Problem Set IV
Fall 2010
Economics 212
1. The normal form game below is repeated in
f
nitely. Both players discount payo
f
streams at the
discount factor
δ
. Consider the following strategies. Play
B
in the
f
rst stage, and play
B
if
(
B,B
)
or
(
C, C
)
was played in the previous round, and play
C
otherwise.
2
AB
C
A
1
,
15
,
00
,
0
1
B
0
,
54
,
40
,
1
C
0
,
01
,
0
−
1
,
−
1
a. For what discount factors will the strategies be a subgame perfect equilibrium?
Suppose the stage game in part a is played twice and that the players’ preferences are the
undiscounted sum of the stage game payo
f
s.
b. Is there a subgame perfect equilibrium in which both players play
A
in the
f
rst stage?
c. Is there a Nash equilibrium which is
not
subgame perfect in which both players play
A
in the
f
rst stage?
2. Consider a symmetric Bertrand duopoly problem in which each of two
f
rms announces a price
simultaneously and the
f
rm that announces the lower price will be able to sell
Q
=13
−
p
i
and the
other
f
rm sells nothing. There is constant marginal cost of producing the good which is equal to
1
.I
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 Spring '12
 gg
 Game Theory, Nash, Subgame perfect equilibrium

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