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Optimal reserve price in static and dynamic sponsored search auctions

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Sponsored search advertising is a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies the optimal reserve price for a generalized second-price auction (GSP) under both static and dynamic settings. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both settings. Different from a static GSP auction where the optimal reserve price is proved to be constant, in a dynamic setting the optimal reserve price is dependent on not only advertisers’ per-click values, but also the number of ad links sold. A search engine should gradually raise reserve price as more qualified advertisers arrive, and maintain the same threshold after all first-page positions are occupied.

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Correspondence to Wei Yang.

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The original version was presented at ICSSSM’2013 held in Hong Kong.

Wei Yang is an associate professor in the Management Department in the College of Management of LIU Post at New York. He received his Ph.D. from Carnegie Mellon in 2004 and Master degree from Tsinghua in 1998. His primary research interests lie in revenue management and vehicle routing. He has published in Production and Operations Management, European Journal of Operational Research and other academic journals. He was visiting assistant professor at Case Western Reserve University, Chinese University of Hong Kong (CUHK) and City University of Hong Kong. Dr. Yang teaches MBA and logistics master programs for LIU, Hofstra, Tsinghua and CUHK. He also consults for companies in the US and Asia on logistics and revenue management.

Jun Qiao is the chairman and professor in the College of Marketing and Logistics Management at Nanjing University of Finance and Economics in Jiangsu Province, China. He graduated from Shanghai Jiaotong University and Nanjing Normal University, and received his Master and Ph.D. degrees, respectively. He was a senior visiting scholar at the Institute of Economics of the Chinese Academy of Social Sciences in 1999, and Ohio State University in 2007. Dr. Qiao has published over ten books and dozens of journal articles on urban development, advertising for service and branding theory. He received numerous awards on research and teaching from the city of Nanjing and Jiangsu Province. He is the vice secretary of China Marketing Association, and vice president of Jiangsu Advertising Association. Dr. Qiao consults for companies and Jiangsu government on logistics management and urban development.

Youyi Feng was Professor of Supply Chain Management at the MIT-Zaragoza International Logistics Program and Research Associate at the MIT Center for Transportation and Logistics. He obtained his PhD in industrial engineering from Columbia University. He has over 20 years’ experience as both a private consultant and lecturer, working for companies such as TNT, Enron and the Royal Bank of Scotland. He has held previous academic positions at the National University of Singapore and the Chinese University of Hong Kong, among others. Dr. Feng’s research interests include stochastic control and modeling of manufacturing, economic and social systems. He has published widely in a variety of academic journals including Management Science and Operations Research. He is a member of INFORMS since 1994 and was on the organizing committee for the Global Supply Chain Conference held in Beijing in 2002.

Baichun Xiao is the chairman and professor in the Management Department of College of Management at LIU Post, New York. He received his Ph.D. in operations management from the Wharton School, University of Pennsylvania and MBA from the Catholic University of Leuven, Belgium. Prior to joining the LIU Post, he was professor and chairman of Computing and Decision Sciences Department at Seton Hall University. Dr. Xiao has been visiting professor at the Chinese University of Hong Kong, Beijing University, Tsinghua University, Fudan University, Nanjing University, Sichuan University, Southwest Jiao tong University, and Nanjing University of Finance and Economics. Dr. Xiao serves as member of Board at Trustees of Nanjing University. He has published in Operations Research, Management Science, Mathematical Programming, European Journal of Operational Research, Decision Sciences, IEEE Transactions on Automatic Control, and other leading journals in the areas of management science and operations management. He has conducted many research projects for airline, hotel, pharmaceutical and telecommunication industries.

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Yang, W., Qiao, J., Feng, Y. et al. Optimal reserve price in static and dynamic sponsored search auctions. J. Syst. Sci. Syst. Eng. 22, 440–456 (2013).

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