On approximating optimal auctions
Proceedings of the 3rd ACM conference on Electronic Commerce
On the Hardness of Optimal Auctions
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On optimal single-item auctions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal auctions with correlated bidders are easy
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal and near-optimal mechanism design with interdependent values
Proceedings of the fourteenth ACM conference on Electronic commerce
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We consider the problem of designing a profit-maximizing single-item auction, where the valuations of bidders are correlated. We revisit the k-lookahead auction introduced by Ronen [6] and recently further developed by Dobzinski, Fu and Kleinberg [2]. By a more delicate analysis, we show that the k-lookahead auction can guarantee at least $\frac{e^{1-1/k}}{e^{1-1/k}+1}$ of the optimal revenue, improving the previous best results of $\frac{2k-1}{3k-1}$ in [2]. The 2-lookahead auction is of particular interest since it can be derandomized [2, 5]. Therefore, our result implies a polynomial time deterministic truthful mechanism with a ratio of $\frac{\sqrt{e}}{\sqrt{e}+1}$ ≈ 0.622 for any single-item correlated-bids auction, improving the previous best ratio of 0.6. Interestingly, we can show that our analysis for 2-lookahead is tight. As a byproduct, a theoretical implication of our result is that the gap between the revenues of the optimal deterministically truthful and truthful-in-expectation mechanisms is at most a factor of $\frac{1+\sqrt{e}}{\sqrt{e}}$. This improves the previous best factor of $\frac{5}{3}$ in [2].