Early exclusion leads to cyclical cooperation in repeated group interactions
Open accessAbstract
Explaining the emergence and maintenance of cooperation among selfish individuals from an evolutionary perspective remains a grand challenge in biology, economy and social sciences. Social exclusion is believed to be an answer to this conundrum. However, previously related studies often assume one-shot interactions and ignore how free-riding is identified, which seem to be too idealistic. In this work, we consider repeated interactions where excluders need to pay a monitoring cost to identify free-riders for exclusion and free-riders cannot participate in the following possible game interactions once they are identified and excluded by excluders in the repeated interaction process. We reveal that the introduction of such exclusion can prevent the breakdown of cooperation in repeated group interactions. In particular, we demonstrate that an evolutionary oscillation among cooperators, defectors and excluders can appear in infinitely large populations when early exclusion is implemented. In addition, we find that the population spends most of the time in states where cooperators dominate for early exclusion when stochastic mutation-selection is considered in finite populations. Our results highlight that early exclusion is successful in solving the mentioned enigma of cooperation in repeated group interactions.
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
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In repeated interactions, investors have the opportunity to adjust their actions according to the investment environment they encountered.
“Furthermore, in repeated interactions, investors have the opportunity to adjust their actions according to the investment environment they encountered [30, 34, 28].”
From Conditional investment strategy in evolutionary trust games with repeated group interactions (2022) · cites this paper as [28]
Real interactions are repeated rather than one-shot.
“Indeed, real interactions are repeated rather than the one-shot interaction assumed above [11, 10, 30, 33, 28].”
From Conditional investment strategy in evolutionary trust games with repeated group interactions (2022) · cites this paper as [28]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Hardin, G. (1968) · Science · doi:10.1126/science.162.3859.1243 · Cited by 25,167 · see citing works
Axelrod, R., & Hamilton, W. D. (1981) · Science · doi:10.1126/science.7466396 · Cited by 20,065 · see citing works
Stochastic Processes in Physics and Chemistry
(2007) · Elsevier eBooks · doi:10.1016/b978-0-444-52965-7.x5000-4 · Cited by 9,070 · see citing works
Altruistic punishment in humans
Fehr, E., & Gächter, S. (2002) · Nature · doi:10.1038/415137a · Cited by 5,616 · see citing works
Evolutionary Games and Population Dynamics
Hofbauer, J., & Sigmund, K. (1998) · doi:10.1017/cbo9781139173179 · Cited by 5,502 · see citing works
Cooperation and Punishment in Public Goods Experiments
Fehr, E., & Gächter, S. (2000) · American Economic Review · doi:10.1257/aer.90.4.980 · Cited by 4,416 · cited 1× · see citing works
“1038/nature25763) [30] Fehr E, Gachter S.”
Third-party punishment and social norms
Fehr, E., & Fischbacher, U. (2004) · Evolution and Human Behavior · doi:10.1016/s1090-5138(04)00005-4 · Cited by 2,417 · see citing works
Antisocial Punishment Across Societies
Herrmann, B., Thöni, C., & Gächter, S. (2008) · Science · doi:10.1126/science.1153808 · Cited by 2,038 · see citing works
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 1,824 · see citing works
The evolution of altruistic punishment
Boyd, R., Gintis, H., Bowles, S., & Richerson, P. J. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0630443100 · Cited by 1,748 · see citing works
Social norms and human cooperation
Fehr, E., & Fischbacher, U. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.02.007 · Cited by 1,615 · see citing works
Statistical physics of human cooperation
Perc, M., Jordan, J., Rand, D. G., Wang, Z., Boccaletti, S., & Szolnoki, A. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.05.004 · Cited by 1,572 · see citing works
Self-citationEvolutionary prisoner's dilemma game on a square lattice
