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

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.

The Stop Light GameLight

Red Green

Walk Wait Walk Wait

•

Pedestrian Pedestrian

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 Green

Walk Wait Walk Wait

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?

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?

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?

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?

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?

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?