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You keep saying "change their vote to no". Perhaps it would be educational why you think they should default to "yes" in the first place when offered 0 coins. I
by kmonad 11y ago
You keep saying "change their vote to no". Perhaps it would be educational why you think they should default to "yes" in the first place when offered 0 coins. It really doesn't seem that the problem you see necessarily arises from this specific set of rules for this game. Offered 0 --> vote no; no would at worst be equal and at best be better than yes.
- lmm 11y agoThe point is that everyone voting yes is a possible equilibrium solution (along with the "normal" solution), so a priori there's no rule that tells you which one is the equilibrium the pirates would reach.
- sago 11y agoNo, the point being made is there is no 'equilibrium' because the game is not repeated. Equilibrium meaning 'if everyone votes this way, there is no benefit for any individual to vote differently' - that doesn't apply when the pirates are trying to determine what to vote for the one and only time they'll ever vote on this question, not knowing what anyone else will be voting.
- cousin_it 11y agoThe idea of Nash equilibrium isn't just for repeated games, in fact it was invented for one-shot games. (Now I understand why you keep mentioning "infinite games"...)
- sago 11y agoIt isn't, but it requires knowledge of the other strategies: there is at least a 'starting' strategy. That isn't the case here. Which is why you've been unable to express your disagreement with the puzzle without resorting to language of 'changing' votes, or assuming that you know what other people are going to vote. None of which are reasonable assumptions here.
- kmonad 11y agoOk, I guess I need to understand how this is an equilibrium and read more carefully what the rules of this game are exactly. Because from reading it once I understood that pirates are supposed to decide on a proposed distribution. And according to my understanding, a pirate would never vote YES if offered 0. Therefore, I seem to not see how the situation we are discussing is a viable equilibrium. (I do see how once in this "state" unilateral change of votes means no advantage to any one player, but is this really interesting for this game, i.e. is it a viable outcome of it despite being stable once reached? Maybe I have it all wrong though.)
- lmm 11y ago> I do see how once in this "state" unilateral change of votes means no advantage to any one player Right, so it meets the definition of an equilibrium. > but is this really interesting for this game, i.e. is it a viable outcome of it despite being stable once reached? In "reality" no. But the Nash Equilibrium formalism gives us no way of determining which of the two possible equilibria (this one and the usual solution) will happen in practice. So you need some more powerful idea to solve that (see references to "superrationality" and "trembling hand" elsewhere in this thread), and none of those theories is mathematically complete.
- the_af 11y ago> And according to my understanding, a pirate would never vote YES if offered 0. A pirate will vote YES if offered 0 when the alternative is getting killed in one of the following turns. Pirates always prefer to live first, and only then they prefer to maximize their money.