{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T06:38:21Z","timestamp":1762065501991,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T00:00:00Z","timestamp":1663027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2021YFF0900800"],"award-info":[{"award-number":["2021YFF0900800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Game theory provides a powerful means to study human cooperation and better understand cooperation-facilitating mechanisms in general. In classical game-theoretic models, an increase in group cooperation constantly increases people\u2019s gains, implying that individual gains are a continuously varying function of the cooperation rate. However, this is inconsistent with the increasing number of risk-resistant scenarios in reality. A risk-resistant scenario means once a group does not successfully resist the risk, all individuals lose their resources, such as a community coping with COVID-19 and a village resisting a flood. In other words, individuals\u2019 gains are segmented about the collaboration rate. This paper builds a risk-resistant model to explore whether punishment still promotes collaboration when people resist risk. The results show that central and peer punishments can both encourage collaboration but with different characteristics under different risk-resistant scenarios. Specifically, central punishment constrains the collaboration motivated by peer punishment regardless of risk, while peer punishment limits the collaboration induced by central punishment only when the risk is high. Our findings provide insights into the balance between peer punishment from public autonomy and central punishment from central governance, and the proposed model paves the way for the development of richer risk-resistant models.<\/jats:p>","DOI":"10.3390\/e24091289","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T21:06:52Z","timestamp":1663103212000},"page":"1289","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Authority or Autonomy? Exploring Interactions between Central and Peer Punishments in Risk-Resistant Scenarios"],"prefix":"10.3390","volume":"24","author":[{"given":"Jun","family":"Qian","sequence":"first","affiliation":[{"name":"National Engineering Laboratory for E-Commerce Technologies, Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Sun","sequence":"additional","affiliation":[{"name":"National Engineering Laboratory for E-Commerce Technologies, Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tongda","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yueting","family":"Chai","sequence":"additional","affiliation":[{"name":"National Engineering Laboratory for E-Commerce Technologies, Department of Automation, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1016\/j.jclepro.2018.12.081","article-title":"From nonrenewable to renewable energy and its impact on economic growth: The role of research & development expenditures in Asia-Pacific Economic Cooperation countries","volume":"212","author":"Zafar","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101271","DOI":"10.1016\/j.chieco.2019.01.010","article-title":"Role of China in the development of trade and FDI cooperation with BRICS countries","volume":"57","author":"Gusarova","year":"2019","journal-title":"China Econ. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"112673","DOI":"10.1016\/j.enpol.2021.112673","article-title":"Economic gains from global cooperation in fulfilling climate pledges","volume":"160","author":"Thube","year":"2022","journal-title":"Energy Policy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"112438","DOI":"10.1016\/j.enpol.2021.112438","article-title":"China\u2019s Belt & Road Initiative coal power cooperation: Transitioning toward low-carbon development","volume":"156","author":"Lin","year":"2021","journal-title":"Energy Policy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.trd.2018.08.010","article-title":"Quantifying the environmental and economic benefits of cooperation: A case study in temperature-controlled food logistics","volume":"65","author":"Stellingwerf","year":"2018","journal-title":"Transp. Res. Part Transp. Environ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"105679","DOI":"10.1016\/j.worlddev.2021.105679","article-title":"South-South cooperation and the re-politicization of development in health","volume":"149","year":"2022","journal-title":"World Dev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1016\/j.jiph.2020.05.020","article-title":"Coronavirus disease of 2019 (COVID-19) in the Gulf Cooperation Council (GCC) countries: Current status and management practices","volume":"13","author":"Alandijany","year":"2020","journal-title":"J. Infect. Public Health"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"112999","DOI":"10.1016\/j.socscimed.2020.112999","article-title":"Cross-sectoral cooperation at the ministerial level in three Nordic countries\u2014With a focus on health inequalities","volume":"256","author":"Guldbrandsson","year":"2020","journal-title":"Soc. Sci. Med."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.evolhumbehav.2021.04.002","article-title":"Do descriptive social norms drive peer punishment? Conditional punishment strategies and their impact on cooperation","volume":"42","author":"Li","year":"2021","journal-title":"Evol. Hum. Behav."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.evolhumbehav.2007.04.001","article-title":"Punishing free riders: Direct and indirect promotion of cooperation","volume":"28","author":"Shinada","year":"2007","journal-title":"Evol. Hum. Behav."