multi-attribute English auction mechanism, bidders strategy is made and the structural optimal formulas of quality attributes, price attribute and the bidders' expected benefit are given. According to the bidder's bidding strategy, the auctioneer’s expected benefit is calculated, optimal score function design strategy is derived, and the formula for calculating attribute weights of score function are given.
Finally, through analysis with game theory, the expected revenue between first score sealed-bid auction and multi-attribute Dutch auction is equal and so is expected revenue between multi-attribute English auction and second score sealed-bid auction. The expected revenue between first score sealed-bid auction and multi-attribute English auction is proved to be equal by mathematical computation. So one conclusion is made that the auctioneer’s expected revenue of the above multi-attribute auctions is equal. In addition, at the same time of analyzing the four multi-attribute auction mechanisms, the factors of influencing the auction result are analyzed in detail, such as the number of attribute, the number of bidder and the size of the minimal increment score.
本论文针对目前急需对网上多属性拍卖进行研究的现实需要,采用理论分析的研究方法,依据对多属性拍卖国内外研究现状的分析,结合现实客观情况,找出现有学者Che、Branco和David设计的经典模型的不足,进一步完善了多属性拍卖模型,相对提高了多属性拍卖模型对现实情况的适用性。
然后在本文建立的拍卖数学模型基础之上,主要针对第一得分密封拍卖和多属性英式拍卖这两种多属性拍卖机制,制定了竞拍人的投标策略,给出了竞拍人质量属性和价格属性的最优配置结构化的计算公式以及竞拍人的期望收益计算公式。再根据竞拍人的投标策略计算出拍卖人的期望收益,从而推导出拍卖人的最优评分函数设计策略,给出评分函数中各属性权重计算的公式。
最后,经过博弈分析得出第一得分密封拍卖与多属性荷式拍卖期望收益相等以及多属性英式拍卖与第二得分密封拍卖期望收益相等,再通过数学证明得出第一得分密封拍卖与多属性英式拍卖期望收益相等,从而得出了基于本文建立的多属性拍卖模型,拍卖人在上述四种多属性拍卖机制中期望收益是相等的这一结论。另外,在对四种多属性拍卖机制分析的同时,对影响多属性拍卖结果的影响因素进行了详细分析,如属性个数、竞拍人数、最小加分幅度等因素。
With economic development and popularization of Internet, multi-attribute auction shows broad prospects. Because multi-attribute auction has an outstanding advantage to satisfy the diverse needs of auctioneers to the last degree and give full play to bidders’competitive advantages, it can increase their mutual benefit. Especially in procurement, adoption of multi-attribute reverse auction on the net has more advantages. However, the existing models of multi-attribute auction are simple and their parameter values are fixed so that they can not suit the need of implementing multi-attribute auction on the internet. The problem will hinder the wide use of multi-attribute auction and the rapid development online government procurement and B2B transactions. The above problem urgently needs to be solved.
Firstly this thesis focuses on the current urgent need to research online multi-attribute auction, takes the method of theoretical analysis, based the domestic and foreign research status of the multi-attribute auction, combined with the reality, and finds out the shortcomings of existing classic model designed by Che, Branco and David. The model of multi-attribute auction is perfected and the model applicability is improved.
Then based on the mathematical auction model in this paper, mainly for the first score-sealed bid auction mechanism and multi-attribute English auction mechanism, bidders strategy is made and the structural optimal formulas of quality attributes, price attribute and the bidders' expected benefit are given. According to the bidder's bidding strategy, the auctioneer’s expected benefit is calculated, optimal score function design strategy is derived, and the formula for calculating attribute weights of score function are given.
Finally, through analysis with game theory, the expected revenue between first score sealed-bid auction and multi-attribute Dutch auction is equal and so is expected revenue between multi-attribute English auction and second score sealed-bid auction. The expected revenue between first score sealed-bid auction and multi-attribute English auction is proved to be equal by mathematical computation. So one conclusion is made that the auctioneer’s expected revenue of the above multi-attribute auctions is equal. In addition, at the same time of analyzing the four multi-attribute auction mechanisms, the factors of influencing the auction result are analyzed in detail, such as the number of attribute, the number of bidder and the size of the minimal increment score.
