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arXiv · 2310.03105

Efficiency of the Generalized Second-Price Auction for Value Maximizers

Yuan Deng·Mohammad Mahdian·Jieming Mao·Vahab Mirrokni·Hanrui Zhang·Song Zuo
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Abstract

We study the price of anarchy of the generalized second-price auction where bidders are value maximizers (i.e., autobidders). We show that in general the price of anarchy can be as bad as $0$. For comparison, the price of anarchy of running VCG is $1/2$ in the autobidding world. We further show a fined-grained price of anarchy with respect to the discount factors (i.e., the ratios of click probabilities between lower slots and the highest slot in each auction) in the generalized second-price auction, which highlights the qualitative relation between the smoothness of the discount factors and the efficiency of the generalized second-price auction.

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Yuan Deng, Mohammad Mahdian, Jieming Mao, Vahab Mirrokni, Hanrui Zhang, Song Zuo. 2023-10-04. Efficiency of the Generalized Second-Price Auction for Value Maximizers. https://arxiv.org/abs/2310.03105

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