An Ascending Multi-Item Auction with Financially Constrained Bidders

Tinbergen Institute Discussion Paper No. 08-017

31 Pages Posted: 26 Feb 2008

See all articles by Gerard van der Laan

Gerard van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Zaifu Yang

Yokohama National University - Faculty of Business Administration; Tilburg University - Department of Econometrics & Operations Research

Date Written: February 2008

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.

Keywords: Ascending auction, multi-item auction, financial constraint

JEL Classification: D44

Suggested Citation

van der Laan, Gerard and Yang, Zaifu, An Ascending Multi-Item Auction with Financially Constrained Bidders (February 2008). Tinbergen Institute Discussion Paper No. 08-017, Available at SSRN: https://ssrn.com/abstract=1096466 or http://dx.doi.org/10.2139/ssrn.1096466

Gerard Van der Laan (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Department of Econometrics and Tinbergen Institute
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Zaifu Yang

Yokohama National University - Faculty of Business Administration ( email )

79-4 Tokiwa-dai Hodogaya-ku
Yokohama, Kanagawa, 2408501
Japan

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands

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