Suppose that N > 2 players choose an integer in {1, 2,…, 100}.

The payoff to each player is 1 if that player has chosen an integer which is closest to 2 3 of the average of the numbers chosen by all the players. If two or more players choose the closest integer, then they equally split the 1. The payoff of other players is 0. Show that the Nash equilibrium is for each player to choose the number 1.