Answers to Practice Test 1
Econ 3M03 – Introduction to Game Theory
Summer 2003
Vaticrat
All references to 'Nash equilibria' should be taken to mean 'pure strategy Nash equilibria'.
1)
I am using A to represent the strategy of Channel 1 showing
Alf
at 7 o'clock (and
Beverly Hills
at 7:30) and B to represent the strategy of showing
Beverly Hills
at 7
o'clock (and
Alf
at 7:30).
Similarly for channel 2, C is the strategy of showing
Cheers
at
7 o'clock (and
Diffrent Strokes
at 7:30) and D is the strategy of showing
Diffrent Strokes
at 7 o'clock (and
Cheers
at 7:30).
This is the resultant extensive form of the game:
1
2
A
B
C
D
C
D
(
)
(
)(
) (
)
11.5
11
11
10.5
10.5
11
11
11.5
Channel 1's strategy set is
{
}
S
A B
1
=
,
and Channel 2's strategy set is
{
}
S
C D
2
=
,
.
2)
Player 2 has 10 different decision nodes (one for each move by player 1) at which
an action needs to be specified by any strategy.
At each node, player 2 has 9 different
actions available (one for each number from 1 to 10 that was not chosen by player 1).
Thus at the first decision node, a strategy can specify 9 actions.
For each of these, at the
second node, there are nine more, leading to 9x9=81 different ways strategies can specify
actions for the first two decision nodes.
Then for each of these, there are nine ways to
specify the action to be taken at the third decision node, leading to 9
3
=729 different ways
strategies can specify actions for the first three decision nodes.
Continuing this reasoning
to accommodate all ten decision nodes, player 2 has 9
10
= 3 486 784 401 different
possible strategies.
An example of a strategy by player 2 is:

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