I've written previously about ultimatum games, and they continue to interest me. See the link for a more extensive background, but essentially the game is this: Player A decides how to split a certain amount of money, and Player B can either accept or reject this split; if he rejects, neither player gets anything.
Does the amount of money at stake matter? Perhaps the B's are violating their economic (or at least monetary) self interest by rejecting low offers (i.e., taking nothing instead of something) because the gratifying feeling of implementing justice or revenge is worth sacrificing $4. Various studies have shown that the stakes do not affect the outcomes; the chances of a 60-40 split (or any other) being accepted was about the same under various payout purses and in various cultures. At the extreme, a 1999 study called "Raising the Stakes of the Ultimate Game: Experimental Evidence from Indonesia" (PDF) ran the ultimatum game with an amount of money equal to three months' pay in Indonesia and found similar results.
While many economists will no doubt disagree with me, I can't help but think that these results would not hold if gargantuan amounts of money were at stake. I believe that there is a certain amount of money at which almost no Player B would reject an offer, no matter how "unfair" it is in comparison to A's windfall. Assuming that you are not already fabulously wealthy, would you turn down $1 million because your Player A kept $9 million for himself? Would sacrificing such a lavish lifestyle really be worth it to prove your point?
The trouble is, such an experiment could never been run, as no one would be willing or able to fund it. I believe that an amount of money that sets someone for life would make people behave far differently than they would with a few months' pay.
However, I wonder is this is all a moot point. Imagine you are Player A in such a game. You can be pretty sure than an even split will be accepted, but there's an ever-so-small chance that a lesser offer may be rejected, even if only for the most wildly irrational reasons. The expected value (the sum of all possible payouts multiplied by their probabilities of occurring) of keeping a few extra million for yourself is higher than an even split because of how extremely unlikely it is for your partner to walk away from a million dollars. But most people (including myself) would be sufficiently risk averse as to err on the side of caution and offer a 50-50 split.
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