There are 6 rational pirates, 1, 2, 3, 4, 5 and 6. They found 242 gold...

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There are 6 rational pirates, 1, 2, 3, 4, 5 and 6. They found 242 gold coins and they must decide how to distribute them. The pirates have a strict order of seniority: pirate 1 is senior to pirate 2, who is senior to pirate 3, who is senior to pirate 4....... and pirate 6 is the most junior of them all. The pirate world's rules of distribution are thus that the most senior pirate should propose a distribution of coins (integers only). The pirates, including the proposer, then vote on whether to accept this distribution. If at least half (including the case of a tie) of the pirates vote for this distribution, then the distribution is accepted, the coins are disbursed and the game ends. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors: (1) each pirate wants to survive, (2) given survival, each pirate wants to maximise the number of gold coins each receives, and (3) if a private is indifferent between accepting a proposal and throwing the proposer overboard, he will vote for "throw overboard". The pirates do not trust each other and will neither make nor honour any promises between pirates apart from a proposed distribution plan that gives a whole number of gold coins to each pirate. Q: How many gold coins does pirate 3 get in the subgame perfect equilibrium? Your answer must be an integer. If this pirate is dead, please enter -999 (with the minus sign) as your answer. There are 6 rational pirates, 1, 2, 3, 4, 5 and 6. They found 242 gold coins and they must decide how to distribute them. The pirates have a strict order of seniority: pirate 1 is senior to pirate 2, who is senior to pirate 3, who is senior to pirate 4....... and pirate 6 is the most junior of them all. The pirate world's rules of distribution are thus that the most senior pirate should propose a distribution of coins (integers only). The pirates, including the proposer, then vote on whether to accept this distribution. If at least half (including the case of a tie) of the pirates vote for this distribution, then the distribution is accepted, the coins are disbursed and the game ends. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors: (1) each pirate wants to survive, (2) given survival, each pirate wants to maximise the number of gold coins each receives, and (3) if a private is indifferent between accepting a proposal and throwing the proposer overboard, he will vote for "throw overboard". The pirates do not trust each other and will neither make nor honour any promises between pirates apart from a proposed distribution plan that gives a whole number of gold coins to each pirate. Q: How many gold coins does pirate 3 get in the subgame perfect equilibrium? Your answer must be an integer. If this pirate is dead, please enter -999 (with the minus sign) as your answer.

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