The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Towards effective payoffs in the prisoner’s dilemma game on scale-free networks
Open accessAbstract
We study the transition towards effective payoffs in the prisoner’s dilemma game on scale-free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent. We show that during this transition the heterogeneity-based ability of scale-free networks to facilitate cooperative behavior deteriorates continuously, eventually collapsing with the results obtained on regular graphs. The strategy donations and adaptation probabilities of agents with different connectivities are studied. Results reveal that strategies generally spread from agents with larger towards agents with smaller degree. However, this strategy adoption flow reverses sharply in the fully normalized payoff limit. Surprisingly, cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate.
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
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Five Rules for the Evolution of Cooperation
Nowak, M. A. (2006) · Science · doi:10.1126/science.1133755 · Cited by 5,894
Evolutionary Games and Population Dynamics
Hofbauer, J., & Sigmund, K. (1998) · doi:10.1017/cbo9781139173179 · Cited by 5,502
A simple rule for the evolution of cooperation on graphs and social networks
Ohtsuki, H., Hauert, C., Lieberman, E., & Nowak, M. A. (2006) · Nature · doi:10.1038/nature04605 · Cited by 2,208
Cooperation Prevails When Individuals Adjust Their Social Ties
Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020140 · Cited by 556
Cited by
Universal scaling for the dilemma strength in evolutionary games
Wang, Z., Kokubo, S., Jusup, M., & Tanimoto, J. (2015) · Physics of Life Reviews · doi:10.1016/j.plrev.2015.04.033 · Cited by 586
Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game
Liu, Y., Chen, X., Zhang, L., Wang, L., & Perc, M. (2012) · PLoS ONE · doi:10.1371/journal.pone.0030689 · Cited by 527
Self-citationInterdependent network reciprocity in evolutionary games
Wang, Z., Szolnoki, A., & Perc, M. (2013) · Scientific Reports · doi:10.1038/srep01183 · Cited by 485
Self-citationEvolution of Cooperation in Multiplex Networks
Gómez-Gardeñes, J., Reinares, I., Arenas, A., & Floría, L. M. (2012) · Scientific Reports · doi:10.1038/srep00620 · Cited by 462
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, W.-X., Lai, Y.-C., & Grebogi, C. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.004 · Cited by 299
Metadata
- Authors
- Szolnoki, A., Perc, M., & Danku, Z.
- Venue
- Physica A: Statistical Mechanics and its Applications
- Publisher
- Elsevier BV
- Published
- 2008-03
- Volume
- 387
- Issue
- 8-9
- Pages
- 2075-2082
- ISSN
- 0378-4371 (ISSN-L)
- OpenAlex
- W2023097644
- Cited by
- 297
- References
- 5
- FWCI
- 53.06
- Type
- journal article
- Language
- en
- Open access
- bronze
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: Towards effective payoffs in the prisoner’s dilemma game on scale-free networks. https://app.cochat.ai/papers/10.1016/j.physa.2007.11.021
- The paper
- Szolnoki, A., Perc, M., & Danku, Z. (2008). Towards effective payoffs in the prisoner’s dilemma game on scale-free networks. Physica A: Statistical Mechanics and its Applications. https://doi.org/10.1016/j.physa.2007.11.021
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.
