{"type":"ScholarlyArticle","title":"Approximating Optimal Combinatorial Auctions for Complements Using Restricted Welfare Maximization","authors":[{"name":"Pingzhong Tang","slug":"pingzhong-tang","given":"Pingzhong","family":"Tang","affiliation":""},{"name":"Tuomas Sandholm","slug":"tuomas-sandholm","given":"Tuomas","family":"Sandholm","affiliation":""}],"abstract":"The VCG mechanism is the gold standard for combinatorial auctions (CAs), and it maximizes social welfare. In contrast, the revenue-maximizing (aka optimal) CA is unknown, and designing one is NP-hard. Therefore, research on optimal CAs has progressed into special settings. Notably, Levin [1997] derived the optimal CA for complements when each agent's private type is one-dimensional. We introduce a new research avenue for increasing revenue where we poke holes in the allocation space — based on the bids — and then use a welfare-maximizing allocation rule within the remaining allocation set. In this paper, the first step down this avenue, we introduce a new form of reserve pricing into CAs. We show that Levin's optimal revenue can be 2-approximated by using monopoly reserve prices to curtail the allocation set, followed by welfare-maximizing allocation and Levin's payment rule. A key lemma of potential independent interest is that the expected revenue from any truthful allocation-monotonic mechanism equals the expected virtual valuation; this generalizes Myerson's lemma [1981] from the single-parameter environment. Our mechanism is close to the gold standard and thus easier to adopt than Levin's. It also requires less information about the prior over the bidders' types, and is always more efficient. Finally, we show that the optimal revenue can be 6-approximated even if the reserve pricing is required to be symmetric across bidders.","doi":"10.5591/978-1-57735-516-8/IJCAI11-072","url":"https://ijcai.org/proceedings/2011/72","pdf":"https://ijcai.org/proceedings/2011/0072.pdf","markdown":"https://ijcai.org/proceedings/2011/72.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/72","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":72,"pages":{"first":379,"last":384},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}