Pure Price of Anarchy for Generalized Second Price Auction

TL;DR

This paper determines the exact pure Price of Anarchy for Generalized Second Price auctions with four or more ad slots, improving previous bounds and providing precise efficiency loss measures.

Contribution

It proves the pure POA is 1.259 for four ad slots and extends this result to more than four slots under specific bidder ranking conditions.

Findings

Pure POA is exactly 1.259 for four ad slots.

Pure POA remains 1.259 for more than four slots under certain permutations.

Improves previous upper bounds on GSP auction efficiency.

Abstract

The Generalized Second Price auction (GSP) has been widely used by search engines to sell ad slots. Previous studies have shown that the pure Price Of Anarchy (POA) of GSP is 1.25 when there are two ad slots and 1.259 when three ad slots. For the cases with more than three ad slots, however, only some untight upper bounds of the pure POA were obtained. In this work, we improve previous results in two aspects: (1) We prove that the pure POA for GSP is 1.259 when there are four ad slots, and (2) We show that the pure POA for GSP with more than four ad slots is also 1.259 given the bidders are ranked according to a particular permutation.