Inference from Auction Prices
Abstract
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).
Keywords
Cite
@article{arxiv.1902.06908,
title = {Inference from Auction Prices},
author = {Jason Hartline and Aleck Johnsen and Denis Nekipelov and Zihe Wang},
journal= {arXiv preprint arXiv:1902.06908},
year = {2020}
}