Assignment:
Fifty people are playing the following game. Each player writes down, on a separate slip of paper, one integer in the set {0, 1,..., 100}, alongside his name. The gamemaster then reads the numbers on each slip of paper, and calculates the average x of all the numbers written by the players. The winner of the game is the player (or players) who wrote down the number that is closest to 2/3 x. The winners equally divide the prize of $1,000 between them. Describe this as a strategic-form game, and find all the Nash equilibria of the game. What would be your strategy in this game? Why?
Provide complete and step by step solution for the question and show calculations and use formulas.