Bayes-Nash Equilibrium of the Generalized Second-Price Auction

Gomes, Renato and Sweeney, Kane (2014) Bayes-Nash Equilibrium of the Generalized Second-Price Auction. Games and Economic Behavior, vol. 86. pp. 421-437.

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Official URL: http://tse-fr.eu/pub/28763

Abstract

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.

Item Type: Article
Language: English
Date: July 2014
Refereed: Yes
Uncontrolled Keywords: Generalized second-price auction, Bayes–Nash equilibrium, Position auctions, Sponsored search, Click–through rates
JEL codes: C78 - Bargaining Theory; Matching Theory
D44 - Auctions
L86 - Information and Internet Services; Computer Software
M37 - Advertising
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 16 Mar 2015 14:52
Last Modified: 24 Jan 2019 00:10
OAI ID: oai:tse-fr.eu:28763
URI: http://publications.ut-capitole.fr/id/eprint/16623

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