The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game
Abstract
Based on learning theory, we adopt a stochastic learning updating rule to investigate the evolution of cooperation in the Prisoner's Dilemma game on Newman-Watts small-world networks with different payoff aspiration levels. Interestingly, simulation results show that the mechanism of intermediate aspiration promoting cooperation resembles a resonancelike behavior, and there exists a ping-pong vibration of cooperation for large payoff aspiration. To explain the nontrivial dependence of the cooperation level on the aspiration level, we investigate the fractions of links, provide analytical results of the cooperation level, and find that the simulation results are in close agreement with analytical ones. Our work may be helpful in understanding the cooperative behavior induced by the aspiration level in society.
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
Axelrod, R., & Hamilton, W. D. (1981) · Science · doi:10.1126/science.7466396 · Cited by 20,065
Evolution and the Theory of Games
Smith, J. M. (1982) · Cambridge University Press eBooks · doi:10.1017/cbo9780511806292 · Cited by 6,922
Evolutionary Games and Population Dynamics
Hofbauer, J., & Sigmund, K. (1998) · doi:10.1017/cbo9781139173179 · Cited by 5,502
Evolutionary games and spatial chaos
Nowak, M. A., & May, R. M. (1992) · Nature · doi:10.1038/359826a0 · Cited by 4,463
Szabó, G., & Fáth, G. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.004 · Cited by 2,974
Scale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation
Santos, F. C., & Pacheco, J. M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.098104 · Cited by 1,804
A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game
Nowak, M., & Sigmund, K. (1993) · Nature · doi:10.1038/364056a0 · Cited by 1,797
Evolutionary prisoner’s dilemma game on a square lattice
Szabó, G., & Tőke, C. (1998) · Physical Review E · doi:10.1103/physreve.58.69 · Cited by 1,659
Spatial structure often inhibits the evolution of cooperation in the snowdrift game
Hauert, C., & Doebeli, M. (2004) · Nature · doi:10.1038/nature02360 · Cited by 1,582
Scaling and percolation in the small-world network model
Newman, M. E. J., & Watts, D. J. (1999) · Physical Review E · doi:10.1103/physreve.60.7332 · Cited by 1,202
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-citation
Metadata
- Authors
- Chen, X., & Wang, L.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2008-01-24
- Volume
- 77
- Issue
- 1
- Pages
- 017103-017103
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W1969173884
- Cited by
- 381
- References
- 24
- FWCI
- 53.43
- Type
- journal article
- Language
- en
- Open access
- closed
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: Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. https://app.cochat.ai/papers/10.1103/physreve.77.017103
- The paper
- Chen, X., & Wang, L. (2008). Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. Physical Review E. https://doi.org/10.1103/physreve.77.017103
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.
