he will take at
each
information set he is to move (
including the information sets that
will not be reached according to this strategy
). Since player 1 moves at 4 information
sets and she has 2 moves at each information set, the number of strategies for player
1 is
2
4
= 16
. Therefore, the following reduced representation
is not
a normal form
representation of the extensive game:
l±
r±
La
2,1
2,1
1,2
1,2
Lb
1,2
1,2
2,1
2,1
R²A
0,0
1,5
0,0
1,5
R²B
0,0
0,0
0,0
0,0
R³A
5,1
1,5
5,1
1,5
R³B
5,1
0,0
5,1
0,0
Each extensive game has the unique normal form representation. The extensive game
given in the homework has the following normal form representation:
l±
r±
La²A
2,1
2,1
1,2
1,2
La²B
2,1
2,1
1,2
1,2
La³A
2,1
2,1
1,2
1,2
La³B
2,1
2,1
1,2
1,2
Lb²A
1,2
1,2
2,1
2,1
Lb²B
1,2
1,2
2,1
2,1
Lb³A
1,2
1,2
2,1
2,1
Lb³B
1,2
1,2
2,1
2,1
Ra²A
0,0
1,5
0,0
1,5
Ra²B
0,0
0,0
0,0
0,0
Ra³A
5,1
1,5
5,1
1,5
Ra³B
5,1
0,0
5,1
0,0
Rb²A
0,0
1,5
0,0
1,5
Rb²B
0,0
0,0
0,0
0,0
Rb³A
5,1
1,5
5,1
1,5
Rb³B
5,1
0,0
5,1
0,0
3. Alice, Bob, and Caroline are moving into a 3-bedroom apartment (with rooms, named