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yan, R., Peng, L., Xie, Y., and Wang, X. (2022). Rough Set-Game Theory Information Mining Model Considering Opponents\u2019 Information. Electronics, 11.","DOI":"10.3390\/electronics11020244"},{"key":"ref_12","first-page":"2020028","article-title":"The language of cooperation: Reputation and honest signalling","volume":"376","author":"Balliet","year":"2021","journal-title":"Philos. Trans. R. Soc. Biol. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5452","DOI":"10.1038\/s41467-021-25734-w","article-title":"Evidence from a long-term experiment that collective risks change social norms and promote cooperation","volume":"12","author":"Szekely","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-020-17286-2","article-title":"Direct and indirect punishment of norm violations in daily life","volume":"11","author":"Molho","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1038\/nature07601","article-title":"Indirect reciprocity provides only a narrow margin of efficiency for costly punishment","volume":"457","author":"Ohtsuki","year":"2009","journal-title":"Nature"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"20200880","DOI":"10.1098\/rsif.2020.0880","article-title":"Mathematical foundations of moral preferences","volume":"18","author":"Capraro","year":"2021","journal-title":"J. R. Soc. Interface"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8693","DOI":"10.1038\/ncomms9693","article-title":"Cooperation is related to dispersal patterns in Sino-Tibetan populations","volume":"6","author":"Wu","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4939","DOI":"10.1038\/ncomms5939","article-title":"Humans display a \u2018cooperative phenotype\u2019 that is domain general and temporally stable","volume":"5","author":"Peysakhovich","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1038\/s41562-021-01170-0","article-title":"Generous with individuals and selfish to the masses","volume":"6","author":"Ritschel","year":"2021","journal-title":"Nat. Hum. Behav."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20211021","DOI":"10.1098\/rspb.2021.1021","article-title":"Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner\u2019s Dilemma","volume":"288","author":"Kim","year":"2021","journal-title":"Proc. R. Soc. Biol. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1038\/s41562-018-0454-9","article-title":"Experience with anonymous interactions reduces intuitive cooperation","volume":"2","author":"McAuliffe","year":"2018","journal-title":"Nat. Hum. Behav."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"20200293","DOI":"10.1098\/rstb.2020.0293","article-title":"Reputation and punishment sustain cooperation in the optional public goods game","volume":"376","author":"Podder","year":"2021","journal-title":"Philos. Trans. R. Soc. Biol. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms1442","article-title":"The evolution of antisocial punishment in optional public goods games","volume":"2","author":"Rand","year":"2011","journal-title":"Nat. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/nature01986","article-title":"Volunteering leads to rock-paper-scissors dynamics in a public goods game","volume":"425","author":"Semmann","year":"2003","journal-title":"Nature"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1038\/415137a","article-title":"Altruistic punishment in humans","volume":"415","author":"Fehr","year":"2002","journal-title":"Nature"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lindig-Le\u00f3n, C., Schmid, G., and Braun, D.A. (2021). Bounded rational response equilibria in human sensorimotor interactions. Proc. R. Soc. Biol. Sci., 288.","DOI":"10.1098\/rspb.2021.2094"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3976","DOI":"10.1038\/ncomms4976","article-title":"Extortion subdues human players but is finally punished in the prisoner\u2019s dilemma","volume":"5","author":"Hilbe","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3567","DOI":"10.1038\/s41467-021-23783-9","article-title":"Adherence to public institutions that foster cooperation","volume":"12","author":"Radzvilavicius","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1038\/s41467-020-20709-9","article-title":"Group-level cooperation in chimpanzees is shaped by strong social ties","volume":"12","author":"Samuni","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"102844","DOI":"10.1016\/j.isci.2021.102844","article-title":"Combination of institutional incentives for cooperative governance of risky commons","volume":"24","author":"Sun","year":"2021","journal-title":"iScience"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"5161","DOI":"10.1038\/s41467-020-18896-6","article-title":"Self-reliance crowds out group cooperation and increases wealth inequality","volume":"11","author":"Gross","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_32","first-page":"2629","article-title":"Collapse and rescue of cooperation in evolving dynamic networks","volume":"9","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1038\/s41562-018-0368-6","article-title":"Conjoining uncooperative societies facilitates evolution of cooperation","volume":"2","author":"Fotouhi","year":"2018","journal-title":"Nat. Hum. Behav."