引文
1 Yves De Smet. Multi-criteria Auctions without Full Comparability of Bids. European Journal of Operational Research. 2007,177(3):1433~1452
2 Richard Engelbrecht-Wiggans. On a Possible Benefit to Bid Takers from Using Multi-Stage Auctions. Management Science. 1988,34(9):1109~1120
3 Friedman L. A Competitive Bidding Strategy. Operations Research,1956,4:104~112
4 Vickrey W. Counterspeculation, Auctions and Competitive Sealed Tenders. Journal of Finance. 1961,(16):8~37
5 Roger B. Myerson. Optimal Auction Design. Mathematics of Operations Research. 1981,(6):58~73
6 John G. Riley, William F.Samuelson. Optimal Auctions. American Economic Review. 1981,(71):381~392
7 Yeon-Koo Che. Design Competition through Multidimensional Auctions. RAND Journal of Economics. 1993,24(4):668~680
8谢安石,李一军,尚维,李燕.拍卖理论的最新进展—多属性网上拍卖研究.管理工程学报. 2006,20(3):17~22
9 Damian R. Beil, Lawrence M. Wein. An Inverse-optimization-based Auction Mechanism to Support a Multi-attribute RFQ Process. Management Science. 2003,49(11):1~6
10郭菊娥,席酉民.我国管理科学发展若干趋势分析.预测. 2004,23(5):1~9
11 Martin Bichler, Jayant Kalagnanam. Configurable Offers and Winner Determination in Multi-Attribute Auctions. European Journal of Operational Research. 2005,160(2):380~394
12 Rama Katkar, David H. Reiley. Public versus Secret Reserve Prices in EBay Auctions: Results from a Pokéman. Field Experiment. 2005:79~85
13 D.C. Parkes, J. Kalagnanam. Iterative Multi-attribute Vickrey Auctions. Management Science. 2004, 9(6):11~17
14 E. David, R. Azoulay-Schwartz, S. Kraus. Protocols and Strategies for Automated Multi-attributes Auctions. Proceedings of the First International Joint Conference on Autonomous Agents and Multiagent Systems. 2002:77~85
15 E. David, R. Azoulay-Schwartz, S. Kraus. An English Auction Protocol for Multi-attributes Items. Revised Papers from the Workshop on Agent Mediated ElectronicCommerce on Agent-Mediated Electronic Commerce IV, Designing Mechanisms and Systems. 2002,2531:52~68
16 E. David, R. Azoulay-Schwartz, S. Kraus. Bidders’Strategy for Multi-attribute Sequential English Auction with a Deadline . Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems.2003,4:52~65
17 E. David, R. Azoulay-Schwartz, S. Kraus. Bidding in Sealed-bid and English Multi-attribute Auctions. Decision Support Systems. 2006,42:527~556
18 N. Vulkan, N.R. Jennings, Efficient Mechanisms for the Supply of Services in Multi-agent Environments. Decision Support Systems. 2000(28):5~19
19 F. Branco. The Design of Multidimensional Auctions. Rand Journal of Economics. 1997,28(1):63~81
20 D.R.Deil, L.M.Wein. An Inverse-Optimization-Based Auction Mechanism to Support a Multi-Attribute RFQ Process. Management Science. 2003,49(1):1529~1545
21 J.E. Teich, H. Wallenius, J. Wallenius, A. Zaitsev. Designing Electronic Auctions: an Internet-based Hybrid Procedure Combining Aspects of Negotiations and Auctions. Journal of Electronic Commerce Research. 2001,1(3):301~314
22 J. E. Teich, H. Wallenius, J. Wallenius, O. R. Koppius. Emerging Multiple Issue E-auctions (invited review). European Journal of Operational Research. 2004,159(1):1~16
23 J.E. Teich, H. Wallenius, J. Wallenius, A. Zaitsev. A Multi-attribute E-auction Mechanism for Procurement: Theoretical Foundations. European Journal of Operational Research. 2006,175(1):90~100
24 Dekrajangpetch. Interior-point Linear Programming Algorithm for Auction Methods. IEEE Transactions on Power Systems. 2000,15(2):572~578
25 M. Bichler, J. Lee, H. S. Lee, and J. Y. Chung. Absolute: An Intelligent Decision Making Framework for E-sourcing. Advanced Issues of E-Commerce and Web-Based Information Systems, WECWIS 2001, Third International Workshop on. San Jose, CA, 2001:195~201
26 T. W. Sandholm, S. Suri. Side Constraints and Non Price Attributes in Markets. Games and Economic Behavior. 2006,55(2):321~330
