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Unformatted text preview: his, first assume that the outcomes generate utilities
. Then
compute the expected utilities of the three lotteries above, and derive a contradiction
between the inequalities corresponding to Jill’s preferences.]
Let
denote the utility Jill gets from
, respectively. If ( ) is an
expected utility representation of Jill’s preference then the expected utility for the
three lotteries are
()
()
()
With
, we must have
()
()
()
( ) means
By definition, ( )
()
()
su tract
on oth sides
divide
on oth sides
()
()
y definition
( ). Therefore, it is impossible to assign
which contradicts the condition ( )
utility numbers to the outcomes so that the ranking of the expected utilities of the
three lotteries matches Jill’s preference ranking 3. For each of the following games, answer the following questions:
i) Find all Pareto efficient outcomes. (Do not assume transferable utility.)
ii) Is the game dominance solvable? If so, find the solution.
iii) Find all purestrategy Nash equilibria, if they exist.
Game a...
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This homework help was uploaded on 03/17/2014 for the course ECON 302 taught by Professor Shihenlu during the Fall '13 term at Simon Fraser.
 Fall '13
 ShihEnLu
 Utility

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