Minority control maximizes cumulative cooperation

Abstract Designing incentives that promote cooperation is a central problem in public policy. Such incentives are typically evaluated by the stable cooperation level, which implicitly assumes that they last forever. In practice, incentives are costly and must end, after which the cooperation they built may erode. Since cooperation counts for as long as it lasts, a more practically relevant question is how to spend a limited budget to maximize the cooperation accumulated over the evolutionary process. Here, we develop a framework for maximizing cumulative cooperation in evolving populations through rewards or punishments. For general social dilemmas, including the prisoner’s dilemma, snowdrift game, and stag-hunt game, we show that reaching a target state at minimum cumulative cost follows a minority-control principle: reward minority cooperators or punish minority defectors. Furthermore, under a fixed control budget, to maximize the cumulative cooperation, the optimal strategy is to apply this principle to drive the population to a desired state, then maintain that state until the budget is exhausted, and finally allow natural evolution. Our results shift the focus from maximizing cooperation at a single time point to maximizing cooperation accumulated over time.