Professor Rod Garratt
December 9, 2005
Econ 210B
Final Exam – Fall 2005
You can earn up to 50 points on this exam.
You have 2 hours to complete this exam.
Explain everything that needs explaining.
Good Luck!
1.
Two identical firms each simultaneously choose a nonnegative quantity of
output. There are no costs. The payoff to firm i as a function of the outputs is
Π
i
(q
i
, q
i
) = (100  q
i
 q
i
)q
i
.
Show that for each firm, any level of output greater
than 50 is strictly dominated.
(5 points)
2.
On the hit TV show Survivor Thailand two tribes competed in a game they called
Thai 21. The game starts with 21 flags in a circle. The teams take turns removing
flags from the circle until they are all gone. The team that removes the last flag
wins immunity. At each turn teams must remove 1, 2 or 3 flags. Team 1 moves
first. How many flags should Team 1 take on its first move?
(5 points)
3.
Consider the twoplayer Bayesian game in which S
1
= {T,B} and S
2
= {L,R},
each
player has two types
Θ
1
=
Θ
2
= {0,1}, and each type profile is equally
likely, i.e., p(0,0) = p(0,1) = p(1,0) = p(1,1) = ¼.
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 Fall '09
 GARRATT
 Game Theory, perfect Bayesian equilibria

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