TY - GEN

T1 - Inference from auction prices

AU - Hartline, Jason

AU - Johnsen, Aleck

AU - Nekipelov, Denis

AU - Wang, Zihe

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85084079669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85084079669&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85084079669

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2472

EP - 2491

BT - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

A2 - Chawla, Shuchi

PB - Association for Computing Machinery

T2 - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

Y2 - 5 January 2020 through 8 January 2020

ER -