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Interpreting utility functions 109
Utility
1.0
0.8
0.6
0.4
0.2
−10 0 10 20 30 40 50 60
Money ($000)
Figure 5.5 – A utility function for the conference organizer
Increase
in utility
through
winning
Decrease
in utility
through
losing the
gamble
Utility
1.0
0.8
0.6
0.4
0.2
0
0 1000 2000
Money ($)
Figure 5.6 – A utility function demonstrating risk aversion
0.5 × $2000 + 0.5 × $0), so according to the EMV criterion he should be
indifferent between keeping his money and gambling. However, when
we apply the utility function to the decision we see that currently the
decision maker has assets with a utility of 0.9. If he gambles he has a
50% chance of increasing his assets so that their utility would increase
to 1.0 and a 50% chance of ending with assets with a utility of 0. Hence
the expected utility of the gamble is 0.5 × 1 + 0.5 × 0, which equals 0.5.
Clearly, the certain money is more attractive than the risky option of
gambling. In simple terms, even though the potential wins and losses