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.
What is the maximum number of coins that pirate A might get?
The answer is 98 which is not intuitive.
A uses the facts below to get 98.
- 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 distribution is (98, 0, 1, 0, 1).