MediumMarket Making & Games
Two-Thirds of the Average
Jane StreetOptiver
Everyone in a large group simultaneously picks a number from 0 to 100. The winner is whoever is closest to two-thirds of the group average. If every player is perfectly rational and knows everyone else is too, what number does game theory say everyone picks?
Approach
Ask which guesses can never win, and delete them — repeatedly.
Answer
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