A generalized oil exploration problem

This paper considers a general version of the oil exploration problem model previously investigated by the author and others. It assumes that a region is hypothesized to contain an unknown number of oilfields represented by a prior ;. The discovery of oilfields is governed by a probability law which is a function of the number of undiscovered sources. Drilling a well costs c and the value of a field is fixed at v. Rewards are additive and discounted by a factor θ, 0•θ<1. On the basis of the history of successful and unsuccessful drillings, the decision maker is faced with three options: retire with no reward; drill a single well; drill two wells, so as to maximize the total expected return.