27 Bichler M. An Experimental Analysis of Multi-attribute Auction. Decision Support System. 2000,(29):249~268
28 S. Strecker, S. Seifert. Electronic Sourcing with Multi-attribute Auctions. Proceedings of the 37th Hawaii International Conference on SystemScience.2004:1~10
29 Ching-Hua Chen-Ritzo, Terry P. Harrison, Anthony M. Kwasnica, Douglas J. Thomas. Better, Faster, Cheaper: an Experimental Analysis of a Multi-attribute Reverse Auction Mechanism with Restricted Information Feedback. Management Science. 2005,51(12):1753~1762
30刘树林,王明喜.多属性采购拍卖理论与应用评述.中国管理科学. 2009,17(1):183~192
31谢安石.面向电子商务的多属性网上拍卖理论研究.哈尔滨工业大学博士论文. 2005:1~52
32谢安石,李一军.基于模糊粗糙集的多属性网上拍卖决策.系统工程理论方法应用. 2005,14(2):182~184
33王海.基于智能代理的多属性网上拍卖研究.哈尔滨工业大学博士论文. 2005:1~46
34武刚,冯玉强,傅丽芳.面向政府采购的多属性电子拍卖机制设计.系统管理学报. 2007,16(3):292~297
35金涬,石纯一.一种暗标叫价的多属性拍卖方法.计算机学报. 2006,29(1):145~152
36金涬,石纯一.一种递增叫价的多属性拍卖方法.计算机研究与发展. 2006,43(7):1135~1141
37张李义,段凌,邓汉华.面向电子采购的多属性拍卖模型.武汉大学学报. 2004,37(4):97~100
38陈湘,胡山立,石曼银.一种安全的多属性拍卖模型.计算机研究与发展. 2007,44(4):680~685
39朱阁,吕廷杰,付瑞雪, Sunanda Sangwan.基于多Agent的在线多属性采购拍卖的机制设计.中国管理科学. 2009,22(1):78~85
40周競,林杰.非线性多属性网上采购拍卖模型及其平台.系统工程. 2009,27(7):54~59
41 R. Preston McAfee, John McMillan. Auctions and Bidding. Journal of Economic Literature.1987,25(2):699~738
42 Elmar Wolfstetter. Auctions: an Introduction. Journal of Economic Surveys. 1989,10(4):367~420
43 Paul Klemperer. Auction Theory: a Guide to the Literature. Journal of Economic Surveys. 1999,13(3):227~286
44岳超源.决策理论与方法.北京:科学出版社. 2003:170~192
45 W. F. Samuelson, Competitive Bidding with Entry Costs. Economic Letters. 1985,17(1-2):53~57
46 McAfee, J. McMillan. Auctions with Entry. Economic Letters. 1987,23:343~347
47 D. Levin, J. L. Smith. Equilibrium in Auctions with Entry. American Economic Review. 1994,84(3):585~599
48 M. Campbell. Coordination in Auctions with Entry. Journal of Economic Theory. 1998,82(2):425~450
2 Richard Engelbrecht-Wiggans. On a Possible Benefit to Bid Takers from Using Multi-Stage Auctions. Management Science. 1988,34(9):1109~1120
3 Friedman L. A Competitive Bidding Strategy. Operations Research,1956,4:104~112
4 Vickrey W. Counterspeculation, Auctions and Competitive Sealed Tenders. Journal of Finance. 1961,(16):8~37
5 Roger B. Myerson. Optimal Auction Design. Mathematics of Operations Research. 1981,(6):58~73
6 John G. Riley, William F.Samuelson. Optimal Auctions. American Economic Review. 1981,(71):381~392
7 Yeon-Koo Che. Design Competition through Multidimensional Auctions. RAND Journal of Economics. 1993,24(4):668~680
8谢安石,李一军,尚维,李燕.拍卖理论的最新进展—多属性网上拍卖研究.管理工程学报. 2006,20(3):17~22
9 Damian R. Beil, Lawrence M. Wein. An Inverse-optimization-based Auction Mechanism to Support a Multi-attribute RFQ Process. Management Science. 2003,49(11):1~6
10郭菊娥,席酉民.我国管理科学发展若干趋势分析.预测. 2004,23(5):1~9
11 Martin Bichler, Jayant Kalagnanam. Configurable Offers and Winner Determination in Multi-Attribute Auctions. European Journal of Operational Research. 2005,160(2):380~394
12 Rama Katkar, David H. Reiley. Public versus Secret Reserve Prices in EBay Auctions: Results from a Pokéman. Field Experiment. 2005:79~85
13 D.C. Parkes, J. Kalagnanam. Iterative Multi-attribute Vickrey Auctions. Management Science. 2004, 9(6):11~17
14 E. David, R. Azoulay-Schwartz, S. Kraus. Protocols and Strategies for Automated Multi-attributes Auctions. Proceedings of the First International Joint Conference on Autonomous Agents and Multiagent Systems. 2002:77~85
15 E. David, R. Azoulay-Schwartz, S. Kraus. An English Auction Protocol for Multi-attributes Items. Revised Papers from the Workshop on Agent Mediated ElectronicCommerce on Agent-Mediated Electronic Commerce IV, Designing Mechanisms and Systems. 2002,2531:52~68