Szabó, G., & Tőke, C. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.58.69 · Cited by 1,507 · see citing works
Punishment allows the evolution of cooperation (or anything else) in sizable groups
Boyd, R., & Richerson, P. J. (1992) · Ethology and Sociobiology · doi:10.1016/0162-3095(92)90032-y · Cited by 1,482 · see citing works
Emergence of cooperation and evolutionary stability in finite populations
Nowak, M. A., Sasaki, A., Taylor, C., & Fudenberg, D. (2004) · Nature · doi:10.1038/nature02414 · Cited by 1,403 · see citing works
Evolutionary dynamics of group interactions on structured populations: a review
Perc, M., Gómez-Gardeñes, J., Szolnoki, A., Florı́a, L. M., & Moreno, Y. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2012.0997 · Cited by 1,394 · see citing works
Self-citationReputation helps solve the ‘tragedy of the commons’
Milinski, M., Semmann, D., & Krambeck, H.-J. (2002) · Nature · doi:10.1038/415424a · Cited by 1,371 · see citing works
Hofbauer, J., & Sigmund, K. (2003) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-03-00988-1 · Cited by 1,366 · see citing works
Rand, D. G., & Nowak, M. A. (2013) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2013.06.003 · Cited by 1,308 · see citing works
Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games
Hauert, C., Monte, S. D., Hofbauer, J., & Sigmund, K. (2002) · Science · doi:10.1126/science.1070582 · Cited by 1,116 · see citing works
The Emergence of Cooperation among Egoists
Axelrod, R. (1981) · American Political Science Review · doi:10.2307/1961366 · Cited by 968 · see citing works
Evolutionary dynamics of group interactions on structured populations: a review
Perz, M., Gómez‐Gardeñes, J., Szolnoki, A., Florı́a, L. M., & Moreno, Y. (2013) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 883 · see citing works
Self-citationVia Freedom to Coercion: The Emergence of Costly Punishment
Hauert, C., Traulsen, A., Brandt, H., Nowak, M. A., & Sigmund, K. (2007) · Science · doi:10.1126/science.1141588 · Cited by 709 · see citing works
Reputation-based partner choice promotes cooperation in social networks
Fu, F., Hauert, C., Nowak, M. A., & Wang, L. (2008) · Physical Review E · doi:10.1103/physreve.78.026117 · Cited by 682 · see citing works
Sigmund, K., Hauert, C., & Nowak, M. A. (2001) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.161155698 · Cited by 644 · see citing works
The Carrot or the Stick: Rewards, Punishments, and Cooperation
Andreoni, J., Harbaugh, W. T., & Vesterlund, L. (2003) · American Economic Review · doi:10.1257/000282803322157142 · Cited by 608 · see citing works
Social learning promotes institutions for governing the commons
Sigmund, K., De Silva, H., Traulsen, A., & Hauert, C. (2010) · Nature · doi:10.1038/nature09203 · Cited by 580 · see citing works
Chimpanzees Recruit the Best Collaborators
Melis, A. P., Hare, B. A., & Tomasello, M. (2006) · Science · doi:10.1126/science.1123007 · Cited by 574 · see citing works
Sigmund, K. (2010) · doi:10.1515/9781400832255 · Cited by 570 · see citing works
Evolution of cooperation and conflict in experimental bacterial populations
Rainey, P. B., & Rainey, K. (2003) · Nature · doi:10.1038/nature01906 · Cited by 568 · see citing works
Inequality, communication, and the avoidance of disastrous climate change in a public goods game
Tavoni, A., Dannenberg, A., Kallis, G., & Löschel, A. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1102493108 · Cited by 497 · see citing works
Evolution of Universal Grammar
Nowak, M. A., Komarova, N. L., & Niyogi, P. (2001) · Science · doi:10.1126/science.291.5501.114 · Cited by 449 · see citing works
Evolutionary cycles of cooperation and defection
Imhof, L. A., Fudenberg, D., & Nowak, M. A. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0502589102 · Cited by 381 · see citing works
Cooperation in a repeated prisoners' dilemma with ostracism
Hirshleifer, D. A., & Rasmusen, E. (1989) · Journal of Economic Behavior & Organization · doi:10.1016/0167-2681(89)90078-4 · Cited by 376 · see citing works
Cooperation under the threat of expulsion in a public goods experiment
