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
This preview has intentionally blurred sections. Sign up to view the full version.
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.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Game Theory, player, dominant wrt

Click to edit the document details