Ad auctions and cascade model: GSP inefficiency and algorithms

TL;DR

This paper analyzes the efficiency of GSP auctions under the cascade user model, comparing it to VCG, and introduces fast algorithms for optimal ad allocation in real-world settings.

Contribution

It provides new insights into GSP's inefficiency relative to VCG under the cascade model and offers efficient algorithms for ad allocation with high accuracy.

Findings

GSP's Price of Anarchy and Stability are analyzed under the cascade model.

Optimal ad allocations can be computed in under 1 second for 1000 ads.

Approximate algorithms achieve over 99% accuracy in less than 20 milliseconds.

Abstract

The design of the best economic mechanism for Sponsored Search Auctions (SSAs) is a central task in computational mechanism design/game theory. Two open questions concern the adoption of user models more accurate than that one currently used and the choice between Generalized Second Price auction (GSP) and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some contributions to answer these questions. We study Price of Anarchy (PoA) and Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we provide exact, randomized, and approximate algorithms, showing that in real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal allocations can be found in less than 1s with up to 1000 ads, and can be approximated in less than 20ms even with more than 1000 ads with an average accuracy greater than 99%.