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arXiv 1003.5326cs.GT
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能力分配博弈中的真值与嫉妒

Truth and Envy in Capacitated Allocation Games

Edith Cohen, Michal Feldman, Amos Fiat, Haim Kaplan, Svetlana Olonetsky

摘要:

我们研究的拍卖与附加估价代理商有一个限制,他们可能会收到的商品数量。我们将这种估值称为{ \em capacitated},并寻求最大化社会福利的机制,同时激励相容,无嫉妒,个人理性,没有正转移。如果容量是无限的,那么顺序重复第二价格Vickrey拍卖满足这些要求。在1983年,伦纳德表明,对于单位容量,VCG与克拉克枢轴付款也羡慕免费。对于所有单位或所有无限的容量,该机制产生瓦尔拉斯定价(受容量约束)。在这里,我们考虑一般能力。对于同质的能力(所有的能力相等),我们表明,VCG与克拉克枢纽付款是嫉妒自由(VCG与克拉克枢纽付款总是激励兼容,个人理性,并没有积极的转移)。因此,不存在激励相容的瓦尔拉斯定价。对于异质的能力,我们表明,没有机制与所有4个属性,但至少在某些情况下,可以实现激励兼容性和嫉妒自由。

英文摘要:

We study auctions with additive valuations where agents have a limit on the number of goods they may receive. We refer to such valuations as {\em capacitated} and seek mechanisms that maximize social welfare and are simultaneously incentive compatible, envy-free, individually rational, and have no positive transfers. If capacities are infinite, then sequentially repeating the 2nd price Vickrey auction meets these requirements. In 1983, Leonard showed that for unit capacities, VCG with Clarke Pivot payments is also envy free. For capacities that are all unit or all infinite, the mechanism produces a Walrasian pricing (subject to capacity constraints). Here, we consider general capacities. For homogeneous capacities (all capacities equal) we show that VCG with Clarke Pivot payments is envy free (VCG with Clarke Pivot payments is always incentive compatible, individually rational, and has no positive transfers). Contrariwise, there is no incentive compatible Walrasian pricing. For heterogeneous capacities, we show that there is no mechanism with all 4 properties, but at least in some cases, one can achieve both incentive compatibility and envy freeness.

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