The Dynamics of Indirect Reciprocity
Abstract
Richard Alexander has argued that moral systems derive from indirect reciprocity. We analyse a simple case of a model of indirect reciprocity based on image scoring. Discriminators provide help to those individuals who have provided help. Even if the help is never returned by the beneficiary, or by individuals who in turn have been helped by the beneficiary, discriminating altruism can be resistant against invasion by defectors. Indiscriminate altruists can invade by random drift, however, setting up a complex dynamical system. In certain situations, defectors can invade only if their invasion attempts are sufficiently rare. We also consider a model with incomplete information and obtain conditions for the stability of altruism which differ from Hamilton's rule by simply replacing relatedness with acquaintanceship.
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All eight of these strategies distinguish justified from unjustified defections.
“All eight of these strategies distinguish justified from unjustified defections.”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
Only eight assessment rules of second and third order lead to cooperation and are evolutionarily stable.
“Only eight of them lead to cooperation and, at the same time, are evolutionarily stable: a homogeneous population of players using such a strategy cannot be invaded by players using other strategies 41 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
A simpler model based on a binary score ('good' or 'bad') was proposed.
“In order to analyse these questions, an even simpler model was proposed, based on a binary score, taking only the values 'good' or 'bad', depending on what the co-player did when last observed 39-41 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
If such a consensual assessment can be achieved, the corresponding strategy is robust.
“If such a consensual assessment can be achieved, the corresponding strategy is robust 38,39,41 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
Both STANDING and JUDGING belong to the leading eight, but neither SCORING nor SHUNNING.
“Both STANDING and JUDGING belong to the leading eight, but neither SCORING nor SHUNNING.”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
Ohtsuki & Iwasa analysed all 4096 strategies and proved that only 8 of them are evolutionarily stable under certain conditions, the so called 'leading eight'.
“In a remarkable calculation, Ohtsuki & Iwasa 41,48 analysed all 4096 strategies and proved that only 8 of them are evolutionarily stable under certain conditions, the so called 'leading eight'.”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
While language might help to compare and synchronize private reputation lists, ultimately reputation is in the eyes of the beholder.
“While language might help to compare and synchronize these lists 41 , ultimately reputation is in the eyes of the beholder.”
From Evolution of indirect reciprocity (2005) · cites this paper as [41]
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Self-citation
- Authors
- Nowak, M. A., & Sigmund, K.
- Affiliations
- Institute for Advanced Study (US)
- University of Vienna (AT)
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 1998-10
- Volume
- 194
- Issue
- 4
- Pages
- 561-574
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2065529435
- Cited by
- 607
- References
- 0
- Citations by year
- 2026: 13 · 2025: 31 · 2024: 20 · 2023: 25 · 2022: 13 · 2021: 40 · 2020: 23 · 2019: 19 · 2018: 33 · 2017: 22 · 2016: 32 · 2015: 25 · 2014: 53 · 2013: 21 · 2012: 24
- FWCI
- 20.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- IIASA PURE (International Institute of Applied Systems Analysis) (submittedVersion)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Evolutionary Psychology and Human Behavior
- Keywords
- indirect reciprocity, image scoring, moral systems, altruism, defectors, invasion dynamics, random drift, incomplete information, Hamilton's rule, relatedness, acquaintanceship, evolutionary stability
- MeSH terms
- Altruism, Biological Evolution, Humans, Models, Psychological
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