The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.
Probabilistic sharing solves the problem of costly punishment
Open accessAbstract
Cooperators that refuse to participate in sanctioning defectors create the second-order free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers—those that cooperate and punish—are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondoʼs paradox.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Altruistic punishment in humans
Fehr, E., & Gächter, S. (2002) · Nature · doi:10.1038/415137a · Cited by 5,616
Evolutionary Games and Population Dynamics
Hofbauer, J., & Sigmund, K. (1998) · doi:10.1017/cbo9781139173179 · Cited by 5,502
An experimental analysis of ultimatum bargaining
Güth, W., Schmittberger, R., & Schwarze, B. (1982) · Journal of Economic Behavior & Organization · doi:10.1016/0167-2681(82)90011-7 · Cited by 4,816
Cooperation and Punishment in Public Goods Experiments
Fehr, E., & Gächter, S. (2000) · American Economic Review · doi:10.1257/aer.90.4.980 · Cited by 4,547
Evolutionary games and spatial chaos
Nowak, M. A., & May, R. M. (1992) · Nature · doi:10.1038/359826a0 · Cited by 4,463
The Handbook of experimental economics
(1995) · Choice Reviews Online · doi:10.5860/choice.33-1645 · Cited by 3,679
Szabó, G., & Fáth, G. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.004 · Cited by 2,974
Evolution of indirect reciprocity by image scoring
Nowak, M. A., & Sigmund, K. (1998) · Nature · doi:10.1038/31225 · Cited by 2,700
In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies
Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., & McElreath, R. (2001) · American Economic Review · doi:10.1257/aer.91.2.73 · Cited by 2,614
The Handbook of Experimental Economics
(1995) · Princeton University Press eBooks · doi:10.1515/9780691213255 · Cited by 2,051
Cited by
Liu, L., Chen, X., & Szolnoki, A. (2019) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202519500428 · Cited by 128
Self-citationThe evolution of cooperation in spatial public goods game with conditional peer exclusion
Quan, J., Li, X., & Wang, X. (2019) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5119395 · Cited by 53
Quan, J., Liu, W., Chu, Y., & Wang, X. (2017) · Scientific Reports · doi:10.1038/s41598-017-16140-8 · Cited by 45
Evolution of cooperation in a hierarchical society with corruption control
Huang, F., Chen, X., & Wang, L. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.04.018 · Cited by 28
Self-citationOhdaira, T. (2016) · Scientific Reports · doi:10.1038/srep25413 · Cited by 26
Metadata
- Authors
- Chen, X., Szolnoki, A., & Perc, M.
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2014-08-07
- Volume
- 16
- Issue
- 8
- Pages
- 083016
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2171286297
- Cited by
- 285
- References
- 55
- FWCI
- 61.61
- Type
- journal article
- Language
- en
- Open access
- gold
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 ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Probabilistic sharing solves the problem of costly punishment. https://app.cochat.ai/papers/10.1088/1367-2630/16/8/083016
- The paper
- Chen, X., Szolnoki, A., & Perc, M. (2014). Probabilistic sharing solves the problem of costly punishment. New Journal of Physics. https://doi.org/10.1088/1367-2630/16/8/083016
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.