Quote from: estevo on April 21, 2011, 11:18:10 PM

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That's pretty much exactly the question. It is his to divide. That's directly stated in the OP.

He gets to propose a split, and you get the final say. That doesn't make the money his. Until the game is concluded, the money remains the Faucet's property, and neither of you have any a priori claim on it.

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There's a rational answer if you can calculate utility.

That's a tautology. Do you mean that only money needs be taken into account in order to calculate utility?

There is a strong hardwired social expectation for a fair (and I won't even use quotes here) split, and there is an emotional cost in overriding that. You can decide it's worth it, but if you just ignore this cost, you are, by definition, not being rational. And once you start factoring any non-monetary factors, the $0.01 vs $4,999.99 Nash equilibrium breaks down.

If you go to the wikipedia page for the Ultimatum Game you'll see that across cultures, almost everyone will reject any offer below some 20%-30%. So, you see, the vast majority of humanity is very "weak" of character.

This and other experiments suggests that we are hardwired to tend towards collaboration and towards punishing defectors, because it has proven evolutionarily stable.

In a real world where almost nobody will take less than 20%, is asking for $4,999 rational?

In the extreme case you were presented before, after the Splitter has killed your family, would you still accept his $10 vs $4,990? What do you mean he "deserves" revenge? That's not any more Nash-rational. What does the killing of your family have to do with the deal, at all? Is there something wrong with your character?

You are right that the majority of humans are weak. That's why we have the problems we do. It's the few strong that carry the weak.

Taking someone who has actually wronged me is much different of a case. What morally wrong act has the splitter committed in the original case?

The optimal play and the "rational" play are two different things. I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.

The interesting thing is, the natural reaction of people is fairly consistent with how one would act in real life, where you don't interact with people just once, there are repetitions to the game, and your reputation travels with you. Our minds have evolved to play the game of life fairly well without actually thinking about it, which is why most people make a lot of fundamental mistakes for toy problems.