Gaia Di Loreto, Matricola n. 73354
3rd Homework
EXPECTED UTILITY
Expected Utility Theory (EUT) states that the decision maker (DM) chooses between risky or
uncertain prospects by comparing their expected utility values, i.e., the weighted sums obtained
by adding the utility values of outcomes multiplied by their respective probabilities.
One action in uncertain condition can create different
results or events, each one with a certain probability to
accour. For example, if I invest € 10.000 in the creation of
my new photo studio, after one year, the total revenue
could be € 17.000 with a probability of 50%, or € 8.000
with a probabiliity of 50%. Lotteries are defined as a
distribution of probabilities asociated to some payoff
(awars). Decisions of subjects in uncertain conditions can
be represented as the choice of a certain prospect in a
series of choices. If people don’t care about risk
connected with a specific uncertain choice, their choices
depend on the expected value, that is the average of
possible (monetary) values of a lottery (money is not all
that matters). The selected prospect (or lottery) will be the one with higher expected value.
However, most of individuals are no risk indifferent. Utility theory led to observ people behaviour
respect to risk and to treat choices in un uncertain scenario in a similar way to choices in a certain
scenario. Utility is an abstract concept: the utility of an outcome depends on how valuable the
oucome is from the decision maker’s point of view:
The Expected utility (EU) of an act is:
EU(a) = p1u1 + p2u2 + … + pnun
A foundamental aspect of choices in uncertain scenario is individuals behaviour in front of risk,
that can be risk adversion, neutrality o seeking. A risk advers indiviadual prefers to choice a cetrain
alterative rather than choice an uncertain alternatice with an expected value of x.
Let’s make an example:
I want to spend my New year in some European capital, but i have two alternatives with a decisive
factor, the cost of the holiday:
High costs for Christmas Holidays (81%)
No high costs for Christmas Holidays (19%)
London
3 days
6 days
Prague
5 days
7 days
Suppose that utility is linear, so u(x)= kx+m
EU(London) = 0.81 x u(3) + 0.19 x u(6) = u(3,57)
EU(Prague) = 0.81 x u(5) + 0.19 x u(7) = u(5,38)
Praga is better since u(5,38) > u(3,57)
Bibliography
www.wikipedia.com
“An introduction to decision theory”, Peterson, Cambridge.