Saturday, 15 December 2007

The Ultimatum Game

Anyone with even a passing interest in popular economics has heard of the Ultimatum Game. Basically, the set-up is this: two people are picked to play the game, it is a one off, and they are assigned, at random to one of two different roles - the proposer and the responder. The proposer is given some amount of money, and told to split it however he likes. The responder is then given the choice to either accept or decline whatever they are offered. If they decline, neither player gets anything, if they accept, they both get to keep their offered amount.

Without too much analysis, it's easy to see that the only sub-game perfect Nash Equilibrium (which is a posh way of saying, the only strategy that both players can stick to if they're fully rational) is for the proposer to offer the responder 1p and the responder to accept. If you reject a "lowball offer", you lose out. But, as you might expect, people *do* reject lowball offers (I'm fairly sure I wouldn't, but I suppose it depends on just how low it was). There are several explanations for this in the literature, and I'm not about to go into any of them now, but there is one point that I came across in an article by Steven Landsburg from Reason magazine a few months ago which I want to consider.

Landsburg's article is actually in the context of the even simpler Dictator Game. This is the same set-up as above, but the responder doesn't get their turn. In other words, you're given an envelope full of money and asked how much of it you want to give to the complete stranger in the next room. There are also variations of this game in which you are told that however much you choose to give to the complete stranger in the next room, the experimenters will double/treble this - so you can give up £1 to give the stranger in the next room £3.

Landsburg makes the very valid point that the money you give to the complete stranger *has to come from somewhere*. In other words, if you do choose to give the complete stranger some of your money, this is no different to simply telling the experimenter they can keep it - no wealth is created or destroyed by playing these games, so you're just passing money between strangers either way. (Either the experimenter keeps the money, or the next person to play the game gets it, or they use it for their next experiment - whatever the scenario, the total amount of wealth in the world is the same, and anything you don't have belongs to a complete stranger).

So what about the variation of the Ultimatum Game in which wealth *is* destroyed. People are willing to pay a small fee so that a complete stranger who they feel has treated them unfairly doesn't get any money, but if they think like Steven Landsburg, they know that this money is going to some other (presumably more deserving) complete stranger. What if this wasn't the case? Was if the alternative to you getting your share and the proposer getting theirs was not that the money went back to the experimenter, but that it was actually destroyed? Would anyone turn down a lowball offer in that game? Does that game actually have any more meaning than the original ultimatum game?

Unfortunately, it's hard to construct a variation of the Dictator Game which works in the same way - perhaps there is one. If there was, if it were somehow possible to create wealth from nowhere in order to play this sort of game, do I think people would behave any differently? No, I don't. I think people in these games actually do behave as though the money they're being given is created out of thin air. As Landsburg notes, this is pretty scary - surely no educated person can believe that money does appear out of thin air - but I think it's probably true. We'll have to wait until someone cleverer than me comes up with a new experiment to test this theory. I hope someone cleverer than me is trying.

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