Pirate game

Five rational, greedy pirates (ranked 5 down to 1) split 100 coins. The highest-ranked proposes a split; everyone votes; if at least half approve, it passes — otherwise the proposer is thrown overboard and the next ranks proposes. Pirates prioritize survival, then coins, then bloodthirst. How many coins does pirate 5 keep?

Show hints (2)+
  1. Work backwards from the case of 2 pirates.
  2. The proposer only needs to buy the cheapest votes.

Answer

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98

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Asked at: Jane Street, Citadel

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