Zealous cooperation does not always promote cooperation in public goods games

There is a conventional belief that prosocial behaviors cannot arise through selfish human nature, because defection always exploits cooperation to achieve a higher payoff at an individual level. Unyieldingly, some people hope to move society to cooperation through their zealous cooperation, regardless of payoffs. From the perspective of spatial evolutionary games, however, such zealous behavior is unnecessary because cooperation can emerge from selfish human nature by aggregating in evolution. Yet, to what extent can zealous cooperation induce others to cooperate? We assume a fraction of zealous agents in spatial public goods games who always cooperate. The results show that a moderate proportion of these zealous cooperators can diminish the cooperation level in the system, and cooperation is only promoted when zealots are many. Regarding spatial behaviors, the areas of zealous cooperation in a medium density can prevent evolutionary cooperation from passing through and aggregating. The phenomenon of zealous cooperation impeding cooperation becomes more pronounced when agents become less random and more selfish. This is because dotted zealous cooperation provides significant payoffs to neighboring defection, making them more solid in fitness. In this way, we also find that when zealous cooperators have low productivity, the neighbors receive fewer benefits by exploitation, thus allowing cooperation to spread. We also study replicator dynamics in unstructured populations where zealous cooperation always promotes cooperation, agreeing that zealous cooperation hindering cooperation is a spatial effect.