Evolution of cooperation through indirect reciprocity
Open accessAbstract
How can cooperation through indirect reciprocity evolve and what would it be like? This problem has previously been studied by simulating evolution in a small group of interacting individuals, assuming no gene flow between groups. In these simulations, certain 'image scoring' strategies were found to be the most successful. However, analytical arguments show that it would not be in an individual's interest to use these strategies. Starting with this puzzle, we investigate indirect reciprocity in simulations based on an island model. This has an advantage in that the role of genetic drift can be examined. Our results show that the image scoring strategies depend on very strong drift or a very small cost of giving help. As soon as these factors are absent, selection eliminates image scoring. We also consider other possibilities for the evolution of indirect reciprocity. In particular, we find that the strategy of aiming for 'good standing' has superior properties. It can be an evolutionarily stable strategy and, even if not, it usually beats image scoring. Furthermore, by introducing quality variation among individuals into the model, we show that the standing strategy can be quality revealing, adding a new dimension to indirect reciprocity. Finally, we discuss general problems with currently popular modelling styles.
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In a population of discriminators, unconditional cooperators can increase by random drift and eventually invite the invasion of defectors.
“In a population of discriminators, unconditional cooperators can increase by random drift and eventually invite the invasion of defectors.”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
The cooperative outcome in the indirect reciprocity model lacks stability.
“The second issue concerns the lack of stability of the cooperative outcome.”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
The simulations display occasional bursts of defection, which are based on a previous build-up of undiscriminating altruists.
“The simulations display occasional bursts of defection, which are based on a previous build-up of undiscriminating altruists.”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
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 [39]
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 [39]
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 [39]
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 [39]
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 [39]
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 [39]
A more sophisticated assessment rule should distinguish between justified and unjustified defection, taking into account the score of the receiver.
“A more sophisticated assessment rule should distinguish between justified and unjustified defection, and thus take into account the score of the receiver: someone withholding help from a 'bad' player should not pay with a reduced score 35,38,39,47 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
This mixture can be vulnerable to the invasion of defectors.
“This mixture can be vulnerable to the invasion of defectors 39,40 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
If the discriminating strategy distinguishes between justified and unjustified defection, the population can converge to discriminators only, which cannot be invaded by unconditional strategies.
“Alternatively, if the discriminating strategy distinguishes between justified and unjustified defection, the population can converge to discriminators only, which cannot be invaded by unconditional strategies 39 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
The concept of justified defection requires information about the past of the co-player, the co-player's co-players, and their co-players etc.
“The problem with the concept of justified defection, however, is that it requires information, not only about the past of the co-player, but also the past of the co-player's co-players, and their co-players etc 35,39 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [39]
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- Authors
- Leimar, O., & Hammerstein, P.
- Affiliations
- Stockholm University (SE)
- Humboldt-Universität zu Berlin (DE)
- Corresponding author
- Leimar, Olof
- Venue
- Proceedings of the Royal Society of London. Series B: Biological Sciences
- Publisher
- The Royal Society
- Published
- 2001-04-07
- Volume
- 268
- Issue
- 1468
- Pages
- 745-753
- ISSN
- 0080-4649 (ISSN-L)
- 0962-8452
- 1471-2954
- OpenAlex
- W1996254446
- Cited by
- 673
- References
- 24
- Citations by year
- 2026: 21 · 2025: 27 · 2024: 35 · 2023: 31 · 2022: 26 · 2021: 39 · 2020: 33 · 2019: 38 · 2018: 22 · 2017: 26 · 2016: 26 · 2015: 24 · 2014: 37 · 2013: 27 · 2012: 19
- FWCI
- 64.51
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Proceedings of the Royal Society B Biological Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Evolutionary Psychology and Human Behavior
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Animal Behavior and Reproduction
- Keywords
- indirect reciprocity, evolution of cooperation, image scoring, island model, genetic drift, evolutionarily stable strategy, cost of helping, quality variation, gene flow
- MeSH terms
- Animals, Behavior, Animal, Cooperative Behavior, Biological Evolution, Hierarchy, Social, Models, Biological
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