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.

Love this game and most other Game Theory thought pieces like it.

Basically the aim of the game for each pirate is kill your superior unless you get less money as a result of it. Despite this the Captain would keep the vast majority of the coins.

What if they were arr-rational pirates though?

Pete Best wrote:Despite this the Captain would keep the vast majority of the coins.

How so? Doesn't he have to pay B and C to buy their votes? For example, proposing something like 15 / 35 / 48 / 1 / 1? How much does he have to pay to convince B and C that they can't do better by killing him?

If it gets down to D, E gets nothing.

If it gets down to C, D gets nothing and E can be bought on the cheap.

If it gets down to B, C gets nothing, D can be easily persuaded, and E gets nothing.

For A, give B nothing, C a little bit, D nothing, E little.

Maybe?

Duff has it, you work backwards from D and E remaining. D has the casting vote so would keep all of what he was offered.

A little bit would be one coin as these rational pirates consider getting one coin better than no coins and the fact that someone has the vast majority doesn't enter into their thinking.

Much like the Ultimatum game, in the real world only Economists would play like this, we'll them and psychopaths. True story.

Any pirate would need 50% of the remaining crew to be happy and it has to be the lowest rank crew member on his side but not the 2nd lowest rank because all things being equal the 2nd last crew member would rather get the same offer from B and A chucked over, an option that lowest rank doesn't have.