Fehr and Gächter's Four-Person Groups Paid to Punish Free Riders, and Contributions Held

In 1979, during the oil crisis, long queues formed at American gas stations. Some drivers tried to cut in. In the words of a passage the paper takes from Robert Frank’s 1994 book, many motorists got into “fistfights and shouting matches,” and “one motorist was shot and killed for butting into line.” Fehr and Gächter read that kind of episode as punishment with no future payoff, since a queue is likely to be a one-off meeting, and they built an experiment around the idea that people punish free riders even when punishing costs them and pays them nothing.

Their paper, “Cooperation and Punishment in Public Goods Experiments” (American Economic Review, September 2000), gives the lab version. When group members could pay to reduce each other’s earnings, cooperation held up. When they could not, it fell apart. In the Stranger version’s final period, average contributions were 1.3 to 2.3 tokens of 20 without punishment and 9.8 to 14.3 with it, six to seven and a half times higher. In the Partner version, 82.5% of subjects gave their whole endowment in the final period of the punishment condition, while 53% of the same subjects gave nothing in the final period of the no-punishment condition. Figures in this piece come from the January 1999 working-paper version.

The game: four people, 20 tokens each

Each round, four people each get 20 tokens. Each can keep tokens or put them in a shared project. Every token in the project pays 0.4 tokens to each of the four players, whoever put it in.

The arithmetic makes the temptation plain. A token kept is worth 1. A token invested returns 0.4 to its owner and 0.4 to each of the other three, so the owner loses 0.6 and the group gains 1.6. If all four invest everything, the project holds 80 tokens and each player collects 0.4 × 80 = 32. If all four keep everything, each has 20. If three invest everything and one keeps their 20, the three earn 24 each (0.4 × 60) and the free rider earns 20 + 24 = 44.

That last case is the one the experiment is about. By standard assumptions about selfish players, keeping everything is the best move every round, whatever the others do, and the group should end up at 20 each rather than 32.

The second stage: paying to dock someone

In the punishment condition, after each round every player saw how much each of the other three had contributed. They could then assign each of them 0 to 10 punishment points. Each point cut the target’s earnings from that round by 10%. Each point had a price for the punisher, set by a table:

Points assigned	1	2	3	4	5	6	7	8	9	10
Cost to the punisher (tokens)	1	2	4	6	9	12	16	20	25	30

Take the lone free rider at 44 tokens. If each of the other three gives them 3 points, the free rider loses 90% of the round’s earnings and keeps 4.4, and each punisher pays 4. That is an illustration built from the paper’s payoff rule, not a case from the data. It shows why the first point is cheap and why a coordinated group can destroy a large gain for a small outlay.

Two details matter for what comes later. Subjects were told only the total points they received and never who had given them. And a selfish player has no reason to punish at all in a game they will not play again, because the cost comes out of their own pocket and the benefit goes to people in future rounds they will never meet. Fehr and Gächter built the Stranger treatment so that the chance of being matched with the same three people in the next round was under 0.05%. In the Partner treatment the same four played all ten rounds together.

What the groups did

Without punishment, contributions slid. Across the no-punishment conditions the paper reports that between 53% and 75% of subjects gave nothing at all in the final period, and the rest gave little.

With punishment, they did not slide. In the Stranger treatment, average contributions in the punishment condition “do not decrease or even increase over time”. In the Partner treatment, all ten groups contributed more with punishment than without (p = 0.0026, Wilcoxon matched-pairs test on group averages).

People were punished in proportion to how far they fell below the others. A Partner-treatment subject who contributed 14 to 20 tokens below the group average received, on average, 6.8 punishment points. Contributing above the average drew much less punishment and no systematic response. Close to the average, punishment dropped off sharply.

The punished changed course. In the Partner treatment there were 125 sanctions against subjects who had contributed less than their full endowment, and in 89% of them the punished subject raised their contribution in the next round, by 4.6 tokens on average. In the Stranger treatment there were 368 such cases; 78% raised their contribution, by 3.8 tokens on average.

