1
EconS 424
Strategy and Game Theory
Homework #1 – Answer Key
Exercise 1
–
From extensive form to normal form representation
Consider the following extensive form game
Player 2
Player 2
Player 1
H
L
a
r
M
Player 2
a
r
a
r
10
0
0
0
5
5
0
0
0
10
0
0
a)
Which are the strategies for player 1?
Three strategies S
1
={H,M,L}
b)
What are the strategies for player 2?
Now the second mover can condition his move to the first player’s action, since he is able
to observe it (unlike in the prisoners’ dilemma game). Hence, S
2
={
aaa, aar, arr, rrr, rra,
raa, ara, rar
} where each of them represents a complete plan of action that specifies what
to do in the event that player 1 chooses H, in the event that player 1 chooses M and in the
case that he chooses L, respectively.
c)
Take your results from
a)
and
b)
and construct a matrix representing its normal form
game representation.
If you take the about three strategies for player 1, and the above eight strategies for player
2, we have the following normal form game.

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