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2954","DOI":"10.1038\/s41467-018-05259-5","article-title":"Exploiting a cognitive bias promotes cooperation in social dilemma experiments","volume":"9","author":"Wang","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1126\/science.1133755","article-title":"Five rules for the evolution of cooperation","volume":"314","author":"Nowak","year":"2006","journal-title":"Science"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"104096","DOI":"10.1016\/j.jesp.2020.104096","article-title":"Different punishment systems in a public goods game with asymmetric endowments","volume":"93","author":"Nockur","year":"2021","journal-title":"J. Exp. Soc. Psychol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1007\/s40974-020-00198-8","article-title":"Government regulation and enterprise decision in China remanufacturing industry: Evidence from evolutionary game theory","volume":"6","author":"Chen","year":"2021","journal-title":"Energy Ecol. Environ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1038\/s41467-020-15661-7","article-title":"The effects of contemporaneous peer punishment on cooperation with the future","volume":"11","author":"Lohse","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1038\/s41562-019-0707-2","article-title":"People prefer coordinated punishment in cooperative interactions","volume":"3","author":"Molleman","year":"2019","journal-title":"Nat. Hum. Behav."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1038\/nature05229","article-title":"The efficient interaction of indirect reciprocity and costly punishment","volume":"444","author":"Rockenbach","year":"2006","journal-title":"Nature"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.jebo.2021.03.004","article-title":"Pool punishment in public goods games: How do sanctioners\u2019 incentives affect us?","volume":"185","author":"Alventosa","year":"2021","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8917","DOI":"10.1038\/srep08917","article-title":"Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations","volume":"5","author":"Sasaki","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jtbi.2014.04.019","article-title":"Sanctions as honest signals\u2014The evolution of pool punishment by public sanctioning institutions","volume":"356","author":"Schoenmakers","year":"2014","journal-title":"J. Theor. Biol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"15792","DOI":"10.1038\/s41598-021-95303-0","article-title":"Peer pressure induced punishment resolves social dilemma on interdependent networks","volume":"11","author":"Hu","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"8211","DOI":"10.1038\/s41598-020-64930-4","article-title":"The role of peer reward and punishment for public goods problems in a localized society","volume":"10","author":"Ozono","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_46","first-page":"1759","article-title":"Individual heterogeneity and costly punishment: A volunteer\u2019s dilemma","volume":"280","author":"Przepiorka","year":"2013","journal-title":"Proc. R. Soc. Biol. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jebo.2020.10.005","article-title":"Uncovering the heterogeneity behind cross-cultural variation in antisocial punishment","volume":"180","author":"Bruhin","year":"2020","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"112827","DOI":"10.1016\/j.jenvman.2021.112827","article-title":"Evaluation of regional transport of PM2.5 during severe atmospheric pollution episodes in the western Yangtze River Delta, China","volume":"293","author":"Sulaymon","year":"2021","journal-title":"J. Environ. Manag."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jrurstud.2020.05.008","article-title":"Water resources conservation and rural livelihoods in protected areas of central Mexico","volume":"78","author":"Figueroa","year":"2020","journal-title":"J. Rural. Stud."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"111293","DOI":"10.1016\/j.envres.2021.111293","article-title":"Effects of short- and long-term exposure to atmospheric pollution on COVID-19 risk and fatality: Analysis of the first epidemic wave in northern Italy","volume":"199","author":"Ho","year":"2021","journal-title":"Environ. Res."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Tonnoir, A., Ciotir, I., Scutariu, A.L., and Dospinescu, O. (2021). A Model for the Optimal Investment Strategy in the Context of Pandemic Regional Lockdown. Mathematics, 9.","DOI":"10.3390\/math9091058"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Yan, H., Wei, H., and Wei, M. (2021). Exploring Tourism Recovery in the Post-COVID-19 Period: An Evolutionary Game Theory Approach. Sustainability, 13.","DOI":"10.3390\/su13169162"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"105431","DOI":"10.1016\/j.eneco.2021.105431","article-title":"Impact of COVID-19 on stock price crash risk: Evidence from Chinese energy firms","volume":"101","author":"Huang","year":"2021","journal-title":"Energy Econ."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1038\/s41893-021-00781-9","article-title":"Nature inequity and higher COVID-19 case rates in less-green neighbourhoods in the United States","volume":"4","author":"Spotswood","year":"2021","journal-title":"Nat. Sustain."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1126\/science.1153808","article-title":"Antisocial Punishment Across Societies","volume":"319","author":"Herrmann","year":"2008","journal-title":"Science"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/9\/1289\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:30:40Z","timestamp":1760142640000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/9\/1289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,13]]},"references-count":55,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["e24091289"],"URL":"https:\/\/doi.org\/10.3390\/e24091289","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,9,13]]}}}