Jul 6, 2012
The so-called “rational” solutions to the Prisoners' Dilemma and Ultimatum Game are suboptimal to say the least. Humans have various kludges added by both nature or nurture to do better, but they're not perfect and they're certainly not simple. They leave entirely open the question of what real people will actually do in these situations, a question which can only be addressed by hard data.
As in so many other areas, our most important information comes from reality television. The Art of Strategy discusses a US game show “Friend or Foe” where a team of two contestants earned money by answering trivia questions. At the end of the show, the team used a sort-of Prisoner's Dilemma to split their winnings: each team member chose “Friend” (cooperate) or “Foe” (defect). If one player cooperated and the other defected, the defector kept 100% of the pot. If both cooperated, each kept 50%. And if both defected, neither kept anything (this is a significant difference from the standard dilemma, where a player is a little better off defecting than cooperating if her opponent defects).
Players chose “Friend” about 45% of the time. Significantly, this number remained constant despite the size of the pot: they were no more likely to cooperate when splitting small amounts of money than large.
Players seemed to want to play “Friend” if and only if they expected their opponents to do so. This is not rational, but it accords with the “Tit-for-Tat” strategy hypothesized to be the evolutionary solution to Prisoner's Dilemma. This played out on the show in a surprising way: players' choices started off random, but as the show went on and contestants began participating who had seen previous episodes, they began to base their decision on observable characteristics about their opponents. For example, in the first season women cooperated more often than men, so by the second season a player was cooperating more often if their opponent was a woman - whether or not that player was a man or woman themselves.
Among the superficial characteristics used, the only one to reach statistical significance according to the study was age: players below the median age of 27 played “Foe” more often than those over it (65% vs. 39%, p < .001). Other nonsignificant tendencies were for men to defect more than women (53% vs. 46%, p=.34) and for black people to defect more than white people (58% vs. 48%, p=.33). These nonsignificant tendencies became important because the players themselves attributed significance to them: for example, by the second season women were playing “Foe” 60% of the time against men but only 45% of the time against women (p<.01) presumably because women were perceived to be more likely to play “Friend” back; also during the second season, white people would play “Foe” 75% against black people, but only 54% of the time against other white people.
(This risks self-fulfilling prophecies. If I am a black man playing a white woman, I expect she will expect me to play “Foe” against her, and she will “reciprocate” by playing “Foe” herself. Therefore, I may choose to “reciprocate” against her by playing “Foe” myself, even if I wasn't originally intending to do so, and other white women might observe this, thus creating a vicious cycle.)
In any case, these attempts at coordinated play worked, but only imperfectly. By the second season, 57% of pairs chose the same option - either (C, C) or (D, D).
Art of Strategy included another great Prisoner's Dilemma experiment. In this one, the experimenters spoiled the game: they told both players that they would be deciding simultaneously, but in fact, they let Player 1 decide first, and then secretly approached Player 2 and told her Player 1's decision, letting Player 2 consider this information when making her own choice.
Why should this be interesting? From the previous data, we know that humans play “tit-for-expected-tat”: they will generally cooperate if they believe their opponent will cooperate too. We can come up with two hypotheses to explain this behavior. First, this could be a folk version of Timeless Decision Theory or Hofstadter's superrationality; a belief that their own decision literally determines their opponent's decision. Second, it could be based on a belief in fairness: if I think my opponent cooperated, it's only decent that I do the same.
The “researchers spoil the setup” experiment can distinguish between these two hypotheses. If people believe their choice determines that of their opponent, then once they know their opponent's choice they no longer have to worry and can freely defect to maximize their own winnings. But if people want to cooperate to reward their opponent, then learning that their opponent cooperated for sure should only increase their willingness to reciprocate.
The results: If you tell the second player that the first player defected, 3% still cooperate (apparently 3% of people are Jesus). If you tell the second player that the first player cooperated.........only 16% cooperate. When the same researchers in the same lab didn't tell the second player anything, 37% cooperated.
This is a pretty resounding victory for the “folk version of superrationality” hypothesis. 21% of people wouldn't cooperate if they heard their opponent defected, wouldn't cooperate if they heard their opponent cooperated, but will cooperate if they don't know which of those two their opponent played.
Moving on to the Ultimatum Game: very broadly, the first player usually offers between 30 and 50 percent, and the second player tends to accept. If the first player offers less than about 20 percent, the second player tends to reject it.
Like the Prisoner's Dilemma, the amount of money at stake doesn't seem to matter. This is really surprising! Imagine you played an Ultimatum Game for a billion dollars. The first player proposes $990 million for herself, $10 million for you. On the one hand, this is a 99-1 split, just as unfair as $99 versus $1. On the other hand, ten million dollars!
Although tycoons have yet to donate a billion dollars to use for Ultimatum Game experiments, researchers have done the next best thing and flown out to Third World countries where even $100 can be an impressive amount of money. In games in Indonesia played for a pot containing a sixth of Indonesians' average yearly income, Indonesians still rejected unfair offers. In fact, at these levels the first player tended to propose fairer deals than at lower stakes - maybe because it would be a disaster if her offer get rejected.
It was originally believed that results in the Ultimatum Game were mostly independent of culture. Groups in the US, Israel, Japan, Eastern Europe, and Indonesia all got more or less the same results. But this elegant simplicity was, like so many other things, ruined by the Machiguenga Indians of eastern Peru. They tend to make offers around 25%, and will accept pretty much anything.
One more interesting finding: people who accept low offers in the Ultimatum Game have lower testosterone than those who reject them.
There is a certain degenerate form of the Ultimatum Game called the Dictator Game. In the Dictator Game, the second player doesn't have the option of vetoing the first player's distribution. In fact, the second player doesn't do anything at all; the first player distributes the money, both players receive the amount of money the first player decided upon, and the game ends. A perfectly selfish first player would take 100% of the money in the Dictator Game, leaving the second player with nothing.
In a metaanalysis of 129 papers consisting of over 41,000 individual games, the average amount the first player gave the second player was 28.35%. 36% of first players take everything, 17% divide the pot equally, and 5% give everything to the second player, nearly doubling our previous estimate of what percent of people are Jesus.
The meta-analysis checks many different results, most of which are insignificant, but a few stand out. Subjects playing the dictator game “against” a charity are much more generous; up to a quarter give everything. When the experimenter promises to “match” each dollar given away (eg the dictator gets $100, but if she gives it to the second player the second player gets $200), the dictator gives much more (somewhat surprising, as this might be an excuse to keep $66 for yourself and get away with it by claiming that both players still got equal money). On the other hand, if the experimenters give the second player a free $100, so that they start off richer than the dictator, the dictator compensates by not giving them nearly as much money.
Old people give more than young people, and non-students give more than students. People from “primitive” societies give more than people from more developed societies, and the more primitive the society, the stronger the effect. The most important factor, though? As always, sex. Women both give more and get more in dictator games.
It is somewhat inspiring that so many people give so much in this game, but before we become too excited about the fundamental goodness of humanity, Art of Strategy mentions a great experiment by Dana, Cain, and Dawes. The subjects were offered a choice: either play the Dictator Game with a second player for $10, or get $9 and the second subject is sent home and never even knows what the experiment is about. A third of participants took the second option.
So generosity in the Dictator Game isn't always about wanting to help other people. It seems to be about knowing, deep down, that some anonymous person who probably doesn't even know your name and who will never see you again is disappointed in you. Remove the little problem of the other person knowing what you did, and they will not only keep the money, but even be willing to pay the experiment a dollar to keep them quiet.