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Effectiveness of conditional punishment for the evolution of public cooperation
Open accessAbstract
Collective actions, from city marathons to labor strikes, are often mass-driven and subject to the snowball effect. Motivated by this, we study evolutionary advantages of conditional punishment in the spatial public goods game. Unlike unconditional punishers who always impose the same fines on defectors, conditional punishers do so proportionally with the number of other punishers in the group. Phase diagrams in dependence on the punishment fine and cost reveal that the two types of punishers cannot coexist. Spontaneous coarsening of the two strategies leads to an indirect territorial competition with the defectors, which is won by unconditional punishers only if the sanctioning is inexpensive. Otherwise conditional punishers are the victors of the indirect competition, indicating that under more realistic conditions they are indeed the more effective strategy. Both continuous and discontinuous phase transitions as well as tricritical points characterize the complex evolutionary dynamics, which is due to multipoint interactions that are introduced by conditional punishment. We propose indirect territorial competition as a generally applicable mechanism relying on pattern formation, by means of which spatial structure can be utilized by seemingly subordinate strategies to avoid evolutionary extinction.
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“However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy.”
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“Unfortunately, numerous studies have shown that punishment-based mechanisms only solve the free-rider problem under restrictive conditions34–38.”
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“Specifically, pool punishment is ineffective when the cost of maintaining central authority outweighs the benefits of cooperation.”
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Cites
Hardin, G. (1968) · Science · doi:10.1126/science.162.3859.1243 · Cited by 25,167
Hardin, G. (2009) · Journal of Natural Resources Policy Research · doi:10.1080/19390450903037302 · Cited by 6,461
Altruistic punishment in humans
Fehr, E., & Gächter, S. (2002) · Nature · doi:10.1038/415137a · Cited by 5,616
Evolutionary games and spatial chaos
Nowak, M. A., & May, R. M. (1992) · Nature · doi:10.1038/359826a0 · Cited by 4,445
House, D., & Keyser, J. C. (2016) · A K Peters/CRC Press eBooks · doi:10.1201/9781315373140-16 · Cited by 3,332
Szabó, G., & Fáth, G. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.004 · Cited by 2,976
Liggett, T. M. (1985) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4613-8542-4 · Cited by 2,935
(2011) · Springer eBooks · doi:10.1007/springerreference_60360 · Cited by 2,894
Antisocial Punishment Across Societies
Herrmann, B., Thöni, C., & Gächter, S. (2008) · Science · doi:10.1126/science.1153808 · Cited by 2,038
Coevolutionary games—A mini review
Perc, M., & Szolnoki, A. (2009) · Biosystems · doi:10.1016/j.biosystems.2009.10.003 · Cited by 1,963
Self-citation
Research works printed but not linked: 1
- Nakamaru, 2005, Evolution of altruism by costly punishment in lattice-structured population, Evol. Ecol. Res., 7, 853
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Self-citationCompetition and cooperation among different punishing strategies in the spatial public goods game
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Metadata
- Authors
- Szolnoki, A., & Perc, M.
- Affiliations
- Institute for Technical Physics and Materials Science (HU)
- University of Maribor (SI)
- Corresponding author
- Szolnoki, Attila
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2013-05
- Volume
- 325
- Pages
- 34-41
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2100165388
- Cited by
- 173
- References
- 91
- Citations by year
- 2026: 13 · 2025: 16 · 2024: 15 · 2023: 13 · 2022: 13 · 2021: 10 · 2020: 5 · 2019: 16 · 2018: 17 · 2017: 14 · 2016: 12 · 2015: 11 · 2014: 10 · 2013: 8
- FWCI
- 42.18
- Type
- journal article
- Language
- en
- Open access
- green
- real.mtak.hu
- Licence
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion, other-oa)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Experimental Behavioral Economics Studies
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Keywords
- public goods game, evolution of cooperation, spatial games, phase transitions, tricritical point, pattern formation, collective action, coexistence of strategies
- MeSH terms
- Cooperative Behavior, Biological Evolution, Game Theory, Humans, Models, Genetic, Models, Psychological, Punishment, Social Justice
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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