TY - GEN

T1 - On revenue maximization in second-price Ad auctions

AU - Azar, Yossi

AU - Birnbaum, Benjamin

AU - Karlin, Anna R.

AU - Nguyen, C. Thach

N1 - Funding Information:
This research was supported by NSF Grant CCF-0635147, a grant from Yahoo! Research, and an NSF Graduate Research Fellowship.

PY - 2009

Y1 - 2009

N2 - Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of more realistically modeling these auctions, we introduce the Second-Price Ad Auctions problem, in which bidders' payments are determined by the GSP mechanism. We show that the complexity of the Second-Price Ad Auctions problem is quite different than that of the more studied First-Price Ad Auctions problem. First, unlike the first-price variant, for which small constant-factor approximations are known, it is NP-hard to approximate the Second-Price Ad Auctions problem to any non-trivial factor. Second, this discrepancy extends even to the 0-1 special case that we call the Second-Price Matching problem (2PM). In particular, offline 2PM is APX-hard, and for online 2PM there is no deterministic algorithm achieving a non-trivial competitive ratio and no randomized algorithm achieving a competitive ratio better than 2. This stands in contrast to the results for the analogous special case in the first-price model, the standard bipartite matching problem, which is solvable in polynomial time and which has deterministic and randomized online algorithms achieving better competitive ratios. On the positive side, we provide a 2-approximation for offline 2PM and a 5.083-competitive randomized algorithm for online 2PM. The latter result makes use of a new generalization of a classic result on the performance of the "Ranking" algorithm for online bipartite matching.

AB - Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of more realistically modeling these auctions, we introduce the Second-Price Ad Auctions problem, in which bidders' payments are determined by the GSP mechanism. We show that the complexity of the Second-Price Ad Auctions problem is quite different than that of the more studied First-Price Ad Auctions problem. First, unlike the first-price variant, for which small constant-factor approximations are known, it is NP-hard to approximate the Second-Price Ad Auctions problem to any non-trivial factor. Second, this discrepancy extends even to the 0-1 special case that we call the Second-Price Matching problem (2PM). In particular, offline 2PM is APX-hard, and for online 2PM there is no deterministic algorithm achieving a non-trivial competitive ratio and no randomized algorithm achieving a competitive ratio better than 2. This stands in contrast to the results for the analogous special case in the first-price model, the standard bipartite matching problem, which is solvable in polynomial time and which has deterministic and randomized online algorithms achieving better competitive ratios. On the positive side, we provide a 2-approximation for offline 2PM and a 5.083-competitive randomized algorithm for online 2PM. The latter result makes use of a new generalization of a classic result on the performance of the "Ranking" algorithm for online bipartite matching.

UR - http://www.scopus.com/inward/record.url?scp=70350391706&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04128-0_14

DO - 10.1007/978-3-642-04128-0_14

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AN - SCOPUS:70350391706

SN - 3642041272

SN - 9783642041273

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 155

EP - 166

BT - Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings

Y2 - 7 September 2009 through 9 September 2009

ER -