Problems from Chapter 3
Find Strategies for Simon
Imagine that you are Simon
• You are really tough and like to fight.
• Mugger is a puny little guy
• But you don’t want to mess with him if he’s
armed
The Mugger Problem
• How many different strategies are there for
Simon? (Remember a strategy specifies what
you will do at every information set.)
• A) 2
• B) 3
• C) 4
• D) 8
Why does it matter.
• If you say there are only two strategies, resist
and not resist, you are telling Simon that he
has to do the same thing whether he sees a
gun or not.
• If Simon can act differently depending on
whether he sees a gun or not, he has 4
strategies.
Strategic form
Simon
Resist/Resist
Mugger
Resist/Give
Give/Resist Give/Give
Show Gun
3,2
3,2
4,5
4,5
Hide Gun
3,2
5,4
3,2
5,4
No Gun
2,6
6,3
2,6
6,3
Simon’s Strategy x/y means Do x if you see a gun,
Do y if you don’t see a gun.
The Stop Light Game
Light
•
Red
Green
Pedestrian
Walk
Pedestrian
Wait
Walk
Wait
Strategies in Stop Light Game
• How many strategies are there for
Pedestrian?
• What are they?
Stop light game
What strategy does this show?
What strategy does this show?
What strategy does this show?
Stop light game
What strategy does this show?
What strategy does this show?
What if you can’t see the light?
Light
Red
Walk
Wait
Green
Walk
Wait
Problem 4
A) If both are rational, are there any strategies that won’t be played?
Figure PR3.4
Harrington: Games, Strategies, and
Problem 4
If both are rational, Player 1 won’t play a and 2 won’t play z
B) If each knows that the other is rational, what can be eliminated?
Figure PR3.4
Harrington: Games, Strategies, and
Problem 4
If Player 1 knows that 2 is rational, he knows that 2 won’t play z.
If 2 won’t play z, payer 1 is always better off with b than with c.
So he won’t play c.
What if Player 2 knows that Player 1 knows that Player 2 is
rational?
Problem 5
a) If both are rational, neither will play strictly dominated strategy
What strategies are strictly dominated?
Figure PR3.5
Harrington: Games, Strategies, and
Problem 5
a) If both are rational, neither will play stricltly dominated strategy
What strategies are dominated?
Figure PR3.5
Harrington: Games, Strategies, and
Problem 5
a) If each believes other is rational , each knows that z and d are not
possible. Reduced game is above. Are there any strictly
dominated strategies now?
Figure PR3.5
Harrington: Games, Strategies, and