The Oil Wildcatter¶

In this example, an oil wildcatter must decide either to drill or not to drill. He is uncertain whether the hole is dry, wet or soaking in oil. The wildcatter can make seismic soundings that will help determine the geological structure of the site. The soundings will give a closed reflection pattern (indication for much oil), an open pattern (indication for some oil) or a diffuse pattern (almost no hope for oil).

The wildcatter has two decisions to make, namely whether to test with seismic soundings costing K$10 and whether to drill costing K$70. The utility gained from drilling is determined by the state of the hole (dry, wet or soaking).

The domain of this problem is modeled by the (limited-memory) influence diagram (LIMID) in Figure 1. Note the link from Seismic to Drill. It specifies that when the decision of Drill has to be made, the state of Seismic is known. If this link is not specified, the computations will be made under the assumption that this observation is not known by the decision maker when she has to make the drill decision.

Figure 1: A LIMID modeling the oil wildcatters decision problem.

In Figure 1, the chance node Oil has states “dry”, “wet”, and “soak”, the chance node Seismic has states “closed”, “open”, and “diff”, the decision node Test has actions “test” and “not”, and the decision node Drill has actions “drill” and “not”. In Tables 1 and 2, the CPTs of the nodes Oil and Seismic are shown. In Table 3 and 4, the utility tables of the utility nodes Pay and Cost are shown.

Table 1: P(Oil).

Table 2: P(Seismic | Oil, Test).

Table 3: Utility function Pay.

Table 4: Utility function Test.

The influence diagram is now constructed using the HUGIN GUI and after compilation and running Single Policy Update, the results can be seen in the initial state of Figure 2 where the policies for the two decisions are shown along with the monitor windows for all nodes.

Figure 2: The results of solving the LIMID using Single Policy Update.

Reading the network, we see that the expected utility of testing is k\$22.5 while the no testing option as zero probability as it is not the optimal choice and therefore zero expected utility. This implies that it will be best for the wildcatter to test with seismic soundings which will give him the states of Seismic. In the monitor windows you can read the expected utility and probability of different states under the optimal strategy identified by Single Policy Updating. This network has been installed on your computer with the HUGIN software. You can find the network in the Samples subdirectory of your HUGIN installation.