Question 2

This is a game for our class.
Each student needs to choose an integer between 1-100 (including 1 and 100) to submit in this TMA, and then all the choices would be taken averaged. The aim of each participant is to make her/his selected number farther away from the average (i.e., to be the outlier). The farthest outlier wins the game. [For example, if we have only 3 students in our class.

The numbers selected are 2, 13, and 25 from these 3 students, then the average is 10. We can see the distance to the average for each number is 8, 3, and 15 respectively, which means the winner is the one with number of 25.] If there is more than one farthest outlier, then there is no winner, the game ends on nothing.

(a) Outline the pure strategy Nash equilibrium(s) if there is(are) any Nash equilibrium(s) in this game or explain why if there is none. (Word limit: 200 words excluding figures, references, or tables)

(b) Write down which number you would like to submit for this game. Explain your opinion on playing the game.