The leading eight: Social norms that can maintain cooperation by indirect reciprocity
Abstract
The theory of indirect reciprocation explains the evolution of cooperation among unrelated individuals, engaging in one-shot interaction. Using reputation, a player acquires information on who are worth cooperating and who are not. In a previous paper, we formalized the reputation dynamics, a rule to assign a binary reputation (good or bad) to each player when his action, his current reputation, and the opponent's reputation are given. We then examined all the possible reputation dynamics, and found that there exist only eight reputation dynamics named "leading eight" that can maintain the ESS with a high level of cooperation, even if errors are included in executing intended cooperation and in reporting the observation to the public. In this paper, we study the nature of these successful social norms. First, we characterize the role of each pivot of the reputation dynamics common to all of the leading eight. We conclude that keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving. Second, we prove the two basic properties of the leading eight, which give a quantitative evaluation of the ESS condition and the level of cooperation maintained at the ESS.
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If players occasionally fail to cooperate although their strategy prescribes it, the situation is altered significantly.
“The situation is altered in a significant way if players occasionally fail to cooperate although their strategy prescribes it 39,49-52 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [49]
In a population consisting entirely of discriminators, undiscriminating co-operators fare just as well and thus spread by neutral drift.
“In a population consisting entirely of discriminators, undiscriminating co-operators fare just as well and thus spread by neutral drift.”
From Evolution of indirect reciprocity (2005) · cites this paper as [49]
If the frequency of undiscriminating co-operators exceeds a certain threshold, defectors can invade and take over.
“If their frequency exceeds a certain threshold, defectors can invade and take over.”
From Evolution of indirect reciprocity (2005) · cites this paper as [49]
In this scenario (occasional failure), a population consisting only of conditional and unconditional altruists is not subject to random drift, but selection leads to a well defined, stable mix of the two types.
“In this scenario, a population consisting only of conditional and unconditional altruists is not subject to random drift, but selection leads to a well defined, stable mix of the two types.”
From Evolution of indirect reciprocity (2005) · cites this paper as [49]
The very fact that individuals are not perfect and sometimes defect involuntarily promotes the stability of cooperation.
“In this case, the very fact that individuals are not perfect and sometimes defect involuntarily promotes the stability of cooperation 49 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [49]
Cites
Fehr, E., & Fischbacher, U. (2003) · Nature · doi:10.1038/nature02043 · Cited by 3,475 · cited 1× · see citing works
“Indirect reciprocity is one of the major driving forces of the evolution of cooperation in humans (Fehr and Fischbacher, 2003).”
BackgroundIndirect reciprocity can stabilize cooperation without the second-order free rider problem
Panchanathan, K., & Boyd, R. (2004) · Nature · doi:10.1038/nature02978 · Cited by 881 · see citing works
Evolution of cooperation through indirect reciprocity
Leimar, O., & Hammerstein, P. (2001) · Proceedings of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rspb.2000.1573 · Cited by 673 · see citing works
A tale of two defectors: the importance of standing for evolution of indirect reciprocity
Panchanathan, K., & Boyd, R. (2003) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(03)00154-1 · Cited by 388 · see citing works
Cooperation among strangers with limited information about reputation
Bolton, G. E., Katok, E., & Ockenfels, A. (2005) · Journal of Public Economics · doi:10.1016/j.jpubeco.2004.03.008 · Cited by 305 · see citing works
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Evolution of indirect reciprocity
Nowak, M. A., & Sigmund, K. (2005) · Nature · doi:10.1038/nature04131 · Cited by 2,762 · see citing works
Reputation-based partner choice promotes cooperation in social networks
Fu, F., Hauert, C., Nowak, M. A., & Wang, L. (2008) · Physical Review E · doi:10.1103/physreve.78.026117 · Cited by 682 · see citing works
Evolution of cooperation in stochastic games
Hilbe, C., Šimsa, Š., Chatterjee, K., & Nowak, M. A. (2018) · Nature · doi:10.1038/s41586-018-0277-x · Cited by 277 · see citing works
Multiple gossip statements and their effect on reputation and trustworthiness
Sommerfeld, R. D., Krambeck, H.-J., & Milinski, M. (2008) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2008.0762 · Cited by 158 · see citing works
Networks of reliable reputations and cooperation: a review
Takács, K., Gross, J., Testori, M., Letina, S., Kenny, A. R., Power, E. A., & Wittek, R. P. M. (2021) · Philosophical Transactions of the Royal Society B · doi:10.1098/rstb.2020.0297 · Cited by 61 · see citing works
Indirect Reciprocity and the Evolution of Prejudicial Groups
Whitaker, R. M., Colombo, G. B., & Rand, D. G. (2018) · Scientific Reports · doi:10.1038/s41598-018-31363-z · Cited by 33 · see citing works
- Authors
- Ohtsuki, H., & Iwasa, Y.
- Affiliations
- Kyushu University (JP)
- Corresponding author
- Ohtsuki, Hisashi
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2006-04
- Volume
- 239
- Issue
- 4
- Pages
- 435-444
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2063832007
- Cited by
- 491
- References
- 5
- Citations by year
- 2026: 29 · 2025: 36 · 2024: 60 · 2023: 39 · 2022: 29 · 2021: 41 · 2020: 22 · 2019: 23 · 2018: 26 · 2017: 13 · 2016: 27 · 2015: 16 · 2014: 20 · 2013: 17 · 2012: 18
- FWCI
- 37.67
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Keywords
- indirect reciprocity, evolution of cooperation, reputation dynamics, social norms, evolutionarily stable strategy, punishment, retaliation, forgiveness, one-shot interactions, unrelated individuals
- MeSH terms
- Cooperative Behavior, Biological Evolution, Game Theory, Humans, Models, Psychological, Punishment, Social Conformity, Social Desirability, Social Values
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