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Summary: 9/22/2010
1
Utility theory
U: O-> R (utility maps from outcomes to a real number)
represents preferences over outcomes
~ means indifference
We need a way to talk about how preferences interact with
uncertainty:
A lottery is a random selection of one of a set of outcomes
according to specified probabilities
Axioms
· Completeness: induces an ordering over
all pairs of the outcome space (allowing
ties)
· Transitivity: if o o and o o then o o· Transitivity: if o1 o2 and o2 o3, then o1 o3
· substitutability : if o1 ~ o2 then
[p:o1, p3:o3 ... pn:o4] ~ [p:o2, p3:o3 ... pn:o4]
· monotonicity: if o1 o2 and p > q then
[p:o1, (1-p):o2] > [q:o1, (1-q):o2]
Axioms
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