多属性逆向同步增价拍卖模型及最优投标策略
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摘要
针对采购商通常通过多属性逆向拍卖来采购多个物品,且物品间具有一定的组合效应,将同步增价拍卖机制引入多属性拍卖中,建立了基于两类非对称供应商的多属性逆向同步增价(分)拍卖模型.首先,在给定采购商评分函数和供应商效用函数的前提下,分析了供应商的非价格属性均衡投标策略.其次,在对地方供应商的均衡价格投标策略进行分析的基础上,运用逆向递推法,分两阶段研究了全局供应商的均衡价格投标策略,从而得出了该拍卖机制的精炼贝叶斯均衡,并对组合效应作了比较静态分析.最后,通过在线拍卖的实例,给出了该新拍卖机制中两类供应商均衡投标策略的计算步骤及结果演示,从而对多物品电子采购的实践提供指导.
The procurer frequently needs to purchase more than one item in multi-attribute reverse auctions with synergies. This paper constructs a multi-attribute reverse simultaneous ascending auction(MARSAA)model with two types of suppliers. Firstly, given the procurer's scoring rule and suppliers' utility functions, the equilibrium non-price attribute strategies of suppliers are determined. Secondly, based on the analysis of the local suppliers' equilibrium price attribute strategies, the global supplier's equilibrium price attribute strategy is examined in two stages with backward induction method. Then this paper clarifies the perfect Bayesian equilibrium strategies and measures the impact of synergies on the equilibrium strategies with a comparative static analysis. Finally, via a case study on e-procurement, the calculation procedure of the suppliers' equilibrium strategies in the new auction mechanism and the corresponding allocations are given, thus facilitating the application of the new mechanism in practice.
The procurer frequently needs to purchase more than one item in multi-attribute reverse auctions with synergies. This paper constructs a multi-attribute reverse simultaneous ascending auction(MARSAA)model with two types of suppliers. Firstly, given the procurer's scoring rule and suppliers' utility functions, the equilibrium non-price attribute strategies of suppliers are determined. Secondly, based on the analysis of the local suppliers' equilibrium price attribute strategies, the global supplier's equilibrium price attribute strategy is examined in two stages with backward induction method. Then this paper clarifies the perfect Bayesian equilibrium strategies and measures the impact of synergies on the equilibrium strategies with a comparative static analysis. Finally, via a case study on e-procurement, the calculation procedure of the suppliers' equilibrium strategies in the new auction mechanism and the corresponding allocations are given, thus facilitating the application of the new mechanism in practice.
引文
[1]田剑,唐小我.在线逆向拍卖研究回顾与展望.管理评论, 2009, 21(12):57–63.Tian J, Tang X W. Review of research on online reverse auction. Management Review, 2009, 21(12):57–63.(in Chinese)
[2] Che Y K. Design competition through multidimensional auctions. RAND Journal of Economics, 1993, 24(4):668–680.
[3] Branco F. The design of multidimensional auctions. RAND Journal of Economics, 1997, 28(1):63–81.
[4] David E, Azoulay-Schwartz R, Kraus S. An English auction protocol for multi-attributes items//Agent Mediated Electronic Commerce:IV. Designing Mechanisms and Systems, LNAI, 2002, 2531:52–68.
[5] David E, Azoulay-Schwartz R, Kraus S. Bidding in sealed-bid and English multi-attribute auctions. Decision Support Systems, 2006,42(2):527–556.
