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A rule is overbidding-proof if no bidder has incentives to bid above his actual valuations. We prove that if an efficient rule is overbidding-proof, then each winning bidder pays a price between his winning bid and what he would pay in a Vickrey auction for the same package. In counterpart, the set of rules that satisfy underbidding-proofness always charge a price below the corresponding Vickrey price. A new characterization of the Vickrey allocation rule is provided with a weak form of strategy-proofness. The Vickrey rule is the only rule that satisfies efficiency, individual rationality, overbidding-proofness and underbidding-proofness. Our results are also valid on the domains of monotonic valuations and of single-minded bidders. Finally a family of overbidding rules is introduced that price the assigned packages at a fixed average of the Vickrey price and the pay-as-bid price.<\/jats:p>","DOI":"10.1007\/s00355-024-01506-5","type":"journal-article","created":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T16:01:42Z","timestamp":1710000102000},"page":"739-759","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Overbidding and underbidding in package allocation problems"],"prefix":"10.1007","volume":"62","author":[{"given":"Marina","family":"N\u00fa\u00f1ez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1061-747X","authenticated-orcid":false,"given":"Francisco","family":"Robles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,9]]},"reference":[{"key":"1506_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2202\/1534-5955.1019","volume":"1","author":"L Ausubel","year":"2002","unstructured":"Ausubel L, Milgrom P (2002) Ascending auctions with package bidding. 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