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UTILITY AND DECISION MAKING 573

Table 13.10 Utility Of Monetary Payoffs for the Swofford Problem
Monetary Value Indifference Value of p Utility Value
E50 000 Does not apply 10.0
30 000 0.95 9.5
20 000 0.90 9.0
0 0.75 7.5
20 000 0.55 5.5
30 000 0.40 4.0
50 000 Does not apply 0.0

Table 13.11 Utility Table for Swofford Problem

State of Nature
Prices Up Prices Stable Prices Down
Decision Alternative s 1 s 2 s 3
Investment A, d 1 9.5 9.0 0.0
10.0 5.5 4.0
Investment B, d 2
7.5 7.5 7.5
Do not invest, d 3

the entries in the utility table is U ij , which denotes the utility associated with decision
alternative d i and state of nature s j . Using this notation, we see that U 23 ¼ 4.0.
Expected Utility Approach

We can now apply the expected value computations introduced in Section 13.3 to
the payoffs in Table 13.11 in order to select an optimal decision alternative for
Swofford, However, because utility values represent such a special case of expected
value, we refer to the expected value when applied to utility values as the expected
utility (EU). In this way, we avoid any possible confusion between the expected value
for the original payoff table and the expected value for the payoff table consisting of
utility values. Thus, the expected utility approach requires the analyst to compute the
expected utility for each decision alternative and then select the alternative yielding
the best expected utility. If there are N possible states of nature, the expected utility
of a decision alternative d i is given by:

X
N
EUðd i Þ¼ Pðs j ÞU ij (13:15)
j¼1
The expected utility for each of the decision alternatives in the Swofford problem is
computed as follows:
EUðd 1 Þ¼ 0:3ð9:5Þþ 0:5ð9:0Þþ 0:2ð0Þ ¼ 7:35
EUðd 2 Þ¼ 0:3ð10Þþ 0:5ð9:0Þþ 0:2ð4:0Þ¼ 6:55
EUðd 3 Þ¼ 0:3ð7:5Þþ 0:5ð7:5Þþ 0:2ð7:5Þ¼ 7:50

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