收入近似的菜单大小复杂性

Moshe Babaioff, Yannai A. Gonczarowski, N. Nisan
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引用次数: 61

摘要

我们考虑一个向单个附加购买者出售n个物品的垄断者,其中购买者对这些物品的价值是根据可能具有无界支持的独立分布F1,F2,…,Fn绘制的。众所周知,与单品拍卖不同,收益最优拍卖(定价方案)可能很复杂,有时需要连续的菜单条目。我们还知道,只有有限数量的菜单项的简单拍卖,只能获得最优收益的一个常数部分。尽管如此,通过有限的菜单大小提取任意高比例的最佳收益的可能性问题仍然存在。本文给出了这个开放问题的肯定答案,证明了对于每一个n和每一个ε>0,存在一个复杂度界C=C(n,ε),使得菜单大小的拍卖最多C足以从任意F1,…,Fn获得最优收益的(1-ε)分数。我们证明了收益近似复杂度C(n,ε)的上界和下界,以及运行达到这种近似的拍卖所需的确定性通信复杂度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The menu-size complexity of revenue approximation
We consider a monopolist that is selling n items to a single additive buyer, where the buyer's values for the items are drawn according to independent distributions F1,F2,…,Fn that possibly have unbounded support. It is well known that - unlike in the single item case - the revenue-optimal auction (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. It is also known that simple auctions with a finite bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, the question of the possibility of extracting an arbitrarily high fraction of the optimal revenue via a finite menu size remained open. In this paper, we give an affirmative answer to this open question, showing that for every n and for every ε>0, there exists a complexity bound C=C(n,ε) such that auctions of menu size at most C suffice for obtaining a (1-ε) fraction of the optimal revenue from any F1,…,Fn. We prove upper and lower bounds on the revenue approximation complexity C(n,ε), as well as on the deterministic communication complexity required to run an auction that achieves such an approximation.
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