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14.12 Game Theory
Fall 2004
Midterm 1
10/13/04 in class
(You have 80 minutes. Good Luck!)
1.
Consider the following game:
A
B
C
a
3,0
0,3
0,x
b
0,3
3,0
0,x
c
x,0
x,0
x,x
a.
(15pts) Compute two Nash equilibria for x = 1.
b.
(10pts) For each equilibrium in part a, check if it remains a Nash
equilibrium when x = 2.
2.
Consider the following game:
1
2,2
2,2
2
X
E
a
b
c
1
L
R
L
R
3,1
0,0
0,0
1,3
a.
(10pts) Compute two subgameperfect equilibria.
b.
(10pts) Represent this game in strategic form.
c.
(5pts) Find a Nash equilibrium that is not subgameperfect.
3.
Consider two players who own a dollar, which they need to share to consume.
Each player cares about his and his opponent’s consumption level. We will first
assume that the players are malevolent. The payoff of a player is
u = x –
α
y,
where x is his own consumption level, y is his opponent’s consumption level, and
α
is a number in (0,1).
a.
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 Spring '05
 MuhammadYildiz
 Game Theory

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