ArticleScientific reports2021
Local stability of cooperation in a continuous model of indirect reciprocity.
Article in Scientific reports, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Incomplete reputation information and punishment in indirect reciprocity.Scientific reports · 2026Article
- Exact conditions for evolutionary stability in indirect reciprocity under noise.PLoS computational biology · 2025Article
- Indirect reciprocity under opinion synchronization.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Computational evolution of social norms in well-mixed and group-structured populations.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
- Indirect reciprocity with stochastic and dual reputation updates.PLoS computational biology · 2023Article
- Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Quantitative assessment can stabilize indirect reciprocity under imperfect information.Nature communications · 2023Article
- Reputation structure in indirect reciprocity under noisy and private assessment.Scientific reports · 2022Article
- Social norms in indirect reciprocity with ternary reputations.Scientific reports · 2022Article
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3 authors.
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Abstract
Reputation is a powerful mechanism to enforce cooperation among unrelated individuals through indirect reciprocity, but it suffers from disagreement originating from private assessment, noise, and incomplete information. In this work, we investigate stability of cooperation in the donation game by regarding each player's reputation and behaviour as continuous variables. Through perturbative calculation, we derive a condition that a social norm should satisfy to give penalties to its close variants, provided that everyone initially cooperates with a good reputation, and this result is supported by numerical simulation. A crucial factor of the condition is whether a well-reputed player's donation to an ill-reputed co-player is appreciated by other members of the society, and the condition can be reduced to a threshold for the benefit-cost ratio of cooperation which depends on the reputational sensitivity to a donor's behaviour as well as on the behavioural sensitivity to a recipient's reputation. Our continuum formulation suggests how indirect reciprocity can work beyond the dichotomy between good and bad even in the presence of inhomogeneity, noise, and incomplete information.
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