Pirates and coins - rFronteddu/general_wiki GitHub Wiki

There are 5 pirates, they must decide how to distribute 100 gold coins among them. The pirates have seniority levels, the senior-most is A, then B, then C, then D, and finally the junior-most is E.

Rules of distribution are:

• The most senior pirate proposes a distribution of coins.
• All pirates vote on whether to accept the distribution.
• The distribution is approved if at least half of the pirates agree (including the proposer)
• If the distribution is accepted, the coins are disbursed and the game ends.
• If not, the proposer is thrown and dies, and the next most senior pirate makes a new proposal to begin the system again.
• In case of a tie vote, the proposer can have the casting vote

Rules every pirate follows.

• Every pirate wants to survive
• Given survival, each pirate wants to maximize the number of gold coins he receives.

Solution

• Consider the situation when A, B, and C die, only D and E are left.
  • E knows that he will not get anything (D is senior and will make a distribution of (100, 0).
  • So E would be fine with anything greater than 0.
• Consider the situation when A and B die, C, D, and E are left.
  • D knows that he will not get anything (C will make a distribution of (99, 0, 1) and E will vote in favor of C).
• Consider the situation when A dies.
  • B, C, D, and E are left.
  • To survive, B only needs to give 1 coin to D.
  • So distribution is (99, 0, 1, 0)
• Similarly, A knows about point 3, so he just needs to give 1 coin to C and 1 coin to E to get them in favor.

So the distribution is (98, 0, 1, 0, 1).