Cinyabuguma, M. M., Page, T., & Putterman, L. G. (2004) · Journal of Public Economics · doi:10.1016/j.jpubeco.2004.05.011 · Cited by 338 · see citing works
Unifying Evolutionary Dynamics
Page, K. M., & Nowak, M. A. (2002) · Journal of Theoretical Biology · doi:10.1006/jtbi.2002.3112 · Cited by 322 · see citing works
Evolution of cooperation in stochastic games
Hilbe, C., Šimsa, Š., Chatterjee, K., & Nowak, M. A. (2018) · Nature · doi:10.1038/s41586-018-0277-x · Cited by 277 · see citing works
Social norm complexity and past reputations in the evolution of cooperation
Santos, F. P., Santos, F. C., & Pacheco, J. M. (2018) · Nature · doi:10.1038/nature25763 · Cited by 265 · see citing works
Unifying Evolutionary Dynamics
Page, K. M. (2002) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(02)93112-7 · Cited by 241 · see citing works
Game-Theoretical Models in Biology
Broom, M., & Rychtář, J. (2013) · Chapman & Hall/CRC eBooks · doi:10.1201/b14069 · Cited by 233 · see citing works
Partner switching stabilizes cooperation in coevolutionary prisoner’s dilemma
Fu, F., Wu, T., & Wang, L. (2009) · Physical Review E · doi:10.1103/physreve.79.036101 · Cited by 219 · see citing works
Quorum sensing and policing of Pseudomonas aeruginosa social cheaters
Wang, M., Schaefer, A. L., Dandekar, A. A., & Greenberg, E. P. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1500704112 · Cited by 217 · see citing works
First carrot, then stick: how the adaptive hybridization of incentives promotes cooperation
Chen, X., Sasaki, T., Brännström, Å., & Dieckmann, U. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2014.0935 · Cited by 210 · see citing works
Self-citationPartners and rivals in direct reciprocity
Hilbe, C., Chatterjee, K., & Nowak, M. A. (2018) · Nature Human Behaviour · doi:10.1038/s41562-018-0320-9 · Cited by 187 · see citing works
Incentives and opportunism: from the carrot to the stick
Hilbe, C., & Sigmund, K. (2010) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2010.0065 · Cited by 184 · see citing works
A bottom-up institutional approach to cooperative governance of risky commons
Vasconcelos, V. V., Santos, F. C., & Pacheco, J. M. (2013) · Nature Climate Change · doi:10.1038/nclimate1927 · Cited by 183 · see citing works
Effectiveness of conditional punishment for the evolution of public cooperation
Szolnoki, A., & Perc, M. (2013) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2013.02.008 · Cited by 173 · see citing works
Self-citationClimate policies under wealth inequality
de Vasconcelos, V. V. L., Santos, F. C., Pacheco, J. M., & Levin, S. A. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1323479111 · Cited by 158 · see citing works
Alliance formation with exclusion in the spatial public goods game
Szolnoki, A., & Chen, X. (2017) · Physical review. E · doi:10.1103/physreve.95.052316 · Cited by 150 · see citing works
Self-citationThe evolution of cooperation by social exclusion
Sasaki, T., & Uchida, S. (2012) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2012.2498 · Cited by 135 · see citing works
HETEROCLINIC CONTOURS IN NEURAL ENSEMBLES AND THE WINNERLESS COMPETITION PRINCIPLE
AFRAIMOVICH, V. S., RABINOVICH, M. I., & VARONA, P. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404009806 · Cited by 129 · see citing works
Ostracism and the provision of a public good: experimental evidence
Maier-Rigaud, F. P., Martinsson, P., & Staffiero, G. (2009) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2009.11.001 · Cited by 127 · see citing works
Emergence of Fairness in Repeated Group Interactions
Segbroeck, S. V., Pacheco, J. M., Lenaerts, T., & Santos, F. C. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.158104 · Cited by 117 · see citing works
Competitions between prosocial exclusions and punishments in finite populations
Liu, L., Chen, X., & Szolnoki, A. (2017) · Scientific Reports · doi:10.1038/srep46634 · Cited by 115 · see citing works
Self-citationSocial exclusion in finite populations
Li, K., Cong, R., Wu, T., & Wang, L. (2015) · Physical Review E · doi:10.1103/physreve.91.042810 · Cited by 112 · see citing works
Kerr, N. L., Rumble, A. C., Park, E. S., Ouwerkerk, J., Parks, C., Gallucci, M., & van Lange, P. (2009) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2009.02.017 · Cited by 102 · see citing works
