Bayes-Nash Equilibria of the Generalized Second-Price Auction

Bayes-Nash Equilibria of the Generalized Second-Price Auction
Renato Gomes
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.

Another publication from the same category: Machine Learning and Data Science

WWW '17 Perth Australia April 2017

Drawing Sound Conclusions from Noisy Judgments

David Goldberg, Andrew Trotman, Xiao Wang, Wei Min, Zongru Wan

The quality of a search engine is typically evaluated using hand-labeled data sets, where the labels indicate the relevance of documents to queries. Often the number of labels needed is too large to be created by the best annotators, and so less accurate labels (e.g. from crowdsourcing) must be used. This introduces errors in the labels, and thus errors in standard precision metrics (such as P@k and DCG); the lower the quality of the judge, the more errorful the labels, consequently the more inaccurate the metric. We introduce equations and algorithms that can adjust the metrics to the values they would have had if there were no annotation errors.

This is especially important when two search engines are compared by comparing their metrics. We give examples where one engine appeared to be statistically significantly better than the other, but the effect disappeared after the metrics were corrected for annotation error. In other words the evidence supporting a statistical difference was illusory, and caused by a failure to account for annotation error.

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