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Spring,2012
Dr. Klaus Becker
ECO 3305
Sec 001
EXAM
#1
Solutions
1. (10p)
Each of the following statements is either true or false.
If true circle "T", if
false
circle "F"
If all the information
sets of all players in a game contain exactly one
decision node then the game is a game of perfect information.
T
A strategic form game is represented by a game tree and an extensive
form game is represented by one or more payoff matrices.
T
A rational player never uses
a
weakly dominated strategy.
A game can have at most one dominant strategy equilibrium profile
If none of the players in a game have a dominant strategy then the game is
T
not dominance solvable.
Draw the game tree for the following simultaneous move game (Golden Balls)
2. (10p)
Player
Player 2
Solit
Steal
1
Split
10, l0
50, 0
Steal
0. 50
0,0
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3. (10p) Construct the payoff matrix for the (rather serious) game played between two countries
and illustrated in the figure below:
a. (10p)
Consider the two-player strategic form game in the figure below:
w
x
v
Z
a
1,2
0,5
)')
4,0
b
1,3
<)
5?
2,0
c
)?
4,0
3,3
6,2
d
3,4
2,7
4,0
75
Derive the strategies that survive the iterative deletion of strictly andlor weakly dominated
strategies by completing the table below:
Step
t
Strategy being eliminated
a
a
,,
11
t
J
Due to being strictly/weakly dominated by
Q
C
,l
4
Y
c)
5
6
J
6
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Z
(s,",sry): (d, e)
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5. (10p)
For a Team Project game, suppose a'Jock" is matched up with a'osorority girl" as shown in
Figure 1
Figure I
Sorority girl
Jock
Low
Moderate
High
Low
3,0
4,1
Moderate
))
5)
-)-
3,4
4,3
High
1,6
)5
3,4
(a) Assume both are rational and the'Jock" knows the" sorority girl" is rational. What
happens? Explain.
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(b) Assume both are rational and the "sorority girl" knows the'Jock" is rational. What
happens?
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6. (10p)
two friends go out to dinner with the understanding that the bill will be divided
equally. The problem is that one might order something expensive knowing that part of
the cost will be paid by the other. To analyze such a situation, suppose that the two
friends have the same food preferences. The table below states the price of each of three
dishes on the menu and how much each person values it. Value is measured by the
maximum amount they would be willing to pay for the meal.
Suppose
Dining Dilemma
Dish
Value
Pasta Primavera
$21.00
$
14.00
$7.00
Salmon
$26.00
$21 .00
$s.00
Filet Mignon
s29.00
$30.00
-$
Price
Surplus
1
.00
Surplus is just the value assigned to the meal less the meal's price. The pasta dish costs
$ 14 and each diner assigns it a value of $21 . Thus, if a diner had to fully pay for the meal
then each diner would buy the pasta dish since the surplus of $7 exceeds the surplus from
either salmon or steak. In fact, a diner would prefer to skip dinner then to pay the $30 for
the steak, as reflected by a negative surplus. A player's payoff equals the value of the
meal she eats less the amount she has to pay. The latter is assumed to equal the total bill
divided by the number of diners. Illustrate this "dining game" in a normal form (payoff
matrix).
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