Combination of institutional incentives for cooperative governance of risky commons
Open accessAbstract
Finding appropriate incentives to enforce collaborative efforts for governing the commons in risky situations is a long-lasting challenge. Previous works have demonstrated that both punishing free-riders and rewarding cooperators could be potential tools to reach this goal. Despite weak theoretical foundations, policy makers frequently impose a punishment-reward combination. Here, we consider the emergence of positive and negative incentives and analyze their simultaneous impact on sustaining risky commons. Importantly, we consider institutions with fixed and flexible incentives. We find that a local sanctioning scheme with pure reward is the optimal incentive strategy. It can drive the entire population toward a highly cooperative state in a broad range of parameters, independently of the type of institutions. We show that our finding is also valid for flexible incentives in the global sanctioning scheme, although the local arrangement works more effectively.
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?
Agents' behaviors may be affected by noise, such as imitation error and behavioral mutation, in the process of social learning.
“Second, agents' behaviors may be affected by noise (such as imitation error and behavioral mutation) in the process of social learning [37, 38, 47], which is usually ignored by previous theoretical models.”
From Conditional investment strategy in evolutionary trust games with repeated group interactions (2022) · cites this paper as [38]
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
Governing the Commons: The Evolution of Institutions for Collective Action
Field, B. C., & Elinor Ostrom, B. (1992) · Land Economics · doi:10.2307/3146384 · Cited by 19,082 · 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
Governing the commons — the evolution of institutions for collective action
Weede, E. (1992) · European Journal of Political Economy · doi:10.1016/0176-2680(92)90034-e · Cited by 3,924 · see citing works
Paris Agreement climate proposals need a boost to keep warming well below 2 °C
Rogelj, J., den Elzen, M., Höhne, N., Fransen, T., Fekete, H., Winkler, H., Schaeffer, R., Sha, F., Riahi, K., & Meinshausen, M. (2016) · Nature · doi:10.1038/nature18307 · Cited by 3,480 · cited 1× · see citing works
“Since the Paris Agreement, we are witnessing the transformation of some countries’ environmental governance to high-quality management (Rogelj et al., 2016).”
BackgroundStatistical 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
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
Via 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
The collective-risk social dilemma and the prevention of simulated dangerous climate change
Milinski, M., Sommerfeld, R. D., Krambeck, H.-J., Reed, F. A., & Marotzke, J. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709546105 · Cited by 613 · 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
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
Quantifying the economic risks of climate change
Diaz, D., & Moore, F. C. (2017) · Nature Climate Change · doi:10.1038/nclimate3411 · Cited by 374 · see citing works
Replicator Dynamics for Optional Public Good Games
Hauert, C., Monte, S. D., Hofbauer, J., & Sigmund, K. (2002) · Journal of Theoretical Biology · doi:10.1006/jtbi.2002.3067 · Cited by 371 · see citing works
Advantages of a polycentric approach to climate change policy
Cole, D. H. (2015) · Nature Climate Change · doi:10.1038/nclimate2490 · Cited by 345 · see citing works
Climate negotiations under scientific uncertainty
Barrett, S., & Dannenberg, A. (2012) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1208417109 · Cited by 330 · see citing works
Punish or perish? Retaliation and collaboration among humans
Sigmund, K. (2007) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2007.06.012 · Cited by 301 · see citing works
Risk of collective failure provides an escape from the tragedy of the commons
Santos, F. C., & Pacheco, J. M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1015648108 · Cited by 278 · see citing works
Second-Order Free-Riding on Antisocial Punishment Restores the Effectiveness of Prosocial Punishment
Szolnoki, A., & Perc, M. (2017) · Physical Review X · doi:10.1103/physrevx.7.041027 · Cited by 228 · see citing works
Self-citationFirst 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-citationSzolnoki, A., & Perc, M. (2013) · Physical Review X · doi:10.1103/physrevx.3.041021 · Cited by 203 · see citing works
Self-citationCompetition of individual and institutional punishments in spatial public goods games
