The Hat Puzzle By Julia Greenberger Game Theory Background Coordination game Players choose corresponding strategies All parties realize maximum gain Game of incomplete information Players do not know color of their own hat ID: 543489
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Slide1
A Closer Look at Game Theory:The Hat Puzzle
By Julia GreenbergerSlide2
Game Theory Background
Coordination game
Players choose corresponding strategies
All parties realize maximum gain
Game of incomplete information
Players do not know color of their own hatSlide3
Least Optimal SolutionEach player randomly guesses the color of their hat
Group will win 1/8 of the time (½ * ½ * ½) Slide4
A Better SolutionThe first two players pass
The third player randomly guesses the color of their hat
Group will win ½ of the timeSlide5
The Optimal Solution If a player sees one red and one blue hat, he will pass
If a player sees two red hats, he will guess blue
If a player sees two blue hats, he will guess red
Group will win ¾ of the timeSlide6
Can a group of WashU students get the optimal solution?
Easier to find strategies when you are actually involved in the problem
Group went through progression of different strategies to reach optimal strategiesSlide7
Questions?