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dc.contributor.authorCai, Yang
dc.contributor.authorDaskalakis, Konstantinos
dc.contributor.authorWeinberg, Seth Matthew
dc.date.accessioned2015-11-20T16:22:11Z
dc.date.available2015-11-20T16:22:11Z
dc.date.issued2012-10
dc.identifier.isbn978-0-7695-4874-6
dc.identifier.isbn978-1-4673-4383-1
dc.identifier.issn0272-5428
dc.identifier.urihttp://hdl.handle.net/1721.1/99955
dc.description.abstractWe provide a reduction from revenue maximization to welfare maximization in multidimensional Bayesian auctions with arbitrary - possibly combinatorial - feasibility constraints and independent bidders with arbitrary - possibly combinatorial-demand constraints, appropriately extending Myerson's single-dimensional result [21] to this setting. We also show that every feasible Bayesian auction - including in particular the revenue-optimal one - can be implemented as a distribution over virtual VCG allocation rules. A virtual VCG allocation rule has the following simple form: Every bidder's type ti is transformed into a virtual type fi(ti), via a bidder-specific function. Then, the allocation maximizing virtual welfare is chosen. Using this characterization, we show how to find and run the revenue-optimal auction given only black-box access to an implementation of the VCG allocation rule. We generalize this result to arbitrarily correlated bidders, introducing the notion of a second-order VCG allocation rule. Our results are computationally efficient for all multidimensional settings where the bidders are additive, or can be efficiently mapped to be additive, albeit the feasibility and demand constraints may still remain arbitrary combinatorial. In this case, our mechanisms run in time polynomial in the number of items and the total number of bidder types, but not type profiles. This is polynomial in the number of items, the number of bidders, and the cardinality of the support of each bidder's value distribution. For generic correlated distributions, this is the natural description complexity of the problem. The runtime can be further improved to polynomial in only the number of items and the number of bidders in itemsymmetric settings by making use of techniques from [15].en_US
dc.description.sponsorshipAlfred P. Sloan Foundation (Fellowship)en_US
dc.description.sponsorshipMicrosoft Research (Faculty Fellowship)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (CAREER Award CCF-0953960)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Award CCF-1101491)en_US
dc.description.sponsorshipNational Science Foundation (U.S.). Graduate Research Fellowshipen_US
dc.language.isoen_US
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/FOCS.2012.88en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleOptimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximizationen_US
dc.typeArticleen_US
dc.identifier.citationCai, Yang, Constantinos Daskalakis, and S. Matthew Weinberg. “Optimal Multi-Dimensional Mechanism Design: Reducing Revenue to Welfare Maximization.” 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (October 2012).en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorCai, Yangen_US
dc.contributor.mitauthorDaskalakis, Konstantinosen_US
dc.contributor.mitauthorWeinberg, Seth Matthewen_US
dc.relation.journalProceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Scienceen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsCai, Yang; Daskalakis, Constantinos; Weinberg, S. Matthewen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5451-0490
mit.licenseOPEN_ACCESS_POLICYen_US


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