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risk between $600,000 and $200,000. The fact that he is indifferent (at p  .5)

allows us to find U(0). The expected utility of the 50–50 gamble is

Since the wildcatter is indifferent to $0 for certain and this gamble, the two

alternatives must have the same utility; that is, U(0) 50.

Finally, the wildcatter uses expected utility as a guide for his decision. The

simple rule is this:

The decision maker should choose the course of action that maximizes his or her

expected utility.

The expected utility of drilling is 40, whereas the utility of not drilling is 50.

Thus, the wildcatter should elect not to drill the site. The decision tree in

Figure 12.7 shows how the expected utility rule is applied. Beside each mone-

tary value in the tree is its associated utility. The expected utility of drilling is

computed and listed by the chance circle. Finally, the “drill” decision branch

has been crossed out because it has the lesser expected utility. The wildcatter’s

preferred option is not to drill.

In the more complicated examples to come, there will be many opportu-

nities to practice the mechanics of expected utility. For the moment, the key

point to remember is this: The decision maker’s job is to assess utilities that

express his or her attitude toward risk. There is no formula for determining the

“right” utilities; they are purely personal and subjective.

In the preceding example, the wildcatter’s key assessment is that $0 for

certain is equivalent (in terms of his preferences) to a 50–50 risk between

$600,000 and $200,000. Notice that this assessment reflects risk aversion on

his part. The 50–50 risk has an expected value of $200,000. Yet the wildcatter’s

stated CE for this risk is $0; this is a considerable risk discount. With this assess-

ment in hand, it becomes a simple matter to compare expected utilities: 40 for

drilling versus 50 for not drilling. We also should note an equivalent way to

explain the decision not to drill. Given his degree of risk aversion, the wild-

catter prefers to drill only if the chances of striking oil are greater than .5.

Because the actual probability of an oil strike on this site is only .4, he naturally

chooses not to drill.

A MORE COMPLICATED OIL DRILLING PROBLEM Figure 12.8a depicts a more

complicated drilling prospect involving four possible monetary outcomes and

associated probabilities. In addition, the wildcatter’s utility value is listed beside

each monetary outcome. He continues to set U(600) 100 and U(200) 0.

Accordingly, U(0) remains 50. The wildcatter also has assessed U(200)  70

and U(120) 25. In other words, he is indifferent to the options of $200,000

for certain and a 70–30 risk between the outcomes, $600,000 and $200,000.

(.5)U(600)(.5)U(200)(.5)(100)(.5)(0)50.

524 Chapter 12 Decision Making under Uncertainty

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