This is a new question, not a copy-paste. It's similar to another, but not the same! :) This one is less complex.

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Consider a game where each player announces a number in the set {1, . . . , K}. A monetary reward of 1 is split equally between all the players whose number is closest to 2/3 of the average number. This game is called the "Guess Two Thirds of the Average" game.

a) Formulate this as a strategic form game with n players

b) Show that the game has a unique mixed strategy Nash equilibrium, in which each player plays a pure strategy

Thanks!