Duality and optimality of auctions for uniform distributions
We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connectio...
| Hoofdauteurs: | , |
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| Formaat: | Journal article |
| Gepubliceerd in: |
Society for Industrial and Applied Mathematics
2018
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| _version_ | 1826304954013319168 |
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| author | Giannakopoulos, Y Koutsoupias, E |
| author_facet | Giannakopoulos, Y Koutsoupias, E |
| author_sort | Giannakopoulos, Y |
| collection | OXFORD |
| description | We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called Straight-Jacket Auction (SJA) which we prove to be exactly optimal for up to 6 items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly, for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints. |
| first_indexed | 2024-03-07T06:25:33Z |
| format | Journal article |
| id | oxford-uuid:f42c1180-2e09-4ee2-898b-67856debc0f2 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:25:33Z |
| publishDate | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:f42c1180-2e09-4ee2-898b-67856debc0f22022-03-27T12:17:40ZDuality and optimality of auctions for uniform distributionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f42c1180-2e09-4ee2-898b-67856debc0f2Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2018Giannakopoulos, YKoutsoupias, EWe develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called Straight-Jacket Auction (SJA) which we prove to be exactly optimal for up to 6 items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly, for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints. |
| spellingShingle | Giannakopoulos, Y Koutsoupias, E Duality and optimality of auctions for uniform distributions |
| title | Duality and optimality of auctions for uniform distributions |
| title_full | Duality and optimality of auctions for uniform distributions |
| title_fullStr | Duality and optimality of auctions for uniform distributions |
| title_full_unstemmed | Duality and optimality of auctions for uniform distributions |
| title_short | Duality and optimality of auctions for uniform distributions |
| title_sort | duality and optimality of auctions for uniform distributions |
| work_keys_str_mv | AT giannakopoulosy dualityandoptimalityofauctionsforuniformdistributions AT koutsoupiase dualityandoptimalityofauctionsforuniformdistributions |