Guess 2/3 of the average

Everyone picks a number in [0,100][0,100]; the winner is whoever is closest to 2/32/3 of the group's average. What is the game-theoretic (Nash equilibrium) answer?

Show hints (2)+
  1. If everyone is rational, no one picks above 2/3 of 100.
  2. Iterate that reasoning to its limit.

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Asked at: Citadel, Two Sigma

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