Difference between revisions of "TADM2E 2.52"

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'''a.''' They want to kill other pirates even if it does not affect their outcome -  
 
'''a.''' They want to kill other pirates even if it does not affect their outcome -  
  
2 pirates - Senior gets it.
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2 piratesSenior gets it.
  
3 pirates - Smallest gets it, because 2nd pirate will vote for kill. So, in order to live he must give dollar to smallest.
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3 pirates: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.
  
4 pirates - 2nd or 3rd smallest will get with 50% chances, because 1st will vote for kill irrespective of weather he gets the dollar or not. And 2nd or 3rd will vote for 4th if they
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4 pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she
get the dollar.
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gets the gold respectively.
  
5 pirates - He is certainly going to die, irrespective of his proposal. Whosoever he chooses other three/four will vote against him.  
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5 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.
  
6 pirates - Here 5th will vote for 6th irrespective of weather he gets the dollar, otherwise he is going to die. And 1st will vote for 6th if he gets the dollar, because if he doesn't he doesn't get the dollar(because the case will reduce to 4 pirates).thus, 6th will live and 1st will get the coin.
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6 pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):
  
'''b.''' They want other pirate to live if it doesn't affect their outcome -  
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• 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.
  
Senior most pirate always gets the coin.
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• 3rd-least-senior pirate: would agree to receive the coin since there would only be a 50% chance he/she would get it as described in the eventually inevitable "4 pirates" situation.
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• 2nd-least-senior pirate: same reasoning as above.
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• Least senior pirate: the least senior pirate would agree to receive the coin since he/she would have a 0% chance to receive the gold as described in the eventually inevitable "4 pirates" situation.
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Thus the result would be that no one dies and either the first, second, third, or fourth-least-senior pirate would receive the coin.
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'''b.''' They want as many other pirates to live if it doesn't affect their outcome -
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Senior most pirate gets the gold.

Latest revision as of 13:36, 23 July 2020

This problem is a famous game-theoretical scenario called the pirate game (http://en.wikipedia.org/wiki/Pirate_game). Assume the senior pirate gets to vote.

Where there is only 1 indivisible dollar: 2 pirates - The senior pirate gets it. 3+ pirates - The least senior pirate gets it.

In general, every 2 + 2^K (k >= 1) pirate will survive, while the others will die

Another Answer : Assume senior pirate also gets to vote.

Based on pirates inherent tendency -

a. They want to kill other pirates even if it does not affect their outcome -

2 pirates: Senior gets it.

3 pirates: Least-senior pirate gets it because the 2nd-least-senior pirate will vote for kill; so in order to live, he/she must give the gold to the least-senior pirate.

4 pirates: 2nd or 3rd-least-senior pirate will get gold (equally likely) because 1st will vote for kill irrespective of whether he/she gets the gold or not, and the 2nd or 3rd-least-senior pirate will vote for the plan if he/she gets the gold respectively.

5 pirates - This pirate is certainly going to die regardless of his/her proposal since there will be at least 3 pirates that don't get the gold and thus vote to kill him/her. This will eventually lead to the above situation where the 2nd or 3rd-least-senior pirate will receive the gold.

6 pirates: The 5th-least-senior pirate will vote for whatever plan the most senior pirate proposes—if the proposal falls down to him/her, then he/she is guaranteed to die as explained above. In order to get the last vote, the most senior pirate can give the gold to any of the remaining four pirates. The reason for each is below—recall, the desire to have the gold surpasses the desire to kill another pirate (e.g., if Pirate A has a 50% chance of getting the gold without killing anyone vs. a 49% chance of getting the gold and killing everyone else, he/she will choose the former):

• 4th-least-senior pirate: would agree to receive the coin, because as mentioned before, if the 5th-least-senior pirate decides, he/she will die. This will eventually result in this pirate having to give away the coin in order to live as described in the "4 pirates" situation.

• 3rd-least-senior pirate: would agree to receive the coin since there would only be a 50% chance he/she would get it as described in the eventually inevitable "4 pirates" situation.

• 2nd-least-senior pirate: same reasoning as above.

• Least senior pirate: the least senior pirate would agree to receive the coin since he/she would have a 0% chance to receive the gold as described in the eventually inevitable "4 pirates" situation.

Thus the result would be that no one dies and either the first, second, third, or fourth-least-senior pirate would receive the coin.

b. They want as many other pirates to live if it doesn't affect their outcome -

Senior most pirate gets the gold.