Guess two-thirds of the average
Asked at Five Rings
Every player in a large group picks a number from to . The winner is whoever is closest to two-thirds of the average of all the numbers chosen.
What number do you pick? What is the game-theoretic answer, and what actually wins in practice?
Show a hint
Work out what the equilibrium is by asking "if everyone reasons this through, where does it end up?" Then ask whether real people actually get there.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.