A Closer Look at Game Theory: The Hat Puzzle

1. A Closer Look at Game Theory:The Hat Puzzle By Julia Greenberger

2. 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

3. Least Optimal Solution • Each player randomly guesses the color of their hat • Group will win 1/8 of the time (½ * ½ * ½)

4. 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

5. 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

6. 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

7. Questions?