A Closer Look at Game Theory:The Hat Puzzle

By Julia Greenberger

Game Theory BackgroundCoordination game

Players choose corresponding strategies All parties realize maximum gain

Game of incomplete informationPlayers do not know color of their own hat

Least Optimal SolutionEach player randomly guesses the color of their

hat

Group will win 1/8 of the time (½ * ½ * ½)

A Better SolutionThe first two players pass

The third player randomly guesses the color of their hat

Group will win ½ of the time

The Optimal SolutionIf 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?