) Three ferocious old pirates are dividing their plunder (100 gold coins) before disbanding. No single coin can be subdivided. A
ccording to pirate code, pirate number 1 P1 suggests a sharing rule (for instance if P1 suggests (34, 33, 33), under this rule P1 gets 34 coins, P2 gets 33 and P3 gets 33). All three pirates vote by roll call on the proposal. If a majority (even a tie is enough) accept, then the division is carried out and the game ends. If the suggestion is not accepted then the first pirate is thrown overboard (which is worse than getting no gold, because of the circling sharks) and P2 makes a proposal, which is subjected to majority vote, and so on. These pirates are crafty enough to perform backward induction, and so cranky that, whenever a pirate is indifferent about voting for or against a proposal, he votes against it. Explain what happens and why.
First: P1 has to bribe P3 additional one gold coin in order to get majority votes, so that he would not be thrown overboard and be kill. Then,
P1 gets 33 coins
P2 gets 33 coins
P3 gets 34 coins
Second: if P2 reject it, P3 could be indifferent. This will lead to the death of P1. And when P2 makes suggestions, P3 rejects it. Therefore P3 gets it all. P3 gets 100 gold coin
