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The members of a hierarchical group of hungry lions face a piece of prey. If lion 1 does not eat the prey, the prey escapes and the game ends. If lion 1 eats the prey, it becomes fat and slow, and lion 2 can eat lion 1. If lion 2 does not eat lion 1, the game ends; if lion 2 eats lion 1, then it may get eaten by lion 3, and so on. Each lion prefers to eat than to be hungry, but prefers to be hungry than to be eaten.

a. Find the subgame perfect Nash equilibrium that models this situation for any number n of lions.
b. Can you find a Nash equilibrium that is different from the subgame perfect Nash equilibrium you found above? If yes, describe it specifically.

Sagot :

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