Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper gives an algorithm to solve the problem of inferring the values of agents in a dominant-strategy mechanism from the social choice function implemented by the mechanism and the per-unit prices paid by the agents (the agent bids are not observed). For single-dimensional agents, this inference problem is a multi-dimensional inversion of the payment identity and is feasible only if the payment identity is uniquely invertible. The inversion is unique for single-unit proportional weights social choice functions (common, for example, in bandwidth allocation); and its inverse can be found efficiently. This inversion is not unique for social choice functions that exhibit complementarities. Of independent interest, we extend a result of Rosen (1965), that the Nash equilbria of "concave games" are unique and pure, to an alternative notion of concavity based on Gale and Nikaido (1965).

中文翻译：

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从拍卖价格推断

计量经济学推理允许分析师从机制规则和代理人的出价中反驳机制中代理人的价值。本文给出了一种算法来解决在主导策略机制中从该机制实现的社会选择函数和代理支付的单位价格（不观察代理出价）推断代理价值的问题。对于一维代理，这个推理问题是支付标识的多维反转，并且只有在支付标识唯一可逆的情况下才可行。单单位比例权重社会选择函数的反演是唯一的（常见的，例如，在带宽分配中）；并且可以有效地找到它的逆。对于表现出互补性的社会选择函数来说，这种倒置并不是唯一的。