Szolnoki, A., Szabó, G., & Czakó, L. (2011) · Physical Review E · doi:10.1103/physreve.84.046106 · Cited by 195 · see citing works
Self-citationIncentives 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
Self-citationRisk-driven migration and the collective-risk social dilemma
Chen, X., Szolnoki, A., & Perc, M. (2012) · Physical Review E · doi:10.1103/physreve.86.036101 · Cited by 182 · see citing works
Self-citationIntra- and intergenerational discounting in the climate game
Jacquet, J., Hagel, K., Hauert, C., Marotzke, J., Röhl, T., & Milinski, M. (2013) · Nature Climate Change · doi:10.1038/nclimate2024 · Cited by 170 · see citing works
Sustainable institutionalized punishment requires elimination of second-order free-riders
Perc, M. (2012) · Scientific Reports · doi:10.1038/srep00344 · Cited by 169 · see citing works
Climate 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
Self-citationThe take-it-or-leave-it option allows small penalties to overcome social dilemmas
Sasaki, T., Brännström, Å., Dieckmann, U., & Sigmund, K. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1115219109 · Cited by 152 · see citing works
Antisocial pool rewarding does not deter public cooperation
Szolnoki, A., & Perc, M. (2015) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2015.1975 · Cited by 145 · see citing works
Self-citationEmergence of social cooperation in threshold public goods games with collective risk
Wang, J., Fu, F., Wu, T., & Wang, L. (2009) · Physical Review E · doi:10.1103/physreve.80.016101 · Cited by 138 · see citing works
The 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
Climate change governance, cooperation and self-organization
Pacheco, J. M., de Vasconcelos, V. V. L., & Santos, F. C. (2014) · Physics of Life Reviews · doi:10.1016/j.plrev.2014.02.003 · Cited by 134 · see citing works
Self-citationAntisocial pool rewarding does not deter public cooperation
Szolnoki, A., & Perc, M. (2015) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 134 · see citing works
Self-citationA balance of bottom-up and top-down in linking climate policies
Green, J., Sterner, T., & Wagner, G. (2014) · Nature Climate Change · doi:10.1038/nclimate2429 · Cited by 123 · 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
Sustainable institutionalized punishment requires elimination of second-order free-riders
Perc, M. (2017) · University of Maribor digital library (University of Maribor) · Cited by 115 · see citing works
Replicator dynamics in public goods games with reward funds
Sasaki, T., & Unemi, T. (2011) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.07.026 · Cited by 101 · see citing works
Cooperative interaction of rich and poor can be catalyzed by intermediate climate targets
Milinski, M., Röhl, T., & Marotzke, J. (2011) · Climatic Change · doi:10.1007/s10584-011-0319-y · Cited by 97 · see citing works
Benefits of tolerance in public goods games
Szolnoki, A., & Chen, X. (2015) · Physical Review E · doi:10.1103/physreve.92.042813 · Cited by 95 · see citing works
Self-citationExploring optimal institutional incentives for public cooperation
Wang, S., Chen, X., & Szolnoki, A. (2019) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2019.104914 · Cited by 94 · see citing works
Self-citationReward and punishment in climate change dilemmas
Góis, A. R., Santos, F. P., Pacheco, J. M., & Santos, F. C. (2019) · Scientific Reports · doi:10.1038/s41598-019-52524-8 · Cited by 89 · see citing works
The economic interaction between climate change mitigation, climate migration and poverty
Marotzke, J., Semmann, D., & Milinski, M. (2020) · Nature Climate Change · doi:10.1038/s41558-020-0783-3 · Cited by 86 · see citing works
Effects of heterogeneous wealth distribution on public cooperation with collective risk
Wang, J., Fu, F., & Wang, L. (2010) · Physical Review E · doi:10.1103/physreve.82.016102 · Cited by 84 · see citing works
Equity and state representations in climate negotiations
Schroeder, H., Boykoff, M., & Spiers, L. (2012) · Nature Climate Change · doi:10.1038/nclimate1742 · Cited by 78 · see citing works
The choice of institutions to solve cooperation problems: a survey of experimental research
Dannenberg, A., & Gallier, C. (2020) · Experimental Economics · doi:10.1007/s10683-019-09629-8 · 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
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 66 · see citing works
EVOLUTIONARY DYNAMICS OF CLIMATE CHANGE UNDER COLLECTIVE-RISK DILEMMAS
Santos, F. C., de Vasconcelos, V. V. L., Santos, M. D., NEVES, P. N. B., & Pacheco, J. M. (2011) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202511400045 · Cited by 65 · see citing works
Self-citationSecond-order free-riding problem solved?