The bill comes before the payoff

Punishment is not free for the group. Fehr and Gächter measured average group earnings with punishment relative to without it. In round one, the punishment condition cost the group roughly 40% of its earnings in both treatments, because points were being spent and earnings destroyed before anyone had changed their behavior. In the Partner treatment the group was ahead by round 4. In the Stranger treatment it took nine rounds. By the last round, the punishment condition was ahead by roughly 20% (Partner) and 10% (Stranger). For the Partner treatment the paper reports the difference in group incomes over rounds 8 to 10 as statistically significant (p < 0.029).

For free riders the news was worse. Those who contributed nothing in more than half the no-punishment rounds earned 24% less in the Stranger punishment condition and 16% less in the Partner condition, even though they raised their contributions by 10 to 12 tokens, which is 50 to 60% of their endowment.

Laid side by side, the paper’s numbers suggest three questions to ask of any group enforcement arrangement: who pays, who collects, and when. In the lab, the punishers paid first, the whole group collected later, and the free riders paid twice, through the points and through the higher contributions they were pushed into. An arrangement where the cost lands early on the enforcers and the benefit arrives rounds later can still hold, provided everyone expects it to continue. The Partner groups, who stayed together, were ahead by round 4, and the Stranger groups needed nine. The shadow of the future is one reading of that gap, though the authors do not frame it that way and five sessions are too few to separate it from other explanations. Real harbors run on the same arithmetic over longer horizons, as in the escalating warnings Maine’s lobster gangs use.

Why people punished: anger, measured elsewhere

Fehr and Gächter propose that emotions make the threat credible. Free riding makes cooperators angry, and anger makes them willing to pay. To test the idea they gave a different group of subjects hypothetical scenarios in which other people contributed more or less than the reader, and asked them to rate their negative feelings toward a target on a seven-point scale. The paper reports that negative feelings were stronger the further the target fell below the group. That evidence is separate from the main experiment: different people, imagined cases, and a rating scale in place of real money. It fits the theory without confirming that anger drove the punishment decisions in the lab.

What this does and does not say about phone-based accountability

The experiment had five sessions of at most 24 people each. The subjects were strangers, the stakes were small, and the lab setting stripped out the history that real friends carry. Nothing in it concerns alarms, mornings or phones.

What does carry over is the shape of the problem. A group goal erodes when contributing is costly and slacking is cheap, and a credible penalty can hold it up. Two cautions follow from the paper for any app built on that idea. First, penalties did their work through the person understanding that they had fallen below the group’s standard: 89% and 78% of the punished raised their next-round contribution. A penalty that arrives without a clear link to what was missed offers no such signal. Second, the penalties were costly to the people delivering them, and the paper’s theory leans on anger to explain why anyone paid.

DontSnooze takes the opposite path on both counts: its sanction is a photo sent automatically to the friends you chose, so it costs the witnesses nothing and needs no anger. That spares friendships the awkwardness the Zurich subjects tolerated, and it leaves out the thing the paper’s theory credits with making a threat believable, a person who minds. The experiment cannot say which matters more for someone trying to get up at 6:30. For people whose friends will not scold, the automatic version is a reasonable substitute; for a friend who will really call at 6:35, that call is probably stronger. An automatic sanction can also behave like the fine in the Israeli daycare study, a price people accept instead of a reproach they feel.

Frequently asked questions

Is this the same paper as Fehr and Gächter’s 2002 Nature article?

No. This post covers “Cooperation and Punishment in Public Goods Experiments”, American Economic Review 90(4), September 2000, pp. 980-994. The 2002 Nature paper, “Altruistic punishment in humans” (415, pp. 137-140), is a later experiment. The numbers here come from the January 1999 working-paper version of the AER article, so check the printed paper before quoting them.

Could people build a reputation as a punisher, or as a cooperator?

No. Each subject’s own contribution was always shown in the first column of the screen and the other three were listed in random columns, so no one could link a contribution to a particular person across rounds. Subjects also never learned who had punished them, only the total they received. A separate Perfect Stranger treatment, in which every subject met every other subject exactly once, was run as a robustness check.

How big was the evidence base?

Five sessions: three of the Stranger treatment with 24 people each, and two of the Partner treatment, one of which had only 16 participants because that many showed up. Group averages, not individuals, were the unit in the Wilcoxon tests.