i know it is backward, but i got stuck and can't move because i don't see my mistake:
if there is only one pirate, he got all money
if there are two, then they split 500/500, because otherwise they will never agree to anything ("the majority should be strict" meaning we need 2 vote to accept or kill the proposal)
if there are three, then the one making a proposal can leave himself 499 and let the other one (randomly chosen) has 501. in this case the randomly chosen one will vote in favor of the proposal, because if he kills it, he ll get only 500
if there are four, then the one making a proposal needs two more votes. he should give some money to first two pirates, but how much to give? both of them randomly getting 0 or 501... should he gave them 1 and 1, or should i calculate average payoff and give 1 coin more above it?
i got stuck.... if you have 5 minutes, help!