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Problems from Chapter 3
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Find Strategies for Simon
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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
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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
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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.
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Strategic form
3,2 3,2 4,5 4,5
3,2 5,4 3,2 5,4
2,6 6,3 2,6 6,3
Resist/Resist Resist/Give Give/Resist Give/Give
Simon
Mugger
Show Gun
Hide Gun
No Gun
Simon’s Strategy x/y means Do x if you see a gun, Do y if you don’t see a gun.
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The Stop Light GameLight
Red Green
Walk Wait Walk Wait
•
Pedestrian Pedestrian
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Strategies in Stop Light Game
• How many strategies are there for Pedestrian?
• What are they?
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Stop light game What strategy does this show?
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What strategy does this show?
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What strategy does this show?
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Stop light game What strategy does this show?
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What strategy does this show?
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What if you can’t see the light? Light
Red Green
Walk Wait Walk Wait
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Figure PR3.4Harrington: Games, Strategies, and Decision Making, First EditionCopyright © 2009 by Worth Publishers
Problem 4
A) If both are rational, are there any strategies that won’t be played?
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Figure PR3.4Harrington: Games, Strategies, and Decision Making, First EditionCopyright © 2009 by Worth Publishers
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?
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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?
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Figure PR3.5Harrington: Games, Strategies, and Decision Making, First EditionCopyright © 2009 by Worth Publishers
Problem 5
a) If both are rational, neither will play strictly dominated strategy What strategies are strictly dominated?
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Figure PR3.5Harrington: Games, Strategies, and Decision Making, First EditionCopyright © 2009 by Worth Publishers
Problem 5
a) If both are rational, neither will play stricltly dominated strategy What strategies are dominated?
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Figure PR3.5Harrington: Games, Strategies, and Decision Making, First EditionCopyright © 2009 by Worth Publishers
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?