The nature of E-commerce over the Internet has seen significant changes over the
years. Instead of companies selling items to consumers, consumers are increasingly
selling items to fellow consumers on a global-scale, and Internet auctions have been
the mechanism of choice in achieving this. In fact, auctioning allows the departure
from the fixed price model, which some regard as too rigid to be able to respond
swiftly to varying supply and demand fluctuations and changes, and the Internet
plays a pivotal role in catalysing the widespread acceptance of such a variable pricing
model on a global scale.
Internet auctions exhibit characteristics which are often not shared by conventional auctions, e.g. auctions of xed duration which encourage sniping (bidders
submit their bids moments before the close of an auction thereby preventing other
bidders from submitting counter-bids), the acceptance of multiple bids in a single
auction, and a maximum threshold whereby the auction will terminate at that price
point. Internet auctions have significantly greater scope incorporating algorithms
of increased complexity than conventional auction procedures. In this thesis, the
characteristics and properties of different Internet auction algorithms are modelled
mathematically based on a series of operational assumptions which characterise the
arrival rate of bids, as well as the distribution from which the private values of buyers
are sampled. From this, closed-form expressions of several key performance metrics
are determined, including the average selling price in a given auction, as well as the
average auction duration. In cases where a seller may be selling a commodity and
auctions repeat themselves with the same items for sale multiple times, the income
per unit time may also be qunatified. Simulation experiments have been performed
and analysed in the context of the mathematical models, and reasonable agreements
are observed.