Analysis of single and networked auctions

Abstract

Web-based computerized auctions are increasingly present in the Internet. We can imagine that in the future this trend will actually be extended to situations where virtual buyer and seller agents will conduct automated transactions across the network, and that large sectors of the economy may be strucured in this manner. The purpose of this article is to model automated bidders and sellers which interact through a network. We model the bidding process as a random arrival process while the price attained by a good is modeled as a discrete random variable. We obtain analytical solutions allowing us to compute the income from a single auction, or the income per unit time from a repeated sequence of auctions. A variety of single-auction models are studied, including English and Vickrey auctions, and the income per unit time is derived as a function of other parameters, including the rate of arrival of bids, the seller's decision time, the value of the good, and the “rest time” of the seller between successive auctions. We illustrate the results via numerical examples. We also introduce a model for networked auctions where bidders can circulate among a set of interconnected auctions which we call the Mobile Bidder Model (MBM). We obtain an analytical solution for the MBM under the assumption,which we call the “active bidders assumption,” that activities that are internal to an auction (bids and sales) are much more frequent than changes that occur in the number of bidders at each auction.