Improved Efficiency Guarantees in Auctions with Budgets

Pinyan Lu; Tao Xiao

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arXiv · 1407.8325

Improved Efficiency Guarantees in Auctions with Budgets

Pinyan Lu·Tao Xiao

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Abstract

We study the efficiency guarantees in the simple auction environment where the auctioneer has one unit of divisible good to be distributed among a number of budget constrained agents. With budget constraints, the social welfare cannot be approximated by a better factor than the number of agents by any truthful mechanism. Thus, we follow a recent work by Dobzinski and Leme (ICALP 2014) to approximate the liquid welfare, which is the welfare of the agents each capped by her/his own budget. We design a new truthful auction with an approximation ratio of $\frac{\sqrt{5}+1}{2} \approx 1.618$, improving the best previous ratio of $2$ when the budgets for agents are public knowledge and their valuation is linear (additive). In private budget setting, we propose the first constant approximation auction with approximation ratio of $34$. Moreover, this auction works for any valuation function. Previously, only $O(\log n)$ approximation was known for linear and decreasing marginal (concave) valuations, and $O(\log^2 n)$ approximation was known for sub-additive valuations.

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BibTeX RIS

Pinyan Lu, Tao Xiao. 2015-02-13. Improved Efficiency Guarantees in Auctions with Budgets. https://arxiv.org/abs/1407.8325

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