Game-Theoretical Models in Biology
Broom, M., & Rychtář, J. (2022) · Chapman & Hall/CRC eBooks · doi:10.1201/9781003024682 · Cited by 87 · see citing works
Han, T. A., Perret, C., & Powers, S. T. (2021) · Cognitive Systems Research · doi:10.1016/j.cogsys.2021.02.003 · Cited by 78 · see citing works
Ostracism in work teams: a public good experiment
David Masclet, B. (2003) · International Journal of Manpower · doi:10.1108/01437720310502177 · Cited by 75 · see citing works
Avoiding or restricting defectors in public goods games?
Han, T. A., Pereira, L. M., & Lenaerts, T. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2014.1203 · Cited by 74 · see citing works
Apology and forgiveness evolve to resolve failures in cooperative agreements
Martínez-Vaquero, L. A., Han, T. A., Pereira, L. M., & Lenaerts, T. (2015) · Scientific Reports · doi:10.1038/srep10639 · Cited by 73 · see citing works
Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models
Helbing, D. (1993) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(93)90034-2 · Cited by 70 · see citing works
Ecological Advantages and Evolutionary Limitations of Aggregative Multicellular Development
Pentz, J. T., Márquez-Zacarías, P., Bozdag, G. O., Burnetti, A., Yunker, P. J., Libby, E., & Ratcliff, W. C. (2020) · Current Biology · doi:10.1016/j.cub.2020.08.006 · Cited by 60 · see citing works
On the stability of double homoclinic and heteroclinic cycles
Han, M., Hu, S., & Liu, X. (2003) · Nonlinear Analysis · doi:10.1016/s0362-546x(02)00301-2 · Cited by 59 · see citing works
Mediating artificial intelligence developments through negative and positive incentives
Han, T. A., Pereira, L. M., Lenaerts, T., & Santos, F. C. (2021) · PLoS ONE · doi:10.1371/journal.pone.0244592 · Cited by 57 · see citing works
The 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 · see citing works
Shaw, K. M., Park, Y., Chiel, H. J., & Thomas, P. J. (2012) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/110828976 · Cited by 41 · see citing works
A synergy of costly punishment and commitment in cooperation dilemmas
Han, T. A., & Lenaerts, T. (2016) · Adaptive Behavior · doi:10.1177/1059712316653451 · Cited by 41 · see citing works
Behavioral heterogeneity in quorum sensing can stabilize social cooperation in microbial populations
Zhao, K., Liu, L., Chen, X., Huang, T. L., Du, L., Lin, J., Yuan, Y., Zhou, Y., Yue, B., Wei, K., et al. (2019) · BMC Biology · doi:10.1186/s12915-019-0639-3 · Cited by 38 · see citing works
Self-citationStochastic Dynamics through Hierarchically Embedded Markov Chains
de Vasconcelos, V. V. L., Santos, F. P., Santos, F. C., & Pacheco, J. M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.058301 · Cited by 34 · see citing works
Conditional punishment is a double-edged sword in promoting cooperation
Huang, F., Chen, X., & Wang, L. (2018) · Scientific Reports · doi:10.1038/s41598-017-18727-7 · Cited by 33 · see citing works
Self-citationIncidental ostracism emerges from simple learning mechanisms
Lindström, B., & Tobler, P. N. (2018) · Nature Human Behaviour · doi:10.1038/s41562-018-0355-y · Cited by 28 · see citing works
Balancedness among competitions for biodiversity in the cyclic structured three species system
Park, J. (2017) · Applied Mathematics and Computation · doi:10.1016/j.amc.2017.09.047 · Cited by 27 · see citing works
Parent-preferred dispersal promotes cooperation in structured populations
Chen, X., Brännström, Å., & Dieckmann, U. (2019) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2018.1949 · Cited by 23 · see citing works
Self-citationWhen agreement-accepting free-riders are a necessary evil for the evolution of cooperation
Martínez-Vaquero, L. A., Han, T. A., Pereira, L. M., & Lenaerts, T. (2017) · Scientific Reports · doi:10.1038/s41598-017-02625-z · Cited by 22 · see citing works
Learning enables adaptation in cooperation for multi-player stochastic games
Huang, F., Cao, M., & Wang, L. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0639 · Cited by 20 · see citing works
Does insurance against punishment undermine cooperation in the evolution of public goods games?
