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Game Theory and Strategy
ECONUA 216
Solutions to Problem Set 1
1
Strictly and weakly dominated strategies
Here is an example of a twoplayer game matrix where Player 2’s strategy
l
is strictly dominated by both
strategies
c
and
r
, while Player 1’s strategy
M
weakly dominates
U.
l
c
r
U
2,1
2,3
5,2
M
3,2
3,3
5,4
D
4,0
1,5
2,6
2
Iterative deletion of dominated strategies
Part A
l
c
r
U
1,1
0,1
3,1
M
1,0
2,2
1,3
D
1,3
3,1
2,2
The game has no strictly dominated strategy. Strategy
r
for Player 2 weakly dominates
c
, while for Player
1 notice that
D
weakly dominates
M.
Part B
We ﬁrst delete strategies
c
and
M
and then notice that in the reduced game below
r
and
D
are weakly
dominated.
l
r
U
1,1
3,1
D
1,3
2,2
The outcome given by Iterated Deletion of Weakly Dominated Strategies is
{
U,l
}
.
1
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View Full DocumentGame Theory
Solutions to P. Set 1
Part C
Notice that the problem with this NE outcome is that : intuitively, Player 2 is indiﬀerent between
l,c,r
when Player 1 plays
U
. If Player 2 switches to
c,
in which case Player 1 is left with a zero payoﬀ.
3
Hotelling’s location game
Part A
First notice that when he plays strategy 1 and his opponent picks any other pure strategy
s
2
6
= 1, Player
1 gets a payoﬀ
π
1
= 10
s
2
2
(when
s
2
= 1, they both get 50). The easiest way to get the answer is, as the
text suggest, to guess and verify. In particular, a good strategy is to try to imagine what the worst case is.
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 Spring '09
 Game Theory

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