Bayes-Nash equilibria of the generalized second-price auction

• 成果类型: Article
• 署名作者: Gomes, Renato; Sweeney, Kane
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2012.09.001
• 发表日期: 2014
• 页码: 421-437
• 关键词: Generalized second-price auction; Bayes-Nash equilibrium; Position auctions; Sponsored search; Click-through rates

摘要

We develop a Bayes-Nash analysis of the generalized second-price (GSP) auction, the multi-unit auction used by search engines to sell sponsored advertising positions. Our main result characterizes the efficient Bayes-Nash equilibrium of the GSP and provides a necessary and sufficient condition that guarantees existence of such an equilibrium. With only two positions, this condition requires that the click-through rate of the second position is sufficiently smaller than that of the first. When an efficient equilibrium exists, we provide a necessary and sufficient condition for the auction revenue to decrease as click-through rates increase. Interestingly, under optimal reserve prices, revenue increases with the click-through rates of all positions. Further, we prove that no inefficient equilibrium of the GSP can be symmetric. Our results are in sharp contrast with the previous literature that studied the GSP under complete information. (C) 2012 Elsevier Inc. All rights reserved.