Zhang, J., Chu, T., & Weissing, F. J. (2013) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2012.12.019 · Cited by 18 · see citing works
Rationality alters the rank between peer punishment and social exclusion
Sui, X., Wu, B., & Wang, L. (2018) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/121/38003 · Cited by 16 · see citing works
High frequency repeated games with costly monitoring
Lehrer, E., & Solan, E. (2018) · Theoretical Economics · doi:10.3982/te2627 · Cited by 4 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Evolution of cooperation driven by sampling punishment
Xiao, J., Liu, L., Chen, X., & Szolnoki, A. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.128879 · Cited by 48 · see citing works
Self-citationConditional investment strategy in evolutionary trust games with repeated group interactions
Liu, L., & Chen, X. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.073 · Cited by 45 · see citing works
Self-citationFacilitating the evolution of cooperation through altruistic punishment with adaptive feedback
Hua, S., & Liu, L. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113669 · Cited by 43 · see citing works
Self-citationSharma, G., Guo, H., Shen, C., & Tanimoto, J. (2023) · Journal of The Royal Society Interface · doi:10.1098/rsif.2023.0301 · Cited by 35 · see citing works
Jia, D., Chen, S., Dai, X., Wang, X., Xing, J., Tao, P., Shi, Y., & Wang, Z. (2024) · Knowledge-Based Systems · doi:10.1016/j.knosys.2024.111962 · Cited by 33 · see citing works
Hua, S., Hui, Z., & Liu, L. (2023) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2023.0949 · Cited by 31 · see citing works
Self-citationOptions for mobility and network reciprocity to jointly yield robust cooperation in social dilemmas
Li, W., Chen, Z., Jin, K.-Z., Wang, J., Lin, Y., Gu, C., Jiang, L.-L., & Perc, M. (2022) · Applied Mathematics and Computation · doi:10.1016/j.amc.2022.127456 · Cited by 24 · see citing works
Competition of alliances in a cyclically dominant eight-species population
Park, J., Chen, X., & Szolnoki, A. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.113004 · Cited by 21 · see citing works
Self-citationIndirect exclusion can promote cooperation in repeated group interactions
Liu, L., & Chen, X. (2022) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2022.0290 · Cited by 20 · see citing works
Self-citationBi, Y., & Yang, H. (2022) · Applied Mathematics and Computation · doi:10.1016/j.amc.2022.127818 · Cited by 20 · see citing works
Evolution of trust in the N -player trust game with transformation incentive mechanism
Liu, Y., Wang, L., Guo, R., Hua, S., Liu, L., Zhang, L., & Han, T. A. (2025) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0726 · Cited by 19 · see citing works
Self-citationEco-evolutionary dynamics of bimatrix games
Shu, L., & Fu, F. (2022) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2022.0567 · Cited by 18 · see citing works
Social dilemma in the excess use of antimicrobials incurring antimicrobial resistance
Ito, H., Wada, T., Ichinose, G., Tanimoto, J., Yoshimura, J., Yamamoto, T., & Morita, S. (2022) · Scientific Reports · doi:10.1038/s41598-022-25632-1 · Cited by 14 · see citing works
Zealous cooperation does not always promote cooperation in public goods games
Wang, C., & Sun, C. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0138258 · Cited by 14 · see citing works
N -player repeated evolutionary trust game under government management
Liu, Y., Liu, L., Guo, R., & Zhang, L. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114031 · Cited by 14 · see citing works
