Beauty Contest- Revisited I?! _’| l'; ‘_"

- Recall the game: " " i‘ '

' Each person picks an integer between 1 and 100.

- I calculate the average

- Target is mmverage

- Whoever guesses closest to the target wins

Question: Can we solve this game using [EDS?

Answer: Yes. HM

Theory of level-k Thinking: - Level 0 thinkers: Randon'ly choose between 1,..1EHJ =1v Average:50

- Level 1 minkers: Thinks all others are level 0 ==- Plays 33

0 Level 2 thinkers: Thinks all others are level 1 =2- Playe 22 .....and so on with level-k people best responding to level k—1. 4. (25 points) We return to the Beauty Contest game. See course slides for a reminder of the set-up.

(a) Let k = %

i. Using the Iterated Equilibrium of Dominated Strategies approach (BEDS), predict the equilibrium. Explain ii. Find all Nash Equilibrium. Explain. (b)Letk=l i. Using the Iterated Equilibrium of Dominated Strategies approach (IEDS), predict the equilibrium.

Explain. ii. Find all Nash Equilbria. Explain.