Seven rules to avoid the tragedy of the commons

Cooperation among self-interested players in a social dilemma is fragile and easily interrupted by mistakes. In this work, we study the repeated $n$-person public-goods game and search for a strategy that forms a cooperative Nash equilibrium in the presence of implementation error with a guarantee that the resulting payoff will be no less than any of the co-players'. By enumerating strategic possibilities for $n=3$, we show that such a strategy indeed exists when its memory length $m$ equals three. It means that a deterministic strategy can be publicly employed to stabilize cooperation against error with avoiding the risk of being exploited. We furthermore show that, for general $n$-person public-goods game, $m \geq n$ is necessary to satisfy the above criteria.