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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Altruistic punishment is ineffective when counter-punishments are possible.
“However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy.”
From Cooperation without punishment (2023) · cites this paper as [34]
The Introduction (p. 1) says antisocial punishment might render sanctioning ineffective, which supports the concern behind the claim. It does not establish that punishment is ineffective whenever counter-punishment is possible; the cited passage is explicitly hedged, and the paper does not address noisy social interactions in this connection. (LLM, conf=0.83)
Experimental — accuracy not yet measuredPunishment-based mechanisms only solve the free-rider problem under restrictive conditions.
“Unfortunately, numerous studies have shown that punishment-based mechanisms only solve the free-rider problem under restrictive conditions34–38.”
From Cooperation without punishment (2023) · cites this paper as [34]
The Introduction (p. 2) says that second-order free-riders can seriously challenge sanctioning and that cooperation requires a minimum fine. The Discussion (p. 7) shows that punishment’s effectiveness depends on its cost and the fine imposed. These findings support limits on punishment, but not the broader assertion that punishment-based mechanisms solve the free-rider problem only under restrictive conditions. (LLM, conf=0.80)
Experimental — accuracy not yet measuredPool punishment is ineffective when the cost of maintaining central authority outweighs the benefits of cooperation.
“Specifically, pool punishment is ineffective when the cost of maintaining central authority outweighs the benefits of cooperation.”
From Cooperation without punishment (2023) · cites this paper as [34]
The Results (p. 7) compare the cost and effectiveness of conditional and unconditional punishment, not pool punishment. The Introduction (p. 1) mentions institutionalized punishment but does not assess the cost of maintaining central authority against the benefits of cooperation. Searches for pool punishment and that cost–benefit condition found no passage addressing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredAltruistic punishment is ineffective when social interactions are noisy.
“However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy.”
From Cooperation without punishment (2023) · cites this paper as [34]
The Introduction (p. 1) says antisocial punishment might make sanctioning ineffective, but it does not address noisy social interactions. Searches for noise, noisy interactions, and counter-punishment found no passage establishing that punishment is ineffective because interactions are noisy. (LLM, conf=0.75)
Experimental — accuracy not yet measured
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- 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 › Safety Research › 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
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