[6]孙亚辉,冯玉强.多属性密封拍卖模型及最优投标策略.系统工程理论与实践, 2010, 30(7):1185–1189.Sun Y H, Feng Y Q. Multi-attribute sealed-bid auction model and optimal bidding strategies. Systems Engineering:Theory&Practice, 2010, 30(7):1185–1189.(in Chinese)
[7]曾宪科,冯玉强.基于非对称投标人的反向多属性英式拍卖模型及最优投标策略.系统工程理论与实践, 2012, 32(4):769–775.Zeng X K, Feng Y Q. Reverse multi-attribute English auction model and optimal bidding strategies based on asymmetric bidders.Systems Engineering:Theory&Practice, 2012, 32(4):769–775.(in Chinese)
[8]王明喜,谢海滨,胡毅.基于简单加权法的多属性采购拍卖模型.系统工程理论与实践, 2014, 34(11):2772–2782.Wang M X, Xie H B, Hu Y. A multi-attribute procurement auction model based on the simple additive weighting method. Systems Engineering:Theory&Practice, 2014, 34(11):2772–2782.(in Chinese)
[9] Krishna V, Rosenthal R W. Simultaneous auctions with synergies. Games and Economic Behavior, 1996, 17(1):1–31.
[10]黄河,陈剑.采购组合拍卖投标均衡策略研究.系统工程理论与实践, 2007, 27(10):93–97.Huang H, Chen J. Study on bidding strategies in procurement combinatorial auction. Systems Engineering:Theory&Practice, 2007,27(10):93–97.(in Chinese)
[11]黄河,陈剑,徐鸿雁.多因素采购组合拍卖动态机制设计研究.中国管理科学, 2008, 16(1):104–110.Huang H, Chen J, Xu H Y. Research on multi-attribute procurement combinatorial auction dynamic mechanism design. Chinese Journal of Management Science, 2008, 16(1):104–110.(in Chinese)
[12]姚升保.卖方边际成本可变的多物品多属性逆向拍卖研究.中国管理科学, 2010, 18(1):113–119.Yao S B. Multi-unit multi-attribute reverse auctions with variable marginal costs for suppliers. Chinese Journal of Management Science, 2010, 18(1):113–119.(in Chinese)
[13] Zhang Z X, Jin M Z. Iterative multi-attribute multi-unit reverse auctions. The Engineering Economist, 2007, 52(4):333–354.
[14]黄瑞刚,张旭昆.拍卖理论综述.经济学动态, 2005, 3(1):109–124.Huang R G, Zhang X K. Review of auction theory. Economic Perspectives, 2005, 3(1):109–124.(in Chinese)
[15] Milgrom P. Putting Auction Theory to Work. New York:Cambridge University Press, 2004:265–293.
[16] Zheng C Z. Jump bidding and overconcentration in decentralized simultaneous ascending auctions. Games and Economic Behavior,2012, 76(2):648–664.
[17] Goeree J K, Lien Y. An equilibrium analysis of the simultaneous ascending auction. Journal of Economic Theory, 2014, 153(1):506–533.
[18] Albano G L, Germano F, Lovo S. Ascending auctions for multiple objects:The case for the Japanese design. Economic Theory,2006, 28(2):331–355.
[19] Milgrom P. Putting auction theory to work:The simultaneous ascending auction. Journal of Political Economy, 2000, 108(2):245–272.
[20] Bykowsky M, Cull R, Ledyard J. Mutually destructive bidding:The FCC auction design problem. Journal of Regulatory Economics,2000, 17(3):205–228.
[21]洪宗友,汪定伟.多属性招标拍卖中买卖双方的最优策略研究.系统工程学报, 2014, 29(4):458–467.Hong Z Y, Wang D W. Optimal strategies of auctioneer and bidders in multi-attribute procurement auctions. Journal of Systems Engineering, 2014, 29(4):458–467.(in Chinese)
[2] Che Y K. Design competition through multidimensional auctions. RAND Journal of Economics, 1993, 24(4):668–680.
[3] Branco F. The design of multidimensional auctions. RAND Journal of Economics, 1997, 28(1):63–81.
[4] David E, Azoulay-Schwartz R, Kraus S. An English auction protocol for multi-attributes items//Agent Mediated Electronic Commerce:IV. Designing Mechanisms and Systems, LNAI, 2002, 2531:52–68.
[5] David E, Azoulay-Schwartz R, Kraus S. Bidding in sealed-bid and English multi-attribute auctions. Decision Support Systems, 2006,42(2):527–556.
