Question

BONUS QUESTION: There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them. The pirates have a strict order of seniority: A is superior to B who is superior to C, who is superior to D, who is superior to E. The pirate world's rules of distribution are thus that the most senior pirate coins. The pirates, including the proposer, then vote on whether to accept this distribution. In case of a tie vote the proposer has the deciding vote. If 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. a. First of all, each pirate wants to survive. b. Second, given survival, each pirate wants to maximize the number of gold coins he receives. c. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal. (7 points)

Answer 1

LET US CONSIDER SCENARIOS IN THIS QUESTION.

SCENARIO 1- THERE ARE ONLY 2 PIRATES IN THE GAME. (Dand E) - D WILL SPLIT THE COINS IN RATIO 100:0 AS HE SURE HE WILL WIN IN ANY CASE WILL GET ALL THE COINS.

SCENARIO 2- NOW THERE ARE 3 PIRATES IN THE GAME. (C,D AND E)- NOW, C BEING THE SENIOR MOST, HE WILL SPLIT THE COINS IN RATIO 99:0:1. HE WILL GIVE ONE COIN TO E TO GET ONE VOTE FROM HIM. ALSO, E WILL VOTE IN FAVOUR OF C BECAUSE HE WILL THINK ITS BETTER TO HAVE 1 COIN RATHER THAN HAVING 0 COIN (IF HE VOTES AGAINST C THEN A WILL LOOSE AND THE DECISION POWER WILL BE TAKEN BY D AND THEN E WILL ULTIMATELY NOT GET ANYTHING AS D WILL SPLIT THE COINS IN RATIO 100:0). ALSO C HAS ALOTTED 0 COINS TO D BECAUSE HE KNOWS THAT D WILL NOT VOTE IN HIS FAVOUR BECAUSE D WANTS TO GET THE DECISION POWER.

SCENARIO 3- NOW THERE ARE 4 PIRATES IN THE GAME. (B,C D AND E)- B WILL SPLIT THE COINS 99 : 0 : 1 : 0. THE REASON IS SAME AS BEFORE, DWILL BE SUPPORTING THIS DECISION. B WILL NOT WASTE COIN ON C BECAUSE C KNOWS IF HE REJECTS THE DEAL HE WILL GET 99 COINS AFTER B WILL DIE. B WILL ALSO NOT GIVE COINS TO E AS E KNOWS THAT IF HE REJECTS THE DECISION , HE WILL RECEIVE 1 COIN FROM C IN THE NEXT ROUND.

SCENARIO 4- THE ACTUAL GAME! A WILL SPLIT THE COINS IN RATIO 98 : 0 : 1 : 0 : 1. BY OFFERING COINS TO C AND E (WHO WOULD NOT GET ANYTHING OTHERWISE) A ASSURED THE DEAL. A WILL NOT GIVE COINS TO B, AS B KNOWS HE CAN GET 99 COINS IF HE VOTE AGAINST A(A WILL DIE). IN THE SAME WAY ,A WILL NOT GIVE COIN TO D, BECAUSE D KNOWS THAT IS HE VOTES AGAINST A, A WILL BE THROWN AND B WILL OFFER HIM HIM 1 COIN .