Comparative Evaluation of Independent Private Values Distributions on Internet Auction Performance

Introduction

Instead of companies selling items to consumers, consumers are now selling items among themselves, with a common mechanism of achieving this being the auction. In fact, auctioning allows for a departure from the fixed price model, which some regard as too rigid to be able to respond rapidly to supply and demand fluctuations and changes. The pervasiveness and ubiquity of the Internet has played a pivotal role in catalysing the widespread acceptance of such a variable pricing model.

Internet auctions exhibit characteristics which are not often shared with conventional auctions, e.g., auctions of fixed 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. Due to lack of regulation, the size of the market and the volume of bidders and sellers, Internet auctions are better suited to incorporating algorithms of increased complexity as opposed to the more established procedures at traditional auction houses. For example, while eBay runs what essentially amounts to an English auction with a fixed duration, Swoopo runs what is known as a penny auction, where each bid incurs a fee and also extends the length of the auction by a short amount (10-20 seconds).

One way to view an auction is to regard it as the determination of bidders' valuations by the seller with the hindrance of concealed information from bidders (Cowell, 2006). The value of the object being sold (or lot) can either be the same for everyone and bids will vary according to the accuracy of the information a bidder holds, or each bidder will have his own private valuation that is unaffected by the valuations of those around him, whether known to him or not. The Independent Private Values model (Parsons et al., 2011) include the assumptions of privacy and independence where the value of the commodity in question is private to the individual buyers, and that different buyers do not know the values other buyers attached to the commodity. In addition, these values are drawn from a common distribution, which is known to the buyers. In probabilistic terms, this essentially amounts to a series of values, which are independent and identically distributed. A common distribution used is the uniform distribution. In this paper, through the use of simulations, we show that the results of auctions, measured through metrics such as average auction income and average auction duration, remain largely insensitive to the underlying private value distribution because the auction incomes tend towards a similar value for high bid rates.

There has been substantial work done on auctions, with several books written on the topic (Cramton, 2006; Klemperer, 2004; Krishna, 2002; Milgrom, 2004). A stochastic number of bidders are studied in McAfee and McMillian (1987) where first-price sealed-bid auctions having constant absolute risk aversion is analysed. As a result of the stochastic analysis, the authors conclude that the seller should conceal the number of bids in order to maximise the selling price. Stochastic models of bid arrival characteristics are studied in Shmueli et al. (2007) and Russo et al. (2008) where the so-called BARISTA (Bid ARrivals InSTAges) model that makes use of non-homogeneous Poisson process is proposed. The probabilistic and statistical properties of these models are analysed and studied and the usefulness of these models for auction modelling is illustrated and discussed.