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.