This is a game for the company, Each employee needs to choose an integer between 1-100 (including 1 and 100) to submit in this assignment, 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 employee. The numbers selected are 2, 13, and 25 from them, 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.

(b) select a number and explain why.