An Ascending Multi-Item Auction with Financially Constrained Bidders

G. van der Laan, Zaifu Yang

Research output: Working paperProfessional

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.
Original languageEnglish
Place of PublicationAmsterdam
PublisherTinbergen Instituut
Publication statusPublished - 2008

Publication series

NameDiscussion paper TI
No.08-017/1

Fingerprint

Auctions
Multi-item auctions
Ascending auctions
Budget constraint
Reservation price
Walrasian equilibrium

Cite this

van der Laan, G., & Yang, Z. (2008). An Ascending Multi-Item Auction with Financially Constrained Bidders. (Discussion paper TI; No. 08-017/1). Amsterdam: Tinbergen Instituut.
van der Laan, G. ; Yang, Zaifu. / An Ascending Multi-Item Auction with Financially Constrained Bidders. Amsterdam : Tinbergen Instituut, 2008. (Discussion paper TI; 08-017/1).
@techreport{7b0904969dbe493eba1760aa1966ab0a,
title = "An Ascending Multi-Item Auction with Financially Constrained Bidders",
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.",
author = "{van der Laan}, G. and Zaifu Yang",
year = "2008",
language = "English",
series = "Discussion paper TI",
publisher = "Tinbergen Instituut",
number = "08-017/1",
type = "WorkingPaper",
institution = "Tinbergen Instituut",

}

van der Laan, G & Yang, Z 2008 'An Ascending Multi-Item Auction with Financially Constrained Bidders' Discussion paper TI, no. 08-017/1, Tinbergen Instituut, Amsterdam.

An Ascending Multi-Item Auction with Financially Constrained Bidders. / van der Laan, G.; Yang, Zaifu.

Amsterdam : Tinbergen Instituut, 2008. (Discussion paper TI; No. 08-017/1).

Research output: Working paperProfessional

TY - UNPB

T1 - An Ascending Multi-Item Auction with Financially Constrained Bidders

AU - van der Laan, G.

AU - Yang, Zaifu

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

M3 - Working paper

T3 - Discussion paper TI

BT - An Ascending Multi-Item Auction with Financially Constrained Bidders

PB - Tinbergen Instituut

CY - Amsterdam

ER -

van der Laan G, Yang Z. An Ascending Multi-Item Auction with Financially Constrained Bidders. Amsterdam: Tinbergen Instituut. 2008. (Discussion paper TI; 08-017/1).