On the approximation ratio of k-lookahead auction

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 e1-1/k/e 1-1/k+1of the optimal revenue, improving the previous best results of 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√e/√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 1+√e/√e. This improves the previous best factor 5/3 of in [2]. © 2011 Springer-Verlag Berlin Heidelberg.