Prof. William H. Sandholm
Department of Economics
University of Wisconsin
March 9, 2006
Midterm Exam – Economics 713
1. (20 points)
Let
G
be a two player normal form game, and suppose that players are only allowed
to choose pure strategies.
Only one of the following statements must be true:
(A)
min
s
2
±
S
2
max
s
1
±
S
1
u
1
(
s
1
,
s
2
)
±
max
s
1
±
S
1
min
s
2
±
S
2
u
1
(
s
1
,
s
2
)
;
(B)
min
s
2
±
S
2
max
s
1
±
S
1
u
1
(
s
1
,
s
2
)
²
max
s
1
±
S
1
min
s
2
±
S
2
u
1
(
s
1
,
s
2
)
.
Prove the statement that must be true, and provide an example in which the other
statement is false.
2. (35 points)
Compute all perfect Bayesian equilibria and sequential equilibria of the game below.
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3. (15 points)
Let
±
be a perfect information extensive form game, and let
G
(
±
) be its reduced
normal form.
(i)
Must every perfect equilibrium of
G
(
±
) correspond to an extensive form
perfect equilibrium of
±
?
Prove that this is true, or provide a counterexample.
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 Spring '08
 SANDHOLM
 Economics, Game Theory, extensive form, extensive form game, social choice function, Department of Economics University of Wisconsin, form perfect equilibrium

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