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An Ascending Multi-Item Auction with Financially Constrained Bidders

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Author Info
Gerard van der Laan () (VU University Amsterdam)
Zaifu Yang () (Yokohama National University)

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Abstract

A number of heterogeneous items are to be sold to a group of potential bidders. Every bidder knows his own values over the items and his own budget privately. Due to budget constraint, bidders may not be able to pay up to their values. In such a market, a Walrasian equilibrium usually fails to exist and also the existing auctions might fail to allocate the items among the bidders. In this paper we first introduce a rationed equilibrium for a market situation with financially constrained bidders. Succeedingly we propose an ascending auction mechanism that always results in an equilibrium allocation and price system. By starting with the reservation price of each item, the auctioneer announces the current prices of the items in each step and the bidders respond with their demand sets at these prices. As long as there is overdemand, the auctioneer adjusts prices upwards for overdemanded items until a price system is reached at which either there is an underdemanded set, or there is neither overdemand nor underdemand anymore. In the latter case the auction stops. In the former case, precisely one item will be sold, the bidder buying the item leaves the auction and the auction continues with the remaining items and the remaining bidders. We prove that the auction finds a rationed equilibrium in a finite number of steps. In addition, we derive various properties of the allocation and price system obtained by the auction.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-017/1.

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Date of creation: 15 Feb 2008
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Handle: RePEc:dgr:uvatin:20080017

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Ascending auction; multi-item auction; financial constraint;

Find related papers by JEL classification:
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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    Other versions:
  4. David J. Salant, 1997. "Up in the Air: GTE's Experience in the MTA Auction for Personal Communication Services Licenses," Journal of Economics & Management Strategy, Blackwell Publishing, vol. 6(3), pages 549-572, 09. [Downloadable!] (restricted)
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  7. Cox, Charles C, 1980. "The Enforcement of Public Price Controls," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 887-916, October. [Downloadable!] (restricted)
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  14. Che, Yeon-Koo & Gale, Ian, 1996. "Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints," Economics Letters, Elsevier, vol. 50(3), pages 373-379, March. [Downloadable!] (restricted)
  15. Talman, A.J.J. & Yang, Z.F., 2007. "A Dynamic Auction for Differentiated Items under Price Rigidities," Discussion Paper 2007-26, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  16. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March. [Downloadable!] (restricted)
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