Multi-unit auctions with budget limits

Shahar Dobzinski; Ron Lavi; Noam Nisan

doi:10.1016/j.geb.2011.08.003

Multi-unit auctions with budget limits

Shahar Dobzinski, Ron Lavi^*, Noam Nisan

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

90 Scopus citations

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.

Original language	English
Pages (from-to)	486-503
Number of pages	18
Journal	Games and Economic Behavior
Volume	74
Issue number	2
DOIs	https://doi.org/10.1016/j.geb.2011.08.003
State	Published - Mar 2012

Bibliographical note

Funding Information:
✩ A preliminary and partial version appeared in FOCS’08. * Corresponding author. E-mail addresses: [email protected] (S. Dobzinski), [email protected] (R. Lavi), [email protected] (N. Nisan). 1 This work was done while this author was supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and by a grant from the Israeli Academy of Sciences. 2 Supported in part by grants from the Israeli Science Foundation, the Bi-national Science Foundation, the Israeli Ministry of Science, and by the Google Inter-university Center for Electronic Markets and Auctions. This work was done while this author was consulting Google Tel Aviv. 3 The nature of what this budget limit means for the bidders themselves is somewhat of a mystery since it often does not seem to simply reflect the true liquidity constraints of the bidding firm. There seems to be some risk control element to it, some purely administrative element to it, some bounded-rationality element to it, and more. 4 See the paper of Nisan et al. (2009) for a more detailed discussion on Google’s auction structure.

Keywords

Budget constraints
Multi-unit auctions
Pareto optimality

Access to Document

10.1016/j.geb.2011.08.003

Cite this

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title = "Multi-unit auctions with budget limits",

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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Multi-unit auctions with budget limits

Abstract

Bibliographical note

Keywords

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