In an enclosed space stand 57 lions and one sheep. The lions, all perfectly rational and well

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In an enclosed space stand 57 lions and one sheep. The lions, all perfectly rational and well trained in game theory, would all like to eat the sheep. For simplicity, we imagine that the lions are numbered from 1 to 57, and sequentially decide whether they would like to eat. (If the sheep is still alive after lion #57 makes his decision, then lion #1 gets to decide again, and the process goes around and around forever.) If any lion begins to eat the sheep, then the other lions will respect his property rights and allow him to finish by himself. The sheep is powerless to stop this. If a lion eats the sheep, then he will fall asleep for one hour, during which time he becomes defenseless and can be eaten by any other lion. (While awake, a lion cannot be eaten by another lion.) The best outcome for a lion would be to eat the sheep, fall asleep, and not be eaten himself. The second best outcome for a lion would be to go hungry. The worst outcome would be to eat, fall asleep, and be eaten. So, in the unique SPNE of this game, what happens to the sheep?

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