Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment

TL;DR

This paper demonstrates that cooperation via indirect reciprocity can be evolutionarily stable under private assessment, highlighting the importance of simple social norms like Simple Standing for maintaining cooperation.

Contribution

It provides the first theoretical proof that cooperation is stable under private assessment, showing that simple norms like SS are effective while complex ones like SJ are not.

Findings

SS can be stable under private assessment

SJ cannot be stable due to error accumulation

Moderate simplicity is key to cooperation stability

Abstract

Indirect reciprocity is a mechanism that explains large-scale cooperation in humans. In indirect reciprocity, individuals use reputations to choose whether or not to cooperate with a partner and update others' reputations. A major question is how the rules to choose their actions and the rules to update reputations evolve. In the public reputation case, where all individuals share the evaluation of others, social norms called Simple Standing (SS) and Stern Judging (SJ) have been known to maintain cooperation. However, in the case of private assessment where individuals independently evaluate others, the mechanism of maintenance of cooperation is still largely unknown. This study theoretically shows for the first time that cooperation by indirect reciprocity can be evolutionarily stable under private assessment. Specifically, we find that SS can be stable, but SJ can never be. This is intuitive because SS can correct interpersonal discrepancies in reputations through its simplicity. On the other hand, SJ is too complicated to avoid an accumulation of errors, which leads to the collapse of cooperation. We conclude that moderate simplicity is a key to success in maintaining cooperation under the private assessment. Our result provides a theoretical basis for evolution of human cooperation.