Please write the payoff at the terminal nodes.

4. This problem is set in ancient Rome where a person, say Androcles, has just been thrown into the arena to face a sequence of hungry lions. Suppose there are n lions, players 1,2,..n. Lion 1 enters the arena and decides whether to eat Androcles or not. If he eats Androcles, he becomes slow and sleepy and the guard lets in Lion 2. If he chooses not to eat Androcles, no other lion is admitted and the game ends. Lion 2 can choose to eat Lion 1, who is too full to resist, in which case Lion 1 ceases to exist and Lion 2 becomes slow and sleepy. If Lion 2 decides not to eat Lion 1, the game ends. Lion 3 is admitted to the arena if Lion 2 has had his fill and so on upto n. The payoffs to the lions are as follows (Androcles has no actions to take): 1. Full and alive: 1. 2. Hungry and alive: 0. 3. Dead, whether full or not: -1. Draw the extensive form