Fowler, J. H. (2005) · Nature · doi:10.1038/nature04201 · Cited by 63 · 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
How selection pressure changes the nature of social dilemmas in structured populations
Pinheiro, F. L., Santos, F. C., & Pacheco, J. M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/7/073035 · Cited by 55 · see citing works
Second-order freeriding on antisocial punishment restores the effectiveness of prosocial punishmentPreprint
Szolnoki, A., & Perc, M. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/198192 · Cited by 55 · see citing works
Self-citationCost-effective external interference for promoting the evolution of cooperation
Han, T. A., & Tran-Thanh, L. (2018) · Scientific Reports · doi:10.1038/s41598-018-34435-2 · Cited by 54 · see citing works
A tale of two contribution mechanisms for nonlinear public goods
Zhang, Y., Fu, F., Wu, T., Xie, G., & Wang, L. (2013) · Scientific Reports · doi:10.1038/srep02021 · Cited by 49 · see citing works
Reward and Punishment in Social Dilemmas
Lange, P. A. M. V., Rockenbach, B., & Yamagishi, T. (2014) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199300730.001.0001 · Cited by 48 · see citing works
Network Engineering Using Autonomous Agents Increases Cooperation in Human Groups
Shirado, H., & Christakis, N. A. (2020) · iScience · doi:10.1016/j.isci.2020.101438 · Cited by 48 · see citing works
Timing uncertainty in collective risk dilemmas encourages group reciprocation and polarization
Domingos, E. F., Grujić, J., Santos, F. C., Burguillo, J. C., Kirchsteiger, G., Santos, F. C., & Lenaerts, T. (2020) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · doi:10.5061/dryad.5qfttdz2t · Cited by 47 · see citing works
Chen, X., Zhang, Y., Huang, T., & Perc, M. (2014) · Physical Review E · doi:10.1103/physreve.90.052823 · Cited by 42 · see citing works
Self-citationA Perspective on Incentive Design: Challenges and Opportunities
Ratliff, L. J., Dong, R., Sekar, S., & Fiez, T. (2018) · Annual Review of Control Robotics and Autonomous Systems · doi:10.1146/annurev-control-053018-023634 · Cited by 42 · see citing works
Cooperation dynamics of polycentric climate governance
de Vasconcelos, V. V. L., Santos, F. C., & Pacheco, J. M. (2015) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202515400163 · Cited by 35 · see citing works
Self-citationEvolution of coordinated punishment to enforce cooperation from an unbiased strategy space
García, J. A., & Traulsen, A. (2019) · Journal of The Royal Society Interface · doi:10.1098/rsif.2019.0127 · Cited by 35 · see citing works
Santos, F. P., Levin, S. A., & de Vasconcelos, V. V. L. (2021) · iScience · doi:10.1016/j.isci.2021.102375 · Cited by 27 · see citing works
Self-citationEvolution of Cooperation in Public Goods Games with Stochastic Opting-Out
Ginsberg, A. G., & Fu, F. (2018) · Games · doi:10.3390/g10010001 · Cited by 25 · see citing works
Tavoni, A. (2013) · Nature Climate Change · doi:10.1038/nclimate1962 · Cited by 19 · see citing works
Xue, L., Wang, W., & Zhang, M. (2020) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2020.122069 · Cited by 16 · see citing works
