Pirates Revisited


A slightly different version of the original pirates problem (read that one first to get all the rules). 6 pirates, only one gold coin. as before, the pirates are super-smart, and they value, in this order: (i) their lives, (ii) getting money, (iii) seeing other pirates die. so if given the choice between two outcomes, in which they get the same amount of money, they’d choose the outcome where they get to see more of the other pirates die. how can pirate 6 save his skin?

thanks to my super smart professor brother

Solution

1 pirate case is obvious. 2 pirate case is obvious, pirate 2 keeps the coin.

3 pirate case: pirate 3 has to give the coin to pirate 1, because if he gives it pirate 2 pirate 2 will say “screw that i wanna see you die and i’m going to get the coin anyway.” so in 3 pirate case, we have pirate 1 gets 1 coin, pirates 2 and 3 get 0.

4 pirate case: pirate 4 can’t give the coin to pirate 1, because pirate 1 would rather see him die since he’s going to get 1 coin anyway. But pirate 4 could give the coin to either pirate 2 or pirate 3.

5 pirate case: pirate 5 just dies, and it goes to the 4 pirate case. there is no way for him to convince two people to vote for him.

6 pirate case: pirate 6 can count on his own vote, plus pirate 5’s vote, because 5 won’t want to die. now who should he give the coin to? he could give it to pirate 1 or to pirate 4, since in the 4 pirate case they are guaranteed to get nothing. it’s unclear whether he could give it to pirate 2 or 3. neither pirate 2 nor pirate 3 is guaranteed to get a coin in the 4 pirate case. so the question is, how do they value (i) definitely getting a coin from pirate 6 vs. (ii) definitely seeing pirates 6 and 5 die, with the chance of getting a coin from pirate 4. since we don’t have enough information to answer that, to be safe, i would just say pirate 6 should offer the coin to pirate 1 or pirate 4.