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      Question

      N people guess an integer between 1 and 100, and the

      winner is the player whose guess is closest to 2 times the mean of the guesses. What is the equilibrium in this case?
      A All saying 100 Correct Answer Incorrect Answer
      B All saying 50 Correct Answer Incorrect Answer
      C All saying 25 Correct Answer Incorrect Answer
      D All saying 75 Correct Answer Incorrect Answer

      Solution

      Each player’s best response is to announce a number closest to twice the average, subject to the Constraint of the 100. So, each person wants to name a number above average, and so nothing is stable except all saying 100.

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