Consider the following game: There are 5 pirates on a boat, conveniently named P

Question

Consider the following game: There are 5 pirates on a boat, conveniently named P1, P2 P3,
P4 and P5. These 5 pirates have just dug up a long lost treasure of 100 gold pieces. They now
need to split the gold amongst themselves, and they agree to do it in the following way:
Pirate P1 will suggest a distribution of the coins. All 5 pirates will vote on his proposal. If an
absolute majority approve the plan, then they proceed according to the plan. If he fails to pass
his proposal by an absolute majority, then P1 must walk the plank, and it becomes P2

Explanation / Answer

Consider the final stage of the game, i.e. the sub game of length 1. Only P5 is left. Therefore he can allocate all the 100 coins to himself.

Now consider the sub game of length two where P4 and P5 are the remaining pirates. P4 knows that he has to offer P5 100 coins since P5 will vote against any allocation profile in which he gets less than 100 coins. And if P4 cannot pass the allocation by a majority then he will have to walk the plank which he prefers less over the outcome of retaining his life but getting zero coins. Therefore P4

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