Indirect reciprocity is an important mechanism for promoting cooperation among self-interested agents. Simplified, it means “you help me; therefore somebody else will help you” (in contrast to direct reciprocity: “you help me; therefore I will help you”). Indirect reciprocity can be achieved via reputation and norms. Strategies, such as the so-called leading eight, relying on these principles can maintain high levels of cooperation and remain stable against invasion, even in the presence of errors. However, this is only the case if the reputation of an agent is modeled as a shared public opinion. If agents have private opinions and hence can disagree as to whether somebody is good or bad, even rare errors can cause cooperation to break apart. We show that most strategies can overcome the private assessment problem by applying pleasing. A pleasing agent acts in accordance with others' expectations of their behaviour (i.e., pleasing them) instead of being guided by their own, private assessment. As such, a pleasing agent can achieve a better reputation than previously considered strategies when there is disagreement in the population. Pleasing is effective even if the opinions of only a few other individuals are considered and when it bears additional costs. Finally, through a more exhaustive analysis of the parameter space than previous studies, we show that some of the leading eight still function under private assessment, i.e., that cooperation rates are well above an objective baseline. Yet, pleasing strategies supersede formerly described ones and enhance cooperation.

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