Efficiency of the Generalized Second-Price Auction for Value Maximizers

TL;DR

This paper analyzes the efficiency loss in generalized second-price auctions with value-maximizing bidders, revealing potential for zero efficiency and relating auction performance to click probability ratios.

Contribution

It provides the first analysis of the price of anarchy for GSP auctions with autobidders, establishing bounds and the impact of discount factors on efficiency.

Findings

Price of anarchy can be zero in worst cases.

VCG auction has a price of anarchy of 1/2 with autobidders.

Efficiency depends on the smoothness of discount factors.

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.