Unformatted text preview: by decomposing the third lottery into a combination of the first two. That is,
if the first lottery is denoted A, the second B, and the third C, find
[ ] such that
(
) violates the independence
(
) . Then show that
axiom.]
} denote the activities “going out” “watching TV” and “working”
Let {
respectively. The options faced by Jill are three lotteries over the three activities:
[
[
[
We know that
.
Consider and . The independence axiom says that if we mixed these two lotteries
with a third one, , in the same proportion, the preference over the mixture would
[ ],
stay the same; that is, for
(
)
(
) Let and . Then,
[
[ But this contradicts that fact that
independence axiom. [
[ [ Therefore Jill’s preference violates the b) Since Jill’s preferences violate the independence axiom, we know that they do not admit
an expected utility representation. Show directly that it is impossible to assign utilities to
the outcomes so that the ranking of the expected utilities of the three lotteries matches
Jill’s preference ranking.
[Hint: To do t...
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 Fall '13
 ShihEnLu
 Game Theory, Utility, Jill, independence axiom, Pareto efficient outcomes

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