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“In this game there is no strictly dominant strategy. However, there is a unique pure strategy Nash equilibrium. This equilibrium can be found by iterated elimination of strictly dominated strategies. Guessing any number that lies above 66.67 is dominated for every player since it cannot possibly be 2/3rds of the average of any guess. These can be eliminated. Once these strategies are eliminated for every player, any guess above 44.45 is strictly dominated for every player since no player will guess above 66.67 and 2/3 of 66.67 is approximately 44.45. This process will continue until all numbers above 0 have been eliminated.” source...