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110 Decision making under uncertainty
Utility
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Utility
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Utility
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(a) (b) (c)
Figure 5.7 – Interpreting the shape of a utility function. (a) A risk-seeking attitude;
(b) risk neutrality, which means that the EMV criterion would represent the decision
maker’s preferences; (c) both a risk-seeking attitude and risk aversion
are the same in monetary terms and even though he has the same chance
of winning as he does of losing, the increase in utility which will occur
if the decision maker wins the gamble is far less than the loss in utility
he will suffer if he loses. He therefore stands to lose much more than he
stands to gain, so he will not be prepared to take the risk.
Figure 5.7 illustrates other typical utility functions. Figure 5.7(a) shows
a utility function which indicates a risk-seeking attitude (or risk proneness).
A person with a utility function like this would have accepted
the gamble which we offered above. The linear utility function in
Figure 5.7(b) demonstrates a risk-neutral attitude. If a person’s utility
function looks like this then the EMV criterion will represent their
preferences. Finally, the utility function in Figure 5.7(c) indicates both a
risk-seeking attitude and risk aversion. If the decision maker currently
has assets of $y then he will be averse to taking a risk. The reverse is true
if currently he has assets of only $x. It is important to note that individual’s
utility functions do not remain constant over time. They may vary
from day to day, especially if the person’s asset position changes. If you
win a large sum of money tomorrow then you may be more willing to
take a risk than you are today.
Utility functions for non-monetary attributes
Utility functions can be derived for attributes other than money. Consider
the problem which is represented by the decision tree in Figure 5.8. This
relates to a drug company which is hoping to develop a new product.
If the company proceeds with its existing research methods it estimates