[6]孙亚辉,冯玉强.多属性密封拍卖模型及最优投标策略.系统工程理论与实践, 2010, 30(7):1185–1189.Sun Y H, Feng Y Q. Multi-attribute sealed-bid auction model and optimal bidding strategies. Systems Engineering:Theory&Practice, 2010, 30(7):1185–1189.(in Chinese)
[7]曾宪科,冯玉强.基于非对称投标人的反向多属性英式拍卖模型及最优投标策略.系统工程理论与实践, 2012, 32(4):769–775.Zeng X K, Feng Y Q. Reverse multi-attribute English auction model and optimal bidding strategies based on asymmetric bidders.Systems Engineering:Theory&Practice, 2012, 32(4):769–775.(in Chinese)
[8]王明喜,谢海滨,胡毅.基于简单加权法的多属性采购拍卖模型.系统工程理论与实践, 2014, 34(11):2772–2782.Wang M X, Xie H B, Hu Y. A multi-attribute procurement auction model based on the simple additive weighting method. Systems Engineering:Theory&Practice, 2014, 34(11):2772–2782.(in Chinese)
[9] Krishna V, Rosenthal R W. Simultaneous auctions with synergies. Games and Economic Behavior, 1996, 17(1):1–31.
[10]黄河,陈剑.采购组合拍卖投标均衡策略研究.系统工程理论与实践, 2007, 27(10):93–97.Huang H, Chen J. Study on bidding strategies in procurement combinatorial auction. Systems Engineering:Theory&Practice, 2007,27(10):93–97.(in Chinese)
[11]黄河,陈剑,徐鸿雁.多因素采购组合拍卖动态机制设计研究.中国管理科学, 2008, 16(1):104–110.Huang H, Chen J, Xu H Y. Research on multi-attribute procurement combinatorial auction dynamic mechanism design. Chinese Journal of Management Science, 2008, 16(1):104–110.(in Chinese)
[12]姚升保.卖方边际成本可变的多物品多属性逆向拍卖研究.中国管理科学, 2010, 18(1):113–119.Yao S B. Multi-unit multi-attribute reverse auctions with variable marginal costs for suppliers. Chinese Journal of Management Science, 2010, 18(1):113–119.(in Chinese)
[13] Zhang Z X, Jin M Z. Iterative multi-attribute multi-unit reverse auctions. The Engineering Economist, 2007, 52(4):333–354.
[14]黄瑞刚,张旭昆.拍卖理论综述.经济学动态, 2005, 3(1):109–124.Huang R G, Zhang X K. Review of auction theory. Economic Perspectives, 2005, 3(1):109–124.(in Chinese)
[15] Milgrom P. Putting Auction Theory to Work. New York:Cambridge University Press, 2004:265–293.
[16] Zheng C Z. Jump bidding and overconcentration in decentralized simultaneous ascending auctions. Games and Economic Behavior,2012, 76(2):648–664.
[17] Goeree J K, Lien Y. An equilibrium analysis of the simultaneous ascending auction. Journal of Economic Theory, 2014, 153(1):506–533.
[18] Albano G L, Germano F, Lovo S. Ascending auctions for multiple objects:The case for the Japanese design. Economic Theory,2006, 28(2):331–355.
[19] Milgrom P. Putting auction theory to work:The simultaneous ascending auction. Journal of Political Economy, 2000, 108(2):245–272.
[20] Bykowsky M, Cull R, Ledyard J. Mutually destructive bidding:The FCC auction design problem. Journal of Regulatory Economics,2000, 17(3):205–228.
[21]洪宗友,汪定伟.多属性招标拍卖中买卖双方的最优策略研究.系统工程学报, 2014, 29(4):458–467.Hong Z Y, Wang D W. Optimal strategies of auctioneer and bidders in multi-attribute procurement auctions. Journal of Systems Engineering, 2014, 29(4):458–467.(in Chinese)