Generalized Second Price Auction with Probabilistic Broad Match

TL;DR

This paper introduces the Probabilistic Broad-Match (PBM) mechanism for GSP auctions, addressing theoretical limitations of existing broad-match methods by analyzing its welfare and revenue guarantees in complex settings.

Contribution

It proposes the PBM-GSP mechanism, the first to extend broad-match analysis beyond single-slot and full-information scenarios, with theoretical welfare and revenue guarantees.

Findings

PBM-GSP can achieve higher social welfare than SBM-GSP under mild conditions.

Theoretical welfare bounds are established for PBM-GSP in worst equilibrium.

Revenue guarantees for PBM-GSP are analyzed in Bayesian settings.

Abstract

Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this issue, we propose a novel broad-match mechanism, which we call the Probabilistic Broad-Match (PBM) mechanism. Different from SBM that puts together the ads bidding on all the keywords matched to a given query for the GSP auction, the GSP with PBM (denoted as PBM-GSP) randomly samples a keyword according to a predefined probability distribution and only runs the GSP auction for the ads bidding on this sampled keyword. We perform a comprehensive study on the theoretical properties of the PBM-GSP. Specifically, we study its social welfare in the worst equilibrium, in both full-information and Bayesian settings. The results show that PBM-GSP can generate larger welfare than SBM-GSP under mild conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in Bayesian setting. To the best of our knowledge, this is the first work on broad-match mechanisms for GSP that goes beyond the single-slot case and the full-information setting.