Experiments with real people show the same thing. One study, reported in 2005, tested college students on a contrived version of the public goods game. Four players were each given tokens (representing money) and told they could contribute as many as they liked into a “public pot,” keeping the rest in their personal account. The experimenter then doubled the number of tokens in the pot. One player at a time was told how much had been contributed to the pot and then given a chance to change his or her contribution. When the game ended (after a random number of rounds), all the tokens were then evenly divided up among all the players.

How would you play? Since, in the end, all four players split the pot equally, the people who put in the least to begin with end up with the most tokens—their share of the pot plus the money they held back in their personal account. Of course, if nobody put any in to begin with, nobody reaped the benefit of the experimenter’s largesse, kind of like a local government forgoing federal matching funds for a highway project. So it would seem to be a good strategy to donate something to the pot. But if you want to get a better payoff than anyone else, you should put in less than the others. Maybe one token. On the other hand, everybody in the group will get more if you put more in the pot to begin with. (That way, you might not get more than everybody else, but you’ll get more than you otherwise would.)

When groups of four played this game repeatedly, a pattern of behavior emerged. Players fell into three readily identifiable groups: cooperators, defectors (or “free riders”), and reciprocators. Since all the players learned at some point how much had been contributed, they could adjust their behavior accordingly. Some players remained stingy (defectors), some continued to contribute generously (cooperators), and others contributed more if others in the group had donated significantly (reciprocators).

Over time, the members of each group earned equal amounts of money, suggesting that something like a Nash equilibrium had been achieved—they all won as much as they could, given the strategy of the others. In other words, in this kind of game, the human race plays a mixed strategy—about 13 percent cooperators,

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