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BrainteasersJane StreetCitadel

A hundred tigers and one sheep

game-theoryinductionbackward-inductionclassic

An island holds 100 tigers and 1 sheep. Tigers can live on grass but would prefer to eat the sheep. If a tiger eats the sheep, that tiger turns into a sheep and could in turn be eaten by another tiger, which would then become a sheep, and so on. Only one tiger can eat at a time. Every tiger is perfectly rational, knows all of this, and values its life above a meal.

Does the sheep get eaten? What if there were 99 tigers?

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Solve it for 1 tiger, then 2, then 3, and look for the pattern.

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Backward Induction in Sequential GamesCommon Knowledge and the Blue-Eyed IslandersThe Pirate Gold-Division GameGames With Incomplete InformationBluffing, Signalling and Reading Intent

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