Multi-unit auctions with budget limits |
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| Authors: | Shahar Dobzinski Ron Lavi Noam Nisan |
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| Affiliation: | 1. Computer Science Department, Cornell University, United States;2. Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Israel;3. School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel;4. Google Tel Aviv, Israel;1. Antai College of Economics and Management, Shanghai Jiao Tong University, No. 535 Fahua Zhen Road, Shanghai 200052, China;2. Department of Economics, The Ohio State University, 1945 North High Street, Columbus, OH 43210, United States;1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, China;2. School of Computing, National University of Singapore, Singapore;3. Department of Computer Science and Engineering, Chinese University of Hong Kong, Hong Kong |
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| Abstract: | We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubel?s “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible. |
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