Reducing revenue to welfare maximization: Approximation algorithms and other generalizations

Yang Cai, Constantinos Daskalakis, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

32 Scopus citations

Abstract

It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly combinatorial) demand constraints. This reduction provides a poly-time solution to the optimal mechanism design problem in all auction settings where welfare optimization can be solved efficiently, but it is fragile to approximation and cannot provide solutions to settings where welfare maximization can only be tractably approximated. In this paper, we extend the reduction to accommodate approximation algorithms, providing an approximation preserving reduction from (truthful) revenue maximization to (not necessarily truthful) welfare maximization. The mechanisms output by our reduction choose allocations via black-box calls to welfare approximation on randomly selected inputs, thereby generalizing also our earlier structural results on optimal multi-dimensional mechanisms to approximately optimal mechanisms. Unlike [12], our results here are obtained through novel uses of the Ellipsoid algorithm and other optimization techniques over non-convex regions.

Original languageEnglish (US)
Title of host publicationProceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
PublisherAssociation for Computing Machinery
Pages578-595
Number of pages18
ISBN (Print)9781611972511
DOIs
StatePublished - 2013
Externally publishedYes
Event24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 - New Orleans, LA, United States
Duration: Jan 6 2013Jan 8 2013

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013
CountryUnited States
CityNew Orleans, LA
Period1/6/131/8/13

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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    Cai, Y., Daskalakis, C., & Weinberg, S. M. (2013). Reducing revenue to welfare maximization: Approximation algorithms and other generalizations. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 (pp. 578-595). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973105.42