Monday, March 2, 2009

Rational Pirates (really ??)

k, somebody sent me this question and a quick googling gave me this wikipedia link to the question itself. The question

There are five 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 should then vote on whether to accept this distribution; the proposer is able to vote, and has the casting vode in the event of a tie. If the proposed allocation is approved by 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. Secondly, each pirate wants to maximize the amount of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.

Wiki link - http://en.wikipedia.org/wiki/Pirate_game

Assuming the reader has read just the question, let me proceed further by strengthening it. What strategy should A employ that he doesn't get thrown overboard ?
Clue: Why not try this with a smaller number of people and then increase to see if it proves to be any helpful.
If n = 2, (say D and E ) are there. Then D obviously splits it as 100:0. So E will always attempt to never reach this situation where only 2 people are left out.
Consider n = 3. C knows that E would not want to in a situation with n = 2, so he would vote for me with any bare min payoff. So he would splits it as 99:0:1.
Now consider n = 4. B clearly knows that D would not want n = 3 situation and by same reasoning would split it as 99:0:1:0 ( note : In this case the casting vote would rule as C and E will vote against the proposition ).

Do you see a pattern readers. Plz note the flipping payoffs. And this is how A would split 98:0:1:0:1.

Easily generalizable. Solved.

Better still, they should all be given swords to finish it off, say, in more pirately manner.

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