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106 Decision making under uncertainty
Choose Luxuria Hotel
Choose Maxima Center
Expected utility
= 0.75
Expected utility
= 0.5
0.6
High attendance
Low attendance
0.4
0.5
High attendance
Low attendance
0.5
Payoffs
$30000
$11000
$60000
−$10000
Figure 5.3 – The conference organizer’s decision tree with utilities
Utility
utilities in the same way as the monetary values we are able to identify
the course of action which leads to the highest expected utility.
Choosing the Luxuria Hotel gives an expected utility of:
0.6 × 0.85 + 0.4 × 0.6 = 0.75
Choosing the Maxima Center gives an expected utility of:
0.5 × 1.0 + 0.5 × 0 = 0.5
Thus the business woman should choose the Luxuria Hotel as the venue
for her exhibition. Clearly, the Maxima Center would be too risky.
It may be useful at this point to establish what expected utilities
actually represent. Indeed, given that we have just applied the concept
to a one-off decision, why do we use the term expected utility? To see
what we have done, consider Figure 5.4(a). Here we have the business
woman’s decision tree with the original monetary sums replaced by the
lotteries which she regarded as being equally attractive. For example,
receiving $30 000 was considered to be equivalent to a lottery offering a
0.85 probability of $60 000 and a 0.15 probability of −$10 000. Obviously,
receiving $60 000 is equivalent to a lottery ticket offering $60 000 for
certain. You will see that every payoff in the tree is now expressed in
0.85
0.6
1.0
0