Game Theory and Strategy
ECON-UA 216
Solutions to Problem Set 1
1
Strictly and weakly dominated strategies
Here is an example of a two-player 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