The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment
Open accessAbstract
The public goods game is a multiplayer version of the prisoner’s dilemma game. In the public goods game, punishment on defectors is necessary to encourage cooperation. There are two types of punishment: peer punishment and pool punishment. Comparing pool punishment with peer punishment, pool punishment is disadvantageous in comparison with peer punishment because pool punishment incurs fixed costs especially if second-order free riders (those who invest in public goods but do not punish defectors) are not punished. In order to eliminate such a flaw of pool punishment, this study proposes the probabilistic pool punishment proportional to the difference of payoff. In the proposed pool punishment, each punisher pays the cost to the punishment pool with the probability proportional to the difference of payoff between his/her payoff and the average payoff of his/her opponents. Comparing the proposed pool punishment with previous pool and peer punishment, in pool punishment of previous studies, cooperators who do not punish defectors become dominant instead of pool punishers with fixed costs. However, in the proposed pool punishment, more punishers and less cooperators coexist, and such state is more robust against the invasion of defectors due to mutation than those of previous pool and peer punishment. The average payoff is also comparable to peer punishment of previous studies.
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Pool 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 [38]
The Model and Discussion (page unavailable) say conventional pool punishment incurs fixed costs and can lose out to cooperators who do not pay them. They do not establish the claimed threshold—that pool punishment becomes ineffective specifically when the cost of maintaining central authority outweighs the benefits of cooperation. (LLM, conf=0.82)
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 [38]
The Introduction (page unavailable) reports that punishment no longer increases cooperation in a public-goods model with the full set of punishment strategies, including antisocial punishment. It does not say that altruistic punishment is ineffective when social interactions are noisy; searches for noisy interactions and counter-punishment found no such condition. (LLM, conf=0.78)
Experimental — accuracy not yet measuredAltruistic 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 [38]
The Introduction (page unavailable) reports a model in which punishment no longer increases cooperation when the full set of punishment strategies, including antisocial punishment, is available. That lends limited support to the counter-punishment point, but the paper does not establish that altruistic punishment is generally ineffective whenever counter-punishments are possible. The cited passages also do not support the sentence’s claim about noisy social interactions. (LLM, conf=0.78)
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 [38]
The Introduction (page unavailable) describes conditions under which particular punishment approaches sustain cooperation, including a limit on pool punishment when second-order free riders are not adequately sanctioned. That supports the claim that punishment can depend on restrictive conditions, but the paper does not establish that punishment-based mechanisms *only* solve the free-rider problem under such conditions in general. (LLM, conf=0.82)
Experimental — accuracy not yet measured
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Cooperation without punishment
Battu, B., & Rahwan, T. (2023) · Scientific Reports · doi:10.1038/s41598-023-28372-y · Cited by 12 · see citing works
- Authors
- Ohdaira, T.
- Affiliations
- Aoyama Gakuin University (JP)
- Corresponding author
- Ohdaira, Tetsushi
- ORCID
- Ohdaira, Tetsushi
- Venue
- Scientific Reports
- Published
- 2022-04-22
- Volume
- 12
- Issue
- 1
- Pages
- 6604-6604
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC9033862
- OpenAlex
- W4224279262
- Cited by
- 25
- References
- 52
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 5 · 2023: 8 · 2022: 4
- FWCI
- 7.91
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- MEXT | Japan Society for the Promotion of Science (JP17K18074, JP20K11959)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Keywords
- public goods game, peer punishment, cooperation, free-riding, evolutionary game theory, evolutionary stability, prisoner's dilemma
- MeSH terms
- Prisoner Dilemma, Cooperative Behavior, Female, Game Theory, Humans, Male, Peer Group, Punishment
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