01 — The payoff table
Grain per season, you first. Hover the cells. Shirking beats toiling whether the village works (118 > 100) or loafs (18 > 44) — so reason says: shirk. But when every villager reasons the same way, all twelve land in the red corner. Individually rational, collectively ruinous: a textbook Nash equilibrium that feeds no one.
The commune's answer was the work point (工分): labor recorded, rations tied to effort. Points can't abolish the dilemma — but they bend the payoffs so that honest work stops being the sucker's move. Test it in the simulation.
02 — The theory
The harvest is a public good: everyone eats from it, whatever they contributed. When contribution is costly and the reward is shared, each villager's rational move is to let the others do the work. No conspiracy is needed — just arithmetic.
If you expect others to toil, shirking pays you more. If you expect them to shirk, toiling pays you even less. Shirking is a dominant strategy, so mutual shirking is the equilibrium — stable, predictable, and starving.
The work point (工分) rewrites the payoff table instead of preaching against it. By tying rations to recorded labor, toiling stops being the sucker's move. Don't beg people to cooperate — change what cooperation pays.
In real communes, points were awarded for presence more than output, and effort was hard to measure. When points can't see real work, the free-rider equilibrium creeps back. Measurement, it turns out, is the whole game.