Gates’ Bidding Model

Abstract

In evaluating closed-bid competitive procurement auctions, the most crucial issue is to determine the probability of placing a winning bid for a given markup level. There has long been disagreement on how this should be done due to the absence of a mathematical derivation of one of the main evaluation techniques—Gates’ method. Gates’ method is shown in this paper to be valid if, and only if, bids can be described using the proportional hazards family of statistical distributions. When markup values are included in Gates’ method, it is seen that the underlying statistical distribution required for the method to work is closely related to the Weibull distribution. Likelihood based methods are suggested for parameter estimation and an illustrative example is provided by analysis of Shaffer and Micheau's 1971 construction contract bidding data.