The Big Problem with the Ultimatum Game
By David Henderson
I’m enjoying some reading for a conference I’m going to later this week. Two of the readings are by Matt Ridley. I loved the first; I don’t love the second. Here’s a quote about the Ultimatum Game from the second reading, Chapter 3 of The Rational Optimist:
The first player is given some money and told to divide it with the second player. The second player is told he can accept or refuse the offer, but not change it. If he accepts, he receives the money; if he refuses, neither he nor the first player gets a penny. The question is, how much money should the first player offer the second player? Rationally, he should tender almost nothing, and the second player should accept it, because however small the sum, refusal will only make the second player worse off than acceptance. But in practice, people usually offer close to half the money. Generosity seems to come naturally, or rather, ungenerous behaviour is irrationally foolish, because the second player will–and does–consider a derisory offer worth rejecting, if only to punish the selfishness of the first player.
When I first read of these kinds of results more than a decade ago, it warmed the cockles of my heart. But then I read Steven Landsburg’s fundamental critique. I posted about it here. Nothing I have seen since has answered that critique.
Here’s the critique, in my words. The experimenters seem to think there are only 2 parties with wealth at stake: the first player and the second player. But this game does not create wealth. It redistributes wealth from the experimenters to the players. The overall game, ignoring the cost of time, is zero-sum, no matter what Player 1 and Player 2 choose.
You could argue that, of course, neither player will take account of this loss to the experimenters. They can tell themselves that the experimenters want to spend this money so that it’s not really a loss. Ok, but even if that’s true, here’s the problem with that. Presumably the experimenters have a fixed budget. When they run out, the experiment stops. If the players in a particular round act so that neither gets any money, this leaves more money for future players. So somehow we’re supposed to think that people are considerate of the stranger they’re playing with but not of other strangers. Maybe that’s true. But then it certainly doesn’t imply what the experimenters say it implies. It suggests that the players focus on who’s playing with them and don’t care about anyone else.
And if we’re supposed to assume that the players don’t think about where the wealth comes from, then that means we’re supposed to assume that the players think there’s a free lunch. That’s hardly grounds for optimism.
Fortunately, the rest of Ridley’s chapter has actual examples of people in the real world cooperating with strangers to create wealth, not just redistribute it.
UPDATE: Here’s a link to one of the Landsburg pieces.