Put people in a repeated public-goods game and contributions start high, then slide toward zero as the cooperative give up on the free-riders. Give them a way to punish, even at a cost to themselves, and cooperation springs back to life.
Cooperation and punishment
The commons lesson predicted zero contribution. Real groups start out generous, then unravel, exactly as free-riding erodes trust. The twist experiments reveal: let players pay to punish free-riders, and cooperation climbs back up, even though punishing is individually costly.
In the public-goods game, the selfish contribution is...
A conditional cooperator contributes...
Predict, then play
Four players contribute to a shared pot. One starts as a free-rider. First play without punishment. Then enable it, choose how many costly punishment points to buy, and compare your payoff with the free-rider’s.
Why did that happen?
Take a guess, then reveal the reason
Most people are conditional cooperators: they give if others do. A few free-ride, and each round the cooperators see themselves exploited and lower their giving to match, so contributions spiral down. Punishment breaks the spiral. Even though paying to dock a free-rider costs you and helps everyone (a second-order public good), enough people do it out of a taste for fairness that free-riding stops paying. Contributions recover, sustained by a threat that standard self-interest says no one should carry out.
The math
The stage game is the usual linear public good: with , endowment , and multiplier , the marginal per-capita return is , so contributing $1 returns only $0.40 to you. The dominant contribution is , yet all contributing fully would give each $32 versus $20 from hoarding, since the total return on each dollar, , exceeds .
Experimentally, contributions start around 40 to 60 percent of the endowment and decay over repeated rounds without punishment, as conditional cooperators withdraw in response to free-riders. Adding a costly punishment stage (pay to reduce a free-rider’s payoff by ) reverses the decay: contributions rise and stay high. Punishing is itself a public good (it benefits everyone but costs the punisher), so pure self-interest predicts no punishment; that people punish anyway is the behavioral finding.
The standard theory has two failures here: it predicts zero contribution from the start (real groups begin generous) and no punishment (real people punish). Both gaps are explained by social preferences: conditional cooperation and a willingness to sacrifice to enforce fairness.
Work it out
Why punishment sustains giving
Contributing $1 grows the pot by $1.60, split four ways, so $0.40 comes back to you: a private loss of $0.60, and the money-maximizing choice is $0. Without enforcement, conditional cooperators watch the free-rider keep everything and cut their own giving to avoid being suckers, and contributions decay toward zero.
Now let a player pay $1 to cut a free-rider’s payoff by $3. The game shows both sides of that transaction: the punisher’s payoff falls by the amount spent and the target’s falls three times as much. Its bot then raises next-round contribution by a disclosed response rule. That response illustrates the experimental pattern; it is not derived as a Nash equilibrium of the stage game.
Key idea
Without enforcement, cooperation in a public good decays as free-riders erode trust. Costly punishment, which self-interest says no one should undertake, revives and sustains contributions in real groups.
Check yourself
Sources
- Fehr, E., and Gächter, S. (2000). Cooperation and punishment in public goods experiments. American Economic Review, 90(4), 980-994.