Determining Optimum Bid Fraction
Authors: Dougherty E.L. , Nozaki M. 
Published: December 2007

Computer studies of bidding for offshore tracts indicate that, because of uncertainty, one should bid less than his estimate of value to cover his mistakes over the long run. Knowing one's competitors and how they are likely to bid are of equal importance to knowing how well one can estimate value.

Introduction
To bid on a tract of unknown value we first estimate the value of the tract and then bid some fraction of our estimate. To determine our optimum bid fraction-the bid fraction that will maximize our expected gain - our analysis must recognize that we will not win all competitions. Furthermore, we must also allow for possible losses on tracts won whose actual value is less than our bid. Optimum bid fraction is greatly influenced by precision of our estimates and nature of the competition. precision of our estimates and nature of the competition. Recent analyses that balance these two factors have shown some surprising results; optimum bid fraction decreases as the number of competitors increases beyond two or three, or as competitors' estimates become more precise. Results of these analyses presented in the literature leave several unanswered questions. How much does our optimum bid fraction change as we become better estimators than our competitors, as we become poorer estimators, or as we all become more precise in our estimates? How does our optimum bid fraction change as competitors change their bid fraction? How do the answers to these questions change as the number of competitors changes? What is our probability of winning and expected gain with the optimum bid fraction? The purpose of this study was to throw light on these important questions. We believed that this would contribute to the growing understanding of the competitive bidding process - a phenomenon of vital importance to the oil industry and the nation today. All results presented were obtained from bidding-model studies on a computer. Our model is similar to that used by Capen et al. We introduced some approximations that greatly reduced the amount of computer time required. We believe these approximations caused only slight changes in the results. We studied the effect of varying the following parameters:uncertainty (standard deviation) of our parameters:uncertainty (standard deviation) of our estimates,uncertainty (standard deviation) of competitor's estimates,number of competitors, andcompetitor's bid fraction.
Given a value for each of these parameters, our computer model varied our bid level until it located the optimum bid fraction. We found that our optimum bid fraction is determined byhow many competitors are in the auction,how aggressively they are bidding, andhow accurately we can estimate compared with them.
Optimum bid fraction varies from aggressive and acquisitive, if competitors are bumbling sheep, to cautious and circumspect, if competitors are tough and informed. The more bumbling sheep in the competition, the more we should throw our weight around; the more tough competitors entered, the meeker we should become. We first review the bases of the bidding model. Then we show the approximations used and tabulate parameter ranges covered. parameter ranges covered. JPT
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