A Strategy for Sealed Bidding
Authors: Arps John J. 
Published: December 2007

Abstract
This paper describes the development of a strategy for sealed bidding on undeveloped leases, which is designed to acquire a maximum number of tracts of acceptable profitability for a given amount of capital. The method is based on the principles of operations research and is particularly applicable when a large amount of statistical material on past sales is available, such as when bidding on leases offshore.
The first step in the application of the proposed method is the preparation of a conventional evaluation of the tracts of interest. Three different evaluation methods are discussed in the paper.
The second step is based on the observation that past bidding patterns on individual tracts appear to follow a log-normal distribution; by methods of regression analysis, a correlation may be developed between the geometric mean of these distributions and the controlling parameters which were known at the time of bidding. From such a correlation the mean bid values for specified tracts at a future lease sale may be estimated. An empirical relationship may also be developed between the probability of being high bidder and the ratio of bid value to mean value.
Finally, from the results of the first and second steps, it is possible to develop an optimum bidding strategy which will maximize the number of tracts purchased for the amount of commitment capital available.

Introduction
The purchase of prospective acreage through sealed bidding at state or federal lease sales plays an important role in the economics of the petroleum industry. For example, at the record March, 1962, sale of offshore leases in the Gulf of Mexico, the industry committed some $920 million in bids, while $446 million was actually collected by the government. This amounted to approximately 20 per cent of the industry's total exploration expenditures for that year. Yet, with many companies devoting such substantial portions of their exploration budgets to this type of lease acquisition, a study of the amounts "left on the table" strongly suggests that the actual choice of numbers in many cases was based more on hunch or intuition than on a systematic study of the subject.
During the last 10 years some 2,529 bids have been submitted on 884 offshore tracts. With enormous investments at stake and with such a wealth of statistical material readily available, an attractive possibility exists to take advantage of certain techniques from the field of operations research in the development of an optimum bidding strategy which will maximize the results per unit of available capital and minimize unnecessary overbidding. The purpose of this paper is to set forth certain basic relationships which may provide guidance in developing such a strategy. It should be emphasized that the examples given and the numbers used in this paper are intended only as a paraphrase of a real situation.
Optimizing Bidding Strategy Through Operations Research
Operations research, or operations analysis, is the application of mathematics to an activity which is currently carried out largely by intuition. In most applications of operations research it is necessary to clearly decide first, (1) what is the goal or purpose of the operation? and, (2) what is the bottle neck, e. g. what is in short supply?
In general terms, an optimum outcome can be anticipated if the results of Operation 1 are maximized per unit of the limiting factor 2.
In the case of sealed bidding for undeveloped acreage, the purpose of the operation is obviously to purchase as many tracts as possible, while still meeting certain profitability requirements. The bottle neck, or limiting factor, is usually the amount of capital available. One should aim, therefore, at the acquisition of a maximum number of tracts of acceptable profitability for a given (limited) amount of capital. The amount of capital available for commitment in bidding on undeveloped acreage is exclusive of the capital to be reserved for testing and development of the acreage to be purchased.
In designing an optimum bidding strategy to achieve this goal, several steps will be necessary. First, a conventional evaluation must be prepared for each individual tract under consideration. Such an evaluation involves a study of potential income, cost and risks, to determine the maximum value of each tract to the bidder, which will satisfy his profitability requirements.
As a second step, it is necessary to evaluate the behavior of the competition. This involves a study of past behavior patterns of potential competitors and of the industry as a whole.
As a third step, the results of the other two are combined into a bidding strategy designed to acquire the maximum number of profitable tracts for a given amount of available commitment capital. Such a strategy will, therefore, also minimize unnecessary overbidding.