In terms of game theory I don’t think this would significantly change things. In that final scenario our observation:

“Thus, it is in Son 8’s best interest to prevent it from coming to two people.”

Becomes:

“Thus, it is in Son 7′s best interest to prevent it from coming to two people.”

Which Son 6 can then use to his advantage making a nominal offer to Son 7, rather than Son 8.

In the end, Son 1 would make nominal offers to 2, 4, 6 and 8 rather than 3, 5 and 7.

Here is why I think that.

Consider three games, with the three players who have to split 60 pieces of gold

In the first game, the voting rule is that they all have to agree or get nothing. The split is going to be 20,20,20. Unless there is a convincing stubborn holdout.

In the second game, the voting rule is majority wins. There are 3 possible 2 persons coalitions, each with 30,30 as the split. Hard to tell which coalition will form.

Now we get to the three person pirates game. The voting rule is the same, but it is in run-off format. The strongest player proposes and needs 2 votes, if his proposal isn’t accepted the middle player proposes and needs 1 vote, and the weak never gets to vote.

This is very similar to the previous coalition game with majority rule – if the strong can form a coalition with the middle or weak, they will have enough votes. But the problem for the middle is this: no verbal commitment to the strong’s proposal is credible – it would always be better to vote against it, promising the weak a greater share.

If the middle was able to scuttle the strong, then the weak, no matter what was promised, will end up being scuttled by the middle.

This is why the weak has a better chance of a coalition with the strong – both need each other equally.

Just a thought – we love to see how groups might manage this.

Additionally, while it may seem that Game Theory misses the mark in *how much* to offer, it is crucial in determining *to whom* to make the offers.