A Closer Look at Game
Theory:
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
Least Optimal Solution
 Each player randomly guesses the color of their hat
 Group will win 1/8 of the time (½ * ½ * ½)
A Better Solution
 The first two players pass
 The third player randomly guesses the color of their hat
 Group will win ½ of the time
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 time
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 strategies
Questions?