Bayes-Nash Equilibria of the Generalized Second Price Auction

22 Pages Posted: 4 Jul 2009

See all articles by Renato D. Gomes

Renato D. Gomes

Northwestern University - Department of Economics

Kane S. Sweeney

affiliation not provided to SSRN

Date Written: July 3, 2009

Abstract

In this paper we develop a Bayes-Nash analysis of the Generalized Second Price (GSP) auction, the mechanism used by search engines to sell sponsored advertising positions. Interestingly, our results are in sharp contrast with the previous literature that adopts a complete information framework. First, we characterize the efficient Bayes-Nash equilibrium of the GSP when such an equilibrium exists. We then obtain sufficient conditions on click-through rates that guarantee existence and show that an efficient equilibrium may fail to exist if click-through rates across slots are sufficiently close. Next, we derive the counter-intuitive result that the seller's revenue may decrease as click-through rates of the second to last slots increase, provided the distribution of advertisers' values per click is concentrated on high values. Fortunately, we show that setting optimal reserve prices reverses this result. Further, we prove that the GSP possesses no mixed strategy equilibrium and that no inefficient equilibrium can be symmetric.

Keywords: search engines, sponsored search, keyword auctions, Bayes-Nash equilibrium, click-through rates

JEL Classification: JEL D44, C78, L86, M37

Suggested Citation

Gomes, Renato D. and Sweeney, Kane S., Bayes-Nash Equilibria of the Generalized Second Price Auction (July 3, 2009). Available at SSRN: https://ssrn.com/abstract=1429585 or http://dx.doi.org/10.2139/ssrn.1429585

Renato D. Gomes (Contact Author)

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States
773 852 7196 (Phone)

HOME PAGE: http://sites.google.com/site/northwesternrenatogomes/

Kane S. Sweeney

affiliation not provided to SSRN ( email )

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
397
Abstract Views
1,625
rank
80,658
PlumX Metrics