Consider a variant on the beauty contest game in which each person picks a number between 0 and 100, and the winner is the person whose guess is p times the class average. In class, we considered the case in which p=2/3. Now consider a game in which p=0.99:

1.1 (5 points) What does standard game theory predict that people will choose? Is this a good guess to make? Explain why or why not.

1.2 (5 points) Compared to our 2/3 beauty contest game, would you choose a higher answer, lower answer, or the same.

1.3 (5 points) How would your answer be affected if you were told that the class was filled with game theorists?

1.4 (5 points) In the beauty contest game we looked at in class, explain why "clumps" of answers appeared in the distribution of guesses. What do you predict the clumps will look like in the p=0.99 version?