We both think you did wrong - How agreement shapes and is shaped by indirect reciprocity

Indirect reciprocity enables cooperation in social dilemmas. It is a reputation-based mechanism in which interactions between individuals are observed, judged and cooperation is then steered to individuals considered good but withheld from those considered bad. Research has focussed on how to avoid disagreement over who is good or bad, since such disagreement can severe problems. But only two models exist to predict such disagreement, and both are limited to highly unrealistic cases. These models assume either an observation probability close to zero or full observation at all times. The former model predicts that agreement only exists by chance, i.e. that it is as small as theoretically possible. We studied intermediate observation rates and provide two major insights. First, for all but the smallest observation rates, agreement is higher than chance, in particular for relevant indirect reciprocity strategies. Second, we introduce a new model to predict reputation and agreement that can accommodate any observation rate. This enables more realistic studies of indirect reciprocity and, in turn, a deeper understanding and practical application of this mechanism, often regarded as a foundation of human morality, in reputation-based multi-agent systems and other real-world settings.