Heterogeneity Stabilizes Reciprocal Altruism Interactions
Abstract
In considering the phenomena of reciprocal altruism few would dispute that there are differences in individual quality-in particular, that for some individuals, at least on occasion, the cost of doing favors will exceed the potential of future benefits. That is, at any given time, a typical population is heterogeneous with respect to the affordability of reciprocal altruism. However, methodological limitations of the traditional analytical framework-Single Type (symmetric) Evolutionary Game Theory-have restricted previous analytical efforts to addressing populations idealized in terms of their averages. Here we use the methods of Multitype Evolutionary Game Theory to analyse the role of individual differences in direct reciprocity interactions. Multitype analysis shows that non-idealized populations possess an ESS profile wherein individuals who cannot afford reciprocity (low-quality) defect, while individuals who derive net benefits from reciprocity (high-quality) cooperate. Furthermore, this cooperation is implemented via unmodified tit-for-tat (TfT) strategy. Hence, our results may help resolve a long-standing problem concerning the evolutionary stability of TfT in direct reciprocal altruism. Finally, this difference between idealized and real populations is not restricted to direct reciprocal cooperation. Previously (Lotem et al., 1999) we have demonstrated evolutionarily stable indirect reciprocal cooperation among high-quality individuals in heterogeneous populations.
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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 [52]
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 [52]
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 [52]
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 [52]
Various assumptions on the distribution of the number of rounds lead to a bi-stable system, where depending on the initial state, the population converges either to the fixation of defectors, or to a stable mix of altruists which cannot be invaded by defectors.
“Various assumptions on the distribution of the number of rounds lead to a bi-stable system, where depending on the initial state, the population converges either to the fixation of defectors, or to a stable mix of altruists which cannot be invaded by defectors 52,53 .”
From Evolution of indirect reciprocity (2005) · cites this paper as [52]
Cited by
Sorted by citations
Evolution of indirect reciprocity
Nowak, M. A., & Sigmund, K. (2005) · Nature · doi:10.1038/nature04131 · Cited by 2,762 · see citing works
From reciprocity to unconditional altruism through signalling benefits
Lotem, A., Fishman, M. A., & Stone, L. (2003) · Proceedings of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rspb.2002.2225 · Cited by 104 · see citing works
Self-citation
- Authors
- FISHMAN, M. A., LOTEM, A., & STONE, L.
- Affiliations
- Tel Aviv University (IL)
- Corresponding author
- FISHMAN, MICHAEL A.
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2001-03
- Volume
- 209
- Issue
- 1
- Pages
- 87-95
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W1985726305
- Cited by
- 36
- References
- 0
- Citations by year
- 2023: 1 · 2022: 3 · 2021: 1 · 2019: 1 · 2018: 1 · 2015: 1 · 2013: 1 · 2012: 2
- FWCI
- 6.89
- 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 › Psychology › Experimental and Cognitive Psychology › Evolutionary Psychology and Human Behavior
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Keywords
- reciprocal altruism, direct reciprocity, individual heterogeneity, evolutionary stability, tit-for-tat, evolutionarily stable strategy, cooperation, indirect reciprocity, population heterogeneity
- MeSH terms
- Altruism, Biological Evolution, Game Theory, Humans, Models, Psychological, Genetic Variation
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