Self-citationHeterogeneous reputation promotes cooperation in spatial public goods game
Bi, Y., & Yang, H. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.129149 · Cited by 12 · see citing works
Emerging solutions from the battle of defensive alliances
Szolnoki, A., & Chen, X. (2023) · Scientific Reports · doi:10.1038/s41598-023-35746-9 · Cited by 12 · see citing works
Self-citationLi, S., Du, C., Li, X., Shen, C., & Ши, Л. (2023) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2023.111665 · Cited by 10 · see citing works
Evolutionary Dynamics of Preguidance Strategies in Population Games
Liu, L., & Chen, X. (2024) · IEEE Transactions on Computational Social Systems · doi:10.1109/tcss.2024.3386501 · Cited by 10 · see citing works
Self-citationRestoring spatial cooperation with myopic agents in a three-strategy social dilemma
Lee, H., Cleveland, C., & Szolnoki, A. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.128226 · Cited by 10 · see citing works
Self-citationZhuo, S., Liu, J., Ren, T., & Sun, J. (2022) · New Journal of Physics · doi:10.1088/1367-2630/aca995 · Cited by 7 · see citing works
Evolution of trust in N-player trust games with loss assessment
Liu, Y., Wang, L., Guo, R., Hua, S., Liu, L., & Liang, Z. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0228886 · Cited by 6 · see citing works
Self-citationEvolutionary dynamics of trust in hierarchical populations with varying investment strategies
Zhou, C., Zhu, Y., Xia, C., & Chica, M. (2025) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0734 · Cited by 6 · see citing works
Lee, H., Cleveland, C., & Szolnoki, A. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128864 · Cited by 6 · see citing works
Self-citationShuvo, M. F. R., & Kabir, K. M. A. (2024) · Royal Society Open Science · doi:10.1098/rsos.240717 · Cited by 5 · see citing works
Kang, H., Li, Z., Shen, Y., Huang, Z., Sun, X., & Chen, Q. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114547 · Cited by 5 · see citing works
Partial intervention promotes cooperation and social welfare in regional public goods game
Wang, J., Dai, W., Zheng, Y., Yu, F., Chen, W., & Xu, W. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114991 · Cited by 5 · see citing works
Shuvo, M. F. R., & Kabir, K. M. A. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128836 · Cited by 5 · see citing works
Impact of trajectory-dependent reputation dynamics on the spatial public goods game
Sun, X., Zhang, X., Kang, H., Shen, Y., Chen, Q., & Zhang, Y. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0308950 · Cited by 4 · see citing works
The survival of the weakest in a biased donation game
Wang, C., Li, J., Wang, X., Zhu, W., & Szolnoki, A. (2026) · Applied Mathematics and Computation · doi:10.1016/j.amc.2026.130073 · Cited by 3 · see citing works
Self-citationTakesue, H. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129676 · Cited by 3 · see citing works
Emergence of oscillatory cooperation in a population with incomplete information
Zhang, J., Zhao, L., Zhang, J., Ma, L., Zheng, G., & Chen, L. (2023) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2023.128682 · Cited by 3 · see citing works
Evolution of cooperation under corrupt institutions
Wang, J., Xu, W., Yu, F., He, J., Chen, W., & Dai, W. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114988 · Cited by 3 · see citing works
Dong, Y., He, Z., Shen, C., Ши, Л., & Tanimoto, J. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0231158 · Cited by 3 · see citing works
Synergistic effects of global exclusion and mutation on replicator dynamics of public cooperation