16 E. David, R. Azoulay-Schwartz, S. Kraus. Bidders’Strategy for Multi-attribute Sequential English Auction with a Deadline . Proceedings of the Second International Joint Conference on Autonomous Agents and Multiagent Systems.2003,4:52~65
17 E. David, R. Azoulay-Schwartz, S. Kraus. Bidding in Sealed-bid and English Multi-attribute Auctions. Decision Support Systems. 2006,42:527~556
18 N. Vulkan, N.R. Jennings, Efficient Mechanisms for the Supply of Services in Multi-agent Environments. Decision Support Systems. 2000(28):5~19
19 F. Branco. The Design of Multidimensional Auctions. Rand Journal of Economics. 1997,28(1):63~81
20 D.R.Deil, L.M.Wein. An Inverse-Optimization-Based Auction Mechanism to Support a Multi-Attribute RFQ Process. Management Science. 2003,49(1):1529~1545
21 J.E. Teich, H. Wallenius, J. Wallenius, A. Zaitsev. Designing Electronic Auctions: an Internet-based Hybrid Procedure Combining Aspects of Negotiations and Auctions. Journal of Electronic Commerce Research. 2001,1(3):301~314
22 J. E. Teich, H. Wallenius, J. Wallenius, O. R. Koppius. Emerging Multiple Issue E-auctions (invited review). European Journal of Operational Research. 2004,159(1):1~16
23 J.E. Teich, H. Wallenius, J. Wallenius, A. Zaitsev. A Multi-attribute E-auction Mechanism for Procurement: Theoretical Foundations. European Journal of Operational Research. 2006,175(1):90~100
24 Dekrajangpetch. Interior-point Linear Programming Algorithm for Auction Methods. IEEE Transactions on Power Systems. 2000,15(2):572~578
25 M. Bichler, J. Lee, H. S. Lee, and J. Y. Chung. Absolute: An Intelligent Decision Making Framework for E-sourcing. Advanced Issues of E-Commerce and Web-Based Information Systems, WECWIS 2001, Third International Workshop on. San Jose, CA, 2001:195~201
26 T. W. Sandholm, S. Suri. Side Constraints and Non Price Attributes in Markets. Games and Economic Behavior. 2006,55(2):321~330
27 Bichler M. An Experimental Analysis of Multi-attribute Auction. Decision Support System. 2000,(29):249~268
28 S. Strecker, S. Seifert. Electronic Sourcing with Multi-attribute Auctions. Proceedings of the 37th Hawaii International Conference on SystemScience.2004:1~10
29 Ching-Hua Chen-Ritzo, Terry P. Harrison, Anthony M. Kwasnica, Douglas J. Thomas. Better, Faster, Cheaper: an Experimental Analysis of a Multi-attribute Reverse Auction Mechanism with Restricted Information Feedback. Management Science. 2005,51(12):1753~1762
30刘树林,王明喜.多属性采购拍卖理论与应用评述.中国管理科学. 2009,17(1):183~192
31谢安石.面向电子商务的多属性网上拍卖理论研究.哈尔滨工业大学博士论文. 2005:1~52
32谢安石,李一军.基于模糊粗糙集的多属性网上拍卖决策.系统工程理论方法应用. 2005,14(2):182~184
33王海.基于智能代理的多属性网上拍卖研究.哈尔滨工业大学博士论文. 2005:1~46
34武刚,冯玉强,傅丽芳.面向政府采购的多属性电子拍卖机制设计.系统管理学报. 2007,16(3):292~297
35金涬,石纯一.一种暗标叫价的多属性拍卖方法.计算机学报. 2006,29(1):145~152
36金涬,石纯一.一种递增叫价的多属性拍卖方法.计算机研究与发展. 2006,43(7):1135~1141
37张李义,段凌,邓汉华.面向电子采购的多属性拍卖模型.武汉大学学报. 2004,37(4):97~100
38陈湘,胡山立,石曼银.一种安全的多属性拍卖模型.计算机研究与发展. 2007,44(4):680~685
39朱阁,吕廷杰,付瑞雪, Sunanda Sangwan.基于多Agent的在线多属性采购拍卖的机制设计.中国管理科学. 2009,22(1):78~85
40周競,林杰.非线性多属性网上采购拍卖模型及其平台.系统工程. 2009,27(7):54~59
41 R. Preston McAfee, John McMillan. Auctions and Bidding. Journal of Economic Literature.1987,25(2):699~738
42 Elmar Wolfstetter. Auctions: an Introduction. Journal of Economic Surveys. 1989,10(4):367~420
43 Paul Klemperer. Auction Theory: a Guide to the Literature. Journal of Economic Surveys. 1999,13(3):227~286
44岳超源.决策理论与方法.北京:科学出版社. 2003:170~192
45 W. F. Samuelson, Competitive Bidding with Entry Costs. Economic Letters. 1985,17(1-2):53~57
46 McAfee, J. McMillan. Auctions with Entry. Economic Letters. 1987,23:343~347
47 D. Levin, J. L. Smith. Equilibrium in Auctions with Entry. American Economic Review. 1994,84(3):585~599
48 M. Campbell. Coordination in Auctions with Entry. Journal of Economic Theory. 1998,82(2):425~450