WarDaft wrote:Except he doesn't have to say anything. It's being deduced that it is more profitable for him to commit absolutely to not betraying. If we deduce that he would only lie, and always betray, then he will always receive 0 gold in the three pirate situation, yet if we can deduce that he will commit to not betraying, then there is an avenue for pirate 2 to make 998 gold and give 2 to pirate 1. 998 > 0 and 2 > 1. Surely, if possible, pirate 2 will commit (not say he will commit, but actually do so, so that we may deduce a desirable course of action about him committing) to anything he must to make this possible.
We can't deduce that, since there's no avenue to enforce that commitment. Surely he'd like there to be one, but the way the problem is set up, there's nothing stopping him from 'betraying' and just taking 1000 gold.