Game Theory

Game Theory Parables for Game Designers

A Pirate Puzzle

Here’s a classic question from Game Theory, one that (of course) has a non-intuitive answer:

Five perfectly rational pirates (cleverly named A, B, C, D, and E) are deciding how to divvy up 100 gold coins. The pirates have a strict order of seniority, with A ahead of B, B ahead of C, etc. The most senior pirate proposes a distribution, then they vote on it, with the proposer holding the tie-breaker vote (if necessary).

If the proposal is accepted, that's how the gold is distributed. If it is rejected, then the proposer is thrown overboard and the next senior pirate makes another proposal.

Pirates want three things:

  1. To survive,

  2. To maximize gold,

  3. And, if all else is equal, to throw another pirate overboard.

(this means that a pirate will never vote for a proposal that gets themselves thrown overboard, and if they have to decide between two proposals, they’ll pick the one that gives them more, but if two proposals give them the same amount, they’ll vote for the one that leads to someone else getting thrown overboard)

Now, put yourself in the piratey shoes of Pirate A.  What proposal would you offer?  That is, how much gold would you give to each of A, B, C, D, and E?

Sam Hillier