Characterization of Revenue Monotonicity in Combinatorial Auctions

Taiki Todo, Atsushi Iwasaki, M. Yokoo
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引用次数: 2

Abstract

An auction mechanism consists of an allocation rule and a payment rule. There have been several studies on characterizing strategy-proof allocation rules; if the allocation rule satisfies a condition called weak-monotonicity, an appropriate payment rule is guaranteed to exist. One desirable property that an auction mechanism should satisfy is revenue monotonicity; a seller's revenue is guaranteed to weakly increase as the number of bidders grows. In this paper, we first identify a simple condition called summation-monotonicity for characterizing strategy-proof and revenue monotone allocation rules. To the best of our knowledge, this is the first attempt to characterize revenue monotone allocation rules. Based on this characterization, we also examine the connections between revenue monotonicity and false-name-proofness, which means a bidder cannot increase his utility by submitting multiple bids under fictitious names. In a single-item auction, we show that they are basically equivalent; a mechanism is false-name-proof if and only if it is strategy-proof and revenue monotone. On the other hand, we show these two conditions cannot coexist in combinatorial auctions under some minor condition.
组合拍卖中收益单调性的表征
拍卖机制由分配规则和支付规则组成。关于无策略分配规则的特征化,已有一些研究;如果分配规则满足弱单调性条件,则保证存在合适的支付规则。拍卖机制应该满足的一个理想属性是收益单调性;卖方的收入肯定会随着投标人数量的增加而微弱增长。在本文中,我们首先确定了一个简单的求和单调性条件,用于描述策略证明和收益单调分配规则。据我们所知,这是第一次尝试描述收入单调分配规则。基于这一特征,我们还研究了收入单调性与假名防伪性之间的联系,这意味着投标人不能通过以假名提交多个投标来增加其效用。在单品拍卖中,我们表明它们基本上是等同的;当且仅当一种机制不受策略影响且收益单调时,该机制是防假名的。另一方面,在一定的条件下,这两种条件在组合拍卖中不能共存。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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