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?