Two gardeners haggle over water from a magical well. One proposes how many buckets to take, the other can agree or refuse. If the deal goes through, the water decreases; if not, the well gradually refills. This haggling repeats hundreds of times, and the gardeners' habits sometimes change randomly, as if they're trying new tactics.
When the water comes quickly, both soon realize: a fair split is the most profitable.
But if the spring barely trickles, disruptions start. In desperation, the gardeners tear up any agreements, and this gives the well time to recover. As soon as the level rises, spite recedes, and fairness returns.
The paradox is that it's precisely the torn-up deals, seemingly harmful behavior, that save the source from total depletion. Remarkably, if one gardener is always greedy, the other, by refusing unfair splits, inadvertently helps them both: the well doesn't run dry, and greed punishes itself.
The idea of such repeated negotiations goes back to John von Neumann, but accounting for the resource's variability flips the predictions.
In a famous experiment where one person divides a reward and the other can refuse, people often reject unfair offers, even losing their own share: this reveals an innate sense of fairness.