Manipulation via endowments in auctions with multiple goods |
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Institution: | 1. Department of Economics, Yokohama National University, 79-3 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan;2. Department of Economics, Otaru University of Commerce, 3-5-21 Midori, Otaru, Hokkaido, 047-8501, Japan;1. TU München, Germany;2. University of Oxford, United Kingdom;1. Carnegie Mellon University, Tepper Business School, Pittsburgh, PA, 15213, USA;2. University of Tsukuba, Faculty of Engineering, Information and Systems, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan;3. Boston College, Department of Economics, Chestnut Hill, MA, 02167, USA;1. Economics Discipline, Business School, The University of Western Australia (M251), 35 Stirling Highway, Crawley WA 6009, Australia;2. Research School of Economics, HW Arndt Building 25A, Australian National University, Canberra ACT 2601, Australia |
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Abstract: | We study manipulation via endowments in a market in an auction setting with multiple goods. In the market, there are buyers whose valuations are their private information, and a seller whose set of endowments is her private information. A social planner, who wants to implement a socially desirable allocation, faces the seller’s manipulation via endowments, in addition to buyers’ manipulation of misreporting their valuations. We call a mechanism immune to the seller’s manipulation via endowments destruction-proof. In general, there exists no mechanism which is destruction-proof, together with strategy-proofness of the buyers, efficiency, and participation. Nevertheless, we find a restricted domain of the buyers’ valuation profiles satisfying a new condition called per-capita goods–buyer submodularity. We show that, in this domain, there exists a mechanism which is destruction-proof, together with the above properties. The restriction is likely to be met when each winner’s valuation is close to the next-highest valuation. We also provide a relation to monopoly theory, and argue that per-capita goods–buyer submodularity is independent of the standard elasticity argument. |
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