Pirates!

I’ll share a fun scenario today, thanks to a student of mine who shared it with me – The Pirate Game:

There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The pirate world’s rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal.

What is the solution? Can pirate A distribute the coins in such a way to guarantee the distribution will be accepted by the 4 others? I’ll post a solution later this week.

[For my students: this game is an extension of the Ultimatum Game we discussed in class. Here is a full treatment of the Pirate Game in Scientific American.]

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2 comments

  1. RSMattson · · Reply

    Avast!

  2. Well, immediately we can throw out an even split of the coins.
    It would make an equal option and that would mean no resolution.

    So, without knowing the buying power of the coins, thus how much sustenance they would cover, Pirate A would, because of his rank, have to propose that he takes a smaller proportion of the coins. 16 for him, 21 apiece for the rest. It maintains his rank due to his ability to provide for his subordinates, as well as assures that he doesn’t put himself above anyone else.

    The issue, of course, do other members of the hierarchy accept this because the highest position offers it. It easily would get the bottom two and the proposer, but not necessarily the middle-two. How does that change the plan? I’d assume that B + C would ask for a higher proportion than D+F; how that is mediated, I have no idea.

    Just a thought.

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