Lenton, T. M. (2013) · Nature Climate Change · doi:10.1038/nclimate2078 · Cited by 15 · see citing works
The Increased Risk of Joint Venture Promotes Social Cooperation
Wu, T., Fu, F., Zhang, Y., & Wang, L. (2013) · PLoS ONE · doi:10.1371/journal.pone.0063801 · Cited by 14 · see citing works
Sugiarto, H. S., Chung, N. N., Lai, C.-K., & Chew, L. Y. (2017) · Journal of Physics Communications · doi:10.1088/2399-6528/aa9b0e · Cited by 11 · see citing works
Inman, M. (2009) · Nature Climate Change · doi:10.1038/climate.2009.112 · Cited by 10 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Hardin G. The tragedy of the commons Science 162 1968 1243 1248 5699198
Cited by
Sorted by citations
Coevolutionary dynamics via adaptive feedback in collective-risk social dilemma game
Liu, L., Chen, X., & Szolnoki, A. (2023) · eLife · doi:10.7554/elife.82954 · Cited by 111 · see citing works
Self-citationAnalysis and visualization of accidents severity based on LightGBM-TPE
Li, K., Xu, H., & Liu, X. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.111987 · Cited by 112 · see citing works
Coevolutionary dynamics of population and institutional rewards in public goods games
Hua, S., & Liu, L. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.121579 · Cited by 78 · see citing works
Self-citationHan, T. A. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0036 · Cited by 63 · see citing works
Cooperation versus social welfare
Han, T. A., Song, Z., Cimpeanu, T., Duong, M. H., Krellner, M., Capraro, V., & Perc, M. (2025) · Physics of Life Reviews · doi:10.1016/j.plrev.2025.11.006 · Cited by 62 · see citing works
Evolutionary mechanisms that promote cooperation may not promote social welfare
Han, T. A., Duong, M. H., & Perc, M. (2024) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0547 · Cited by 58 · see citing works
Evolutionary game analysis of environmental pollution control under the government regulation
Zhou, K., Wang, Q., & Tang, J. (2022) · Scientific Reports · doi:10.1038/s41598-021-04458-3 · Cited by 54 · see citing works
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-citationCoevolutionary dynamics of collective cooperation and dilemma strength in a collective-risk game
Hua, S., Xu, M., Liu, L., & Chen, X. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.023313 · Cited by 42 · see citing works
Self-citationSynergistic effects of adaptive reward and reinforcement learning rules on cooperation
Wang, L., Fan, L., Zhang, L., Zou, R., & Wang, Z. (2023) · New Journal of Physics · doi:10.1088/1367-2630/acd26e · Cited by 40 · see citing works
Sun, Z., Chen, X., & Szolnoki, A. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3279094 · Cited by 36 · see citing works
Self-citationSocial diversity reduces the complexity and cost of fostering fairness
Cimpeanu, T., Stefano, A. D., Perret, C., & Han, T. A. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.113051 · Cited by 35 · see citing works
Limits to the Anthropocene: geopolitical conflict or cooperative governance?
