Multi-unit auctions with budget limits
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 Ausubelʼs “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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- Motty Perry & Philip J. Reny, 2005. "An Efficient Multi-Unit Ascending Auction," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 567-592.
- Ashlagi Itai & Braverman Mark & Hassidim Avinatan & Lavi Ron & Tennenholtz Moshe, 2010. "Position Auctions with Budgets: Existence and Uniqueness," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-32, May.
- Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
- repec:oup:restud:v:68:y:2001:i:1:p:155-79 is not listed on IDEAS
- John William Hatfield & Paul R. Milgrom, 2005.
"Matching with Contracts,"
American Economic Review,
American Economic Association, vol. 95(4), pages 913-935, September.
- Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, 07.
- Mishra, Debasis & Parkes, David C., 2009.
"Multi-item Vickrey-Dutch auctions,"
Games and Economic Behavior,
Elsevier, vol. 66(1), pages 326-347, May.
- Debasis Mishra & David C. Parkes, 2007. "Multi-item Vickrey-Dutch auctions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 07-04, Indian Statistical Institute, New Delhi, India.
- Mallesh M. Pai & Rakesh Vohra, 2008. "Optimal Auctions with Financially Constrained Bidders," Discussion Papers 1471, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Maskin, Eric S., 2000. "Auctions, development, and privatization: Efficient auctions with liquidity-constrained buyers," European Economic Review, Elsevier, vol. 44(4-6), pages 667-681, May.
- Goldberg, Andrew V. & Hartline, Jason D. & Karlin, Anna R. & Saks, Michael & Wright, Andrew, 2006. "Competitive auctions," Games and Economic Behavior, Elsevier, vol. 55(2), pages 242-269, May.
- Kagel, John H & Levin, Dan, 2001. "Behavior in Multi-unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions," Econometrica, Econometric Society, vol. 69(2), pages 413-54, March.
- Eric Budish & Estelle Cantillon, 2012.
"The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard,"
American Economic Review,
American Economic Association, vol. 102(5), pages 2237-71, August.
- Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," ULB Institutional Repository 2013/99376, ULB -- Universite Libre de Bruxelles.
- Budish, Eric & Cantillon, Estelle, 2010. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," CEPR Discussion Papers 7641, C.E.P.R. Discussion Papers.
- Sandro Brusco & Giuseppe Lopomo, 2004. "Simultaneous Ascending Bid Auctions with Privately Known Budget Constraints," Levine's Bibliography 122247000000000373, UCLA Department of Economics.
- repec:oup:restud:v:65:y:1998:i:1:p:1-21 is not listed on IDEAS
- Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
- John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer, vol. 33(3), pages 505-515, September.
- Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
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