福利非支配的小树林机制
Welfare Undominated Groves Mechanisms
摘要：
机制设计的一个共同目标是选择最大化代理人估值总和的结果（例如，资源分配），而不引入激励代理人误报其偏好。Groves类机制实现了这一点;然而，这些机制要求代理人进行支付，从而降低了代理人的总福利。在本文中，我们介绍了一种措施，比较两种机制的最终福利，他们产生。这一措施诱导偏序机制，我们研究的问题，找到最小的元素就这个偏序。特别地，我们说一个非赤字格罗夫斯机制是福利非支配的，如果不存在其他非赤字格罗夫斯机制，总是有一个较小的或相等的支付总额。我们专注于两个领域：（一）拍卖与多个相同的单位和单位需求投标人，和（ii）公共项目问题的机制。在第一个领域中，我们分析了所有匿名且具有线性支付函数的福利非支配Groves机制的特征，通过证明在[6]中引入的最优预期线性再分配机制族，包括Bailey-Cavallo机制[1，2]，与我们研究的设置中匿名且线性的福利非支配Groves机制族一致。在第二个领域中，我们发现，经典的VCG（克拉克）机制是福利不支配的类的公共项目的问题，平等的参与成本，但不是不支配的一个更一般的类。
英文摘要：
A common objective in mechanism design is to choose the outcome (for example, allocation of resources) that maximizes the sum of the agents' valuations, without introducing incentives for agents to misreport their preferences. The class of Groves mechanisms achieves this; however, these mechanisms require the agents to make payments, thereby reducing the agents' total welfare. In this paper we introduce a measure for comparing two mechanisms with respect to the final welfare they generate. This measure induces a partial order on mechanisms and we study the question of finding minimal elements with respect to this partial order. In particular, we say a non-deficit Groves mechanism is welfare undominated if there exists no other non-deficit Groves mechanism that always has a smaller or equal sum of payments. We focus on two domains: (i) auctions with multiple identical units and unit-demand bidders, and (ii) mechanisms for public project problems. In the first domain we analytically characterize all welfare undominated Groves mechanisms that are anonymous and have linear payment functions, by showing that the family of optimal-in-expectation linear redistribution mechanisms, which were introduced in [6] and include the Bailey-Cavallo mechanism [1,2], coincides with the family of welfare undominated Groves mechanisms that are anonymous and linear in the setting we study. In the second domain we show that the classic VCG (Clarke) mechanism is welfare undominated for the class of public project problems with equal participation costs, but is not undominated for a more general class.
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