Consider the following game. You have to choose a number between 0 and 100. Each of your classmates will also choose a number between 0 and 100. The number of points is given by how close your choice is to 2/3 xi , where xi represents the choice of each classmate's decision (including yourself), assuming n students.

a) Explain why the Nash equilibrium of this game is to choose 0.

b) Choose a number and provide a rationale for your choice. (Note, your actual score will depend on how close your decision is to 2/3 xi .)