Each of 15 students simultaneously announces a number in the set {1, 2, . . . , 100}. A prize of 1 TL is split equally between all students whose number is closest to 1/3 of the class average. Show that the game has a unique Nash equilibrium (in pure or mixed strategies).
My answer
I Compute the sequence of sets of pure strategies defining the process of iterated elimination of strictly dominated strategies for every student i.
And I found that (1,1,...,1) is Nash equilibrium. But I cannot prove its uniqueness and show this in a formal way.