Jia, D., & Wang, X. (2024) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ad4e29 · Cited by 2 · see citing works
Framing hybrid allocation scheme in a public good game with heterogeneous endowments
Wang, X., He, Z., Zhao, Q., & Ши, Л. (2025) · Applied Mathematical Modelling · doi:10.1016/j.apm.2025.116682 · Cited by 2 · see citing works
Xu, M., Hua, S., & Liu, L. (2026) · Journal of The Royal Society Interface · doi:10.1098/rsif.2026.0153 · Cited by 2 · see citing works
Self-citationTowards preferential selection in the prisoner’s dilemma game
Qiang, B., Zhang, L., & Huang, C. (2023) · PLoS ONE · doi:10.1371/journal.pone.0282258 · Cited by 2 · see citing works
Bonus-based mercenary punishment promotes cooperation in public goods games
Kang, H., Liu, S., Chen, Q., Shen, Y., & Sun, X. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e22748 · Cited by 2 · see citing works
Effect of distribution of fines on evolution of cooperation in spatial public goods game
Sun, X., Bi, Y.-Z., Kang, H., Shen, Y., & Chen, Q. (2024) · Chinese Physics B · doi:10.1088/1674-1056/ad5aee · Cited by 2 · see citing works
Bi, Y., Hao, Q.-Y., & Wu, W. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.115622 · Cited by 2 · see citing works
Evolutionary dynamics of cooperation in optional public goods games with loners' punishment
Ding, R., Wang, X., Quan, J., Ma, S., & Zhao, J. (2025) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0253511 · Cited by 2 · see citing works
Evolutionary dynamics in public goods games with general frequency-dependent returns
Wang, Q., Liu, Y., Chen, X., & Szolnoki, A. (2026) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2026.135303 · Cited by 1 · see citing works
Self-citationLu, S., Zhu, G., & Dai, J. (2023) · PLoS ONE · doi:10.1371/journal.pone.0280015 · Cited by 1 · see citing works
Evolution of Cooperation in Structured Populations through Pool Exclusion Strategy
Hua, S., Xu, M., & Liu, L. (2024) · Chinese Control Conference (CCC) · doi:10.23919/ccc63176.2024.10662117
Self-citationXue, F., Wang, L., Liu, X., & Zheng, A. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129397
Evolutionary dynamics of collective-risk dilemmas with two-stage adaptive switching incentives
Xu, M., Yan, R., Li, X., & Hua, S. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.119157
Li, Y., Fan, L., Feng, A., & Zhao, Z. (2026) · Acta Psychologica · doi:10.1016/j.actpsy.2026.107879
Xie, X., & Zhou, Q. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.132324
- Authors
- Liu, L., Xiao, Z., Chen, X., & Szolnoki, A.
- Affiliations
- University of Electronic Science and Technology of China (CN)
- Institute for Technical Physics and Materials Science (HU)
- Corresponding author
- Chen, Xiaojie
- Venue
- Journal of The Royal Society Interface
- Publisher
- The Royal Society
- Published
- 2022-03
- Volume
- 19
- Issue
- 188
- Pages
- 20210755-20210755
- ISSN
- 1742-5662 (ISSN-L)
- PMC
- PMC8941418
- OpenAlex
- W4220743453
- Cited by
- 50
- References
- 79
- Citations by year
- 2026: 7 · 2025: 6 · 2024: 14 · 2023: 14 · 2022: 9
- FWCI
- 15.47
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of The Royal Society Interface (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (61976048, 62036002)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Keywords
- cooperation, social exclusion, free-riding, repeated interaction, monitoring costs, finite population, evolutionary game theory, group interaction
- MeSH terms
- Cooperative Behavior, Biological Evolution, Game Theory, Humans, Population Dynamics
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