Scheffran, J. (2023) · Frontiers in Political Science · doi:10.3389/fpos.2023.1190610 · Cited by 34 · 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-citationSuccess-driven opinion formation determines social tensions
Chica, M., Perc, M., & Santos, F. C. (2024) · iScience · doi:10.1016/j.isci.2024.109254 · Cited by 26 · see citing works
Options 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
Zhu, W., Pan, Q., Song, S., & He, M. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113519 · Cited by 23 · see citing works
Evolutionary dynamics of public goods game with tax-based rewarding cooperators
Shen, Y., Lei, W., Kang, H., Li, M., Sun, X., & Chen, Q. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114030 · Cited by 22 · see citing works
Competition of punishment and reward among inequity-averse individuals in spatial public goods games
Wang, X., Ding, R., Zhao, J., Chen, W., & Gu, C. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.111862 · Cited by 21 · see citing works
Dynamic sanctioning mechanism for cooperative multi-agent systems
Liu, L., Wang, L., Niu, W., & Hua, S. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.128873 · Cited by 20 · see citing works
Self-citationEnvironmental quality and population welfare in Markovian eco-evolutionary dynamics
Liu, F., & Wu, B. (2022) · Applied Mathematics and Computation · doi:10.1016/j.amc.2022.127309 · Cited by 20 · see citing works
Indirect 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-citationScheffran, J. (2025) · The anthropocene: Politik - economics - society - science · doi:10.1007/978-3-031-71807-6_8 · Cited by 18 · see citing works
Social exclusion with antisocial punishment in spatial public goods game
Sun, X., Han, L., Wang, M., Liu, S., & Shen, Y. (2023) · Physics Letters A · doi:10.1016/j.physleta.2023.128837 · Cited by 18 · see citing works
Liu, L., & Chen, X. (2022) · Applied Mathematics and Computation · doi:10.1016/j.amc.2022.127069 · Cited by 19 · see citing works
Self-citationCost optimisation of hybrid institutional incentives for promoting cooperation in finite populations
Duong, M. H., Durbac, C. M., & Han, T. A. (2023) · Journal of Mathematical Biology · doi:10.1007/s00285-023-02011-6 · Cited by 17 · see citing works
A reversed form of public goods game: equivalence and difference
Wang, C., & Szolnoki, A. (2022) · New Journal of Physics · doi:10.1088/1367-2630/acab25 · Cited by 15 · see citing works
Self-citationRewarding policies in an asymmetric game for sustainable tourism
Chica, M., Hernández, J. M., & Perc, M. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.128183 · Cited by 15 · see citing works
Both eyes open: Vigilant Incentives help auditors improve AI safety
Bova, P., Stefano, A. D., & Han, T. A. (2024) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad424c · Cited by 15 · see citing works
Trust AI regulation? Discerning users are vital to build trust and effective AI regulation
Alalawi, Z., Bova, P., Cimpeanu, T., Stefano, A. D., Duong, M. H., Domingos, E. F., Han, T. A., Krellner, M., Ogbo, N. B., Powers, S. T., et al. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129627 · Cited by 14 · 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
Evolution of cooperation driven by sampling reward
Xiao, J., Liu, L., Chen, X., & Szolnoki, A. (2023) · Journal of Physics Complexity · doi:10.1088/2632-072x/ad0208 · Cited by 14 · see citing works
Self-citationEvolution of commitment in the spatial public goods game through institutional incentives
Flores, L. S., & Han, T. A. (2024) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.128646 · Cited by 14 · see citing works
Reward and Punishment Mechanism with weighting enhances cooperation in evolutionary games
Zu, J., Xu, F., Jin, T., & Xiang, W. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128165 · Cited by 13 · see citing works
Wang, L., Liu, Y., Guo, R., Liang, Z., Liu, L., & Hua, S. (2024) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2024.0182 · Cited by 13 · see citing works
Self-citationYan, R., Xu, M., Liu, L., & Hua, S. (2024) · Physics Letters A · doi:10.1016/j.physleta.2024.129951 · Cited by 13 · see citing works
Self-citationStatistics of the number of equilibria in random social dilemma evolutionary games with mutation
Duong, M. H., & Han, T. A. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00181-0 · Cited by 13 · see citing works
