Evolutionary cycles of cooperation and defection
Open accessAbstract
The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's dilemma: always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT). We study mutation-selection dynamics in finite populations. Despite ALLD being the only strict Nash equilibrium, we observe evolutionary oscillations among all three strategies. The population cycles from ALLD to TFT to ALLC and back to ALLD. Most surprisingly, the time average of these oscillations can be entirely concentrated on TFT. In contrast to the classical expectation, which is informed by deterministic evolutionary game theory of infinitely large populations, stochastic evolution of finite populations need not choose the strict Nash equilibrium and can therefore favor cooperation over defection.
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- Authors
- Imhof, L. A., Fudenberg, D., & Nowak, M. A.
- Affiliations
- University of Bonn (DE)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2005-07-25
- Volume
- 102
- Issue
- 31
- Pages
- 10797-10800
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC1182423
- OpenAlex
- W2122801036
- Cited by
- 381
- References
- 1
- Citations by year
- 2026: 19 · 2025: 15 · 2024: 16 · 2023: 17 · 2022: 18 · 2021: 26 · 2020: 17 · 2019: 13 · 2018: 16 · 2017: 16 · 2016: 21 · 2015: 17 · 2014: 23 · 2013: 21 · 2012: 25
- FWCI
- 46.17
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- 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 › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Keywords
- evolution of cooperation, iterated prisoner's dilemma, tit-for-tat, finite population, stochastic evolutionary dynamics, strict Nash equilibrium, time averages
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