Math Puzzle: Simple Stacker Edition #2 \ stacker news ~science

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730 sats \ 10 comments \ @SimpleStacker 24 Oct science

Since our fearless puzzle master and physicist @south_korea_ln is on hiatus from the puzzles, here's another one for you to chew on.

Five pirates have just plundered 100 gold coins of treasure. Their ranks, from most senior to least senior, are: Captain (C), First Mate (F), Quartermaster (Q), Boatswain (B), and Deckhand (D).

The captain has to propose a distribution of the gold, i.e. how much gold, including himself, does each pirate get? All the pirates, including the captain, then vote to accept or reject the proposal.

If at least half accept, the proposal is accepted and the gold is split according to the proposed distribution.
If less than half accept, the proposal is rejected and the captain is thrown overboard. The next most senior pirate will then make a proposal according to the same rules.

Assume that the pirates' objective is to maximize their own gold, without getting thrown overboard. If they're ever indifferent between two situations, they'd rather see someone else get thrown overboard than not.

How will the Captain make his initial proposal?

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251 sats \ 2 replies \ @Scroogey 24 Oct

If there are only B and D left, B would propose 100-0 and win with his half of the votes. So, if D wants to get more than 0, he will want to avoid that scenario.

Hence, if Q, B, and D are left, Q would propose 99-0-1 to win with D on his side. B wants to avoid this scenario.

If F, Q, B, and D are left, F would propose 99-0-1-0 to win with B on his side. Q and D want to avoid this scenario.

So, C will propose 98-0-1-0-1 and win with Q and D on his side.

If I were C, I wouldn't risk my life on the assumption that all agents are perfectly rational, and propose something that doesn't infuriate the others.

52 sats \ 1 reply \ @SimpleStacker OP 24 Oct

Indeed, and fairness can be rationalized game theoretically if there are repeated interactions, something we assumed away in this simple setup

22 sats \ 0 replies \ @Undisciplined 24 Oct

We do know, with pretty high certainty, from experimental econ that the pirates would throw the captain overboard for making that offer.

210 sats \ 1 reply \ @Undisciplined 24 Oct

D can't expect any, because if it comes down to B and D, then B can keep it all.

Therefor Q could propose a 99/0/1 split and earn D's vote, so B can't expect any.

Similarly, F could get B's vote with a 99/0/1/0 split, so Q can't expect any.

Finally, C can get Q's and D's votes with a 98/0/1/0/1 split, because they each get zero in the next round.

By quick, and possibly reckless backwards induction, the Captain proposes keeping 98 while the Quartermaster and the Deckhand each get 1.

33 sats \ 0 replies \ @SimpleStacker OP 24 Oct

quick, and possibly reckless backwards induction

Nice turn of phrase

0 sats \ 4 replies \ @0xbitcoiner 24 Oct

20 20 20 20 20 or 34 33 33 0 0 ahahah

11 sats \ 1 reply \ @SimpleStacker OP 24 Oct

Incorrect! What are you, some kind of communist? These are bloodthirsty pirates we're talking about :)

0 sats \ 0 replies \ @0xbitcoiner 24 Oct

If that's the case, then it could be: Q, B, and D reject the first two proposals. C and F die. B and D reject Q's proposal and take half each.

0 sats \ 1 reply \ @Undisciplined 24 Oct

43 sats \ 0 replies \ @0xbitcoiner 24 Oct

Pirates always split the spoils! We don't give anything to people who don't contribute! ahahaha