Ecos3012 Strategic Behavior
Midterm Exam, Semester 1, 2011
NOTE:
This exam consists of 20 multiple choice questions and 2 problems. Each multiple
choice question is worth 3 points and each problem is worth 20 points. Therefore, you can score
a maximum of 100 points.
Your score in this exam is worth 35% of the final grade.
Duration: 2 hours including reading time.
1. Multiple Choice Questions
Instructions.
•
For each of the following, choose the best answer and mark it on the supplied answer
sheets.
•
Those questions marked with a “
?
” may require a bit more computation than others. You
might consider answering those later.
•
Throughout, assume that in finite strategic form games, players
do
not use mixed strategies
unless specified otherwise.
1.
Suppose there are three states of the world and a typical action is given by a triple (
x, y, z
),
denoting the monetary reward in the three states of the world.
Consider two actions
A
= (
x, y, z
) and
B
= (ˆ
x,
ˆ
y, z
).
( Both actions give the same reward in state 3).
Now
consider any other actions
C
= (
x, y, z
*
) and
D
= (ˆ
x,
ˆ
y, z
*
) obtained from A and B by
changing the reward in state 3.
Suppose a Decision Maker (DM) is known to satisfy
Expected Utility Hypothesis and it is known that she strictly prefers A to B.
(a)
•
DM must strictly prefer C to D.
(b)
DM may strictly prefer C to D but depends on the value of
z
*
.
(c)
DM may prefer C to D but this depends on payoffs in the first two states
(d)
None of the above.
Solution
: This is straightforward. If the Expected utility hypothesis holds, then there
must be a probability distribution (
p
1
, p
2
, p
3
, and a utility function
u
such that
U
(
A
)
=
p
1
u
(
x
) +
p
2
u
(
y
) +
p
3
u
(
z
)
(1)
U
(
B
)
=
p
1
u
(
x
0
) +
p
2
u
(
y
0
) +
p
3
u
(
z
)
(2)
U
(
C
)
=
p
1
u
(
x
) +
p
2
u
(
y
) +
p
3
u
(
z
*
)
(3)
U
(
D
)
=
p
1
u
(
x
) +
p
2
u
(
y
) +
p
3
u
(
z
*
)
(4)
It is clear that
U
(
A
)
> U
(
B
) if and only if
U
(
C
)
> U
(
D
).
Ecos3012 Strategic Behavior, Midterm Exam, 2011
1
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2.
Consider a bargaining problem
h
S, d
1
, d
2
i
such that whenever a payoff vector (
u, v
) for the
two players is feasible, then (
v, u
) is also feasible.
Assume that Nash bargaining solution
is applicable.
(a)
The Nash bargaining solution (
u
*
, v
*
) must be such that
u
*
=
v
*
.
(b)
The Nash bargaining solution (
u
*
, v
*
) cannot be such that
u
*
=
v
*
.
(c)
We must have log(
u
*
) = log(
v
*
).
(d)
•
None of the above.
Solution
: It is tempting to say
u
*
=
v
*
thinking that the bargaining problem is symmetric –
however we do not know that it is symmetric. For that, in addition to the given information,
we need to know that the outside options are equal, i.e.
d
*
1
=
d
*
2
.
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 Spring '11
 etw
 Game Theory, Nash, best response

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