Cooperation dynamics in collective risk games with endogenous endowments
Quan, J., Zhang, X. Y., Chen, W., & Wang, X. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0155724 · Cited by 12 · see citing works
Evolution of cooperation in multiplex networks through asymmetry between interaction and replacement
Inaba, M., & Akiyama, E. (2023) · Scientific Reports · doi:10.1038/s41598-023-37074-4 · Cited by 11 · see citing works
Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics
Mondal, S. S., Pathak, M. S., & Chakraborty, S. (2022) · Journal of Physics Complexity · doi:10.1088/2632-072x/ac6c6e · Cited by 11 · see citing works
Evolution of cooperation in a three-strategy game combining snowdrift and stag hunt games
Takesue, H. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129341 · Cited by 8 · see citing works
Synergy and Discount of Punishment in the Public Goods Game
Lv, S., Zhang, X., Zhong, A., Mi, J., & He, Q. (2021) · Physics Letters A · doi:10.1016/j.physleta.2022.127969 · Cited by 8 · see citing works
Wang, C., & Cui, W. (2022) · Frontiers in Public Health · doi:10.3389/fpubh.2022.881330 · Cited by 8 · see citing works
The Evolution of Cooperation in Spatial Public Goods Games Under a Risk-Transfer Mechanism
Ding, R., Wang, X., Zhao, J., Gu, C., & Wang, T. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113236 · Cited by 8 · see citing works
Determinants of successful mitigation in coupled social-climate dynamics
Shu, L., & Fu, F. (2023) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2023.0679 · Cited by 7 · see citing works
Zhou, X., Belloum, A. S. Z., Lees, M., van Engers, T., & de Laat, C. T. A. M. (2022) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2022.0393 · Cited by 7 · see citing works
Governance of risky public goods under the threat of ostracism
Hua, S., & Liu, L. (2023) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2023.133836 · Cited by 7 · see citing works
Self-citationThe impact of memory reputation-induced tax and reward allocation on spatial public goods games
Sun, X., Zhu, H., Kang, H., Bi, Y.-Z., Shen, Y., & Chen, Q. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.116298 · Cited by 6 · see citing works
Feng, Y., Yu, F., & Liu, Z. (2025) · Sustainability · doi:10.3390/su17083475 · Cited by 6 · see citing works
He, N., Wu, K., & Wang, Q. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113668 · Cited by 6 · see citing works
Yue, X., Durrani, S. K., Zhao, S., & Li, F. (2023) · Scientific Reports · doi:10.1038/s41598-023-47369-1 · Cited by 6 · see citing works
Duong, M. H., Durbac, C. M., & Han, T. A. (2024) · Bulletin of Mathematical Biology · doi:10.1007/s11538-024-01344-7 · Cited by 6 · see citing works
Nash Equilibrium in Macro-Task Crowdsourcing Systems With Collective-Effort-Dependent Rewarding
Xu, M., Chen, X., & Szolnoki, A. (2023) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2023.3347766 · Cited by 6 · see citing works
Self-citationAdaptive governance in collective risk social dilemmas
Xu, M., Hua, S., Liu, L., & Szolnoki, A. (2026) · Communications Physics · doi:10.1038/s42005-026-02574-y · Cited by 5 · see citing works
Self-citationThe evolution and social cost of herding mentality promote cooperation
Chica, M., Rand, W. M., & Santos, F. C. (2023) · iScience · doi:10.1016/j.isci.2023.107927 · Cited by 5 · see citing works
The coupling effect between the environment and strategies drives the emergence of group cooperation
Di, C., Zhou, Q., Shen, J., Wang, J., Zhou, R., & Wang, T. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.114138 · Cited by 5 · see citing works
Impact of dynamic compensation with resource feedback on the common pool resource game
Gao, L., Pan, Q., & He, M. (2024) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2024.114545 · Cited by 5 · see citing works
Wang, J., Yu, F., He, J., Chen, W., Xu, W., Dai, W., & Ming, Y. (2023) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2023.113187 · Cited by 5 · see citing works
Hybrid reward-punishment in feedback-evolving game for common resource governance
Lu, Z., Hua, S., Wang, L., & Liu, L. (2024) · Physical review. E · doi:10.1103/physreve.110.034301 · Cited by 4 · see citing works
Self-citationFast deliberation is related to unconditional behaviour in iterated Prisoners’ Dilemma experiments
