Abstract
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].
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Chen, X., Hu, G., Lu, P., Wang, L. (2011). On the Approximation Ratio of k-Lookahead Auction. In: Chen, N., Elkind, E., Koutsoupias, E. (eds) Internet and Network Economics. WINE 2011. Lecture Notes in Computer Science, vol 7090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25510-6_6
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DOI: https://doi.org/10.1007/978-3-642-25510-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25509-0
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