Montero-Porras, E., Lenaerts, T., Gallotti, R., & Grujić, J. (2022) · Scientific Reports · doi:10.1038/s41598-022-24849-4 · Cited by 4 · see citing works
Evolutionary dynamics of information diffusion with sending-receiving interactions
Li, Z., Wang, Y., Ge, C., & Chen, X. (2025) · Applied Mathematical Modelling · doi:10.1016/j.apm.2025.116457 · Cited by 3 · see citing works
Self-citationA new electoral bottom-up model of institutional governance
Garrido, C. M., Santos, F. C., Domingos, E. F., Nunes, A., & Pacheco, J. M. (2025) · Scientific Reports · doi:10.1038/s41598-025-87322-y · Cited by 3 · see citing works
Takesue, H. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2025.129676 · Cited by 3 · see citing works
Revisiting institutional punishment in the N-person prisoner’s dilemma
Ishikawa, B. Y. S., & Fontanari, J. F. (2024) · Theory in Biosciences · doi:10.1007/s12064-024-00432-5 · Cited by 3 · see citing works
Evolution of cooperation under threshold public goods game
Gao, L., Pan, Q., & He, M. (2025) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0256927 · Cited by 2 · see citing works
Qian, J., Sun, X., Zhang, T., & Chai, Y. (2022) · Entropy · doi:10.3390/e24091289 · Cited by 2 · see citing works
Mintz, B., & Fu, F. (2022) · Mathematics · doi:10.3390/math10244818 · Cited by 2 · see citing works
The coordination of collective and individual solutions in risk-resistant scenarios
Qian, J., Zhang, T., Sun, X., & Chai, Y. (2023) · The European Physical Journal B · doi:10.1140/epjb/s10051-023-00487-1
A new simulation method in public goods games based on GPU matrix operations in lattice network
Han, Z., An, Y., Mao, Y., Hu, Q., & Ma, Y. (2024) · Physics Letters A · doi:10.1016/j.physleta.2024.130111
Shi, S., Wang, S., Yu, C., Mu, M., & Xie, Z. (2025) · Iranian Journal of Science · doi:10.1007/s40995-025-01784-3
Nikooeinejad, Z., Heydari, M., & Engwerda, J. C. (2025) · Computational Economics · doi:10.1007/s10614-025-11154-1
Duong, M. H., Durbac, C. M., & Han, T. A. (2026) · Dynamic Games and Applications · doi:10.1007/s13235-025-00696-6
Coevolution of cooperative behavior and collective risk via adaptive feedback in finite populations
Zhao, X., Hu, K., Tao, Y., Li, W., & Shi, L. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118473
Beyond cooperation and cost: Welfare-optimal incentives in structured populations
Duong, H. N., Ngo, L. Q. D., Nguyen, T., Nguyen, H. T., Song, Z., Duong, M. H., Trang, L. H., & Han, T. A. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118843
Evolution of cooperation and adaptive intervention under perceptual environmental bias
Lu, Z., Liu, S., Hua, S., Xu, M., Wang, L., Zhang, L., & Liu, L. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118965
Self-citationRevenue-feedback and the institutional governance of global risky commons
Pacheco, J. M., Garrido, C. M., & Domingos, E. F. (2026) · Journal of The Royal Society Interface · doi:10.1098/rsif.2026.0508
A new reputation-based levy and bidirectional subsidy mechanism in the networked trust game
Liu, Y., Wang, J., & Xia, C. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.132181
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
- Authors
- Sun, W., Liu, L., Chen, X., Szolnoki, A., & Vasconcelos, V. V.
- Affiliations
- University of Electronic Science and Technology of China (CN)
- Institute for Technical Physics and Materials Science (HU)
- University of Amsterdam (NL)
- Corresponding author
- Chen, Xiaojie
- Venue
- iScience
- Publisher
- Elsevier BV
- Published
- 2021-08
- Volume
- 24
- Issue
- 8
- Pages
- 102844
- ISSN
- 2589-0042 (ISSN-L)
- PMC
- PMC8334382
- OpenAlex
- W3180739853
- Cited by
- 80
- References
- 71
- Citations by year
- 2026: 8 · 2025: 13 · 2024: 12 · 2023: 26 · 2022: 19 · 2021: 2
- FWCI
- 20.44
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- iScience (publishedVersion, cc-by-nc-nd)
- PubMed Central (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- UvA-DARE (University of Amsterdam) (publishedVersion, cc-by-nc-nd)
- Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Fundamental Research Funds for the Central Universities
- National Natural Science Foundation of China (61976048, 62036002)
- 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
- commons governance, cooperative behavior, institutional incentives, free-riding, sustainability of cooperation
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