{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:03:38Z","timestamp":1760144618292,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["JP23K05943","JP23K21017","JP21KK0027","JP23K25160"],"award-info":[{"award-number":["JP23K05943","JP23K21017","JP21KK0027","JP23K25160"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>\u201cPaying it forward\u201d is a behavior in which people help someone else because they were helped in the past. Although experimental evidence exists that indicates that real human beings often \u201cpay-it-forward\u201d even in the face of free-rider risks, the theoretical basis for the evolution of this behavior remains unclear. In this paper, we propose a game-theoretical model that explains how pay-it-forward behavior can evolve despite the temptation to free-ride. By assuming that human beings exhibit cognitive distortions, as predicted by prospect theory, and that free-riding is punished with a tiny probability, we demonstrate that pay-it-forward, alongside unconditional altruistic behavior, can evolve and effectively deter free-riding behavior.<\/jats:p>","DOI":"10.3390\/g15030016","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T03:23:47Z","timestamp":1714101827000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evolution of \u201cPay-It-Forward\u201d in the Presence of the Temptation to Free-Ride"],"prefix":"10.3390","volume":"15","author":[{"given":"Satoshi","family":"Uchida","sequence":"first","affiliation":[{"name":"Research Center for Ethi-Culture Studies, RINRI Institute, Tokyo 102-8561, Japan"},{"name":"High-Tech Research Center, Kokushikan University, Tokyo 154-8515, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4635-1389","authenticated-orcid":false,"given":"Tatsuya","family":"Sasaki","sequence":"additional","affiliation":[{"name":"Department of Community Development, Koriyama Women\u2019s College, Fukushima 963-8503, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7966-2629","authenticated-orcid":false,"given":"Hitoshi","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Faculty of Business Administration, Rissho University, Tokyo 141-8602, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9943-2668","authenticated-orcid":false,"given":"Isamu","family":"Okada","sequence":"additional","affiliation":[{"name":"Department of Business Administration, Soka University, Tokyo 192-8577, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5334","DOI":"10.1073\/pnas.0913149107","article-title":"Cooperative behavior cascades in human social networks","volume":"107","author":"Fowler","year":"2010","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1080\/17439760.2014.965269","article-title":"It\u2019s good to do good and receive good: The impact of a \u201cpay it forward\u201d style kindness intervention on giver and receiver well-being","volume":"10","author":"Pressman","year":"2015","journal-title":"J. Posit. Psychol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1098\/rspb.2006.0125","article-title":"Upstream reciprocity and the evolution of gratitude","volume":"274","author":"Nowak","year":"2007","journal-title":"Proc. R. Soc. B"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ostrom, E. (1990). Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press.","DOI":"10.1017\/CBO9780511807763"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Nowak, M.A. (2006). Evolutionary Dynamics, Harvard University Press.","DOI":"10.2307\/j.ctvjghw98"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sigmund, K. (2010). The Calculus of Selfishness, Princeton University Press.","DOI":"10.1515\/9781400832255"},{"key":"ref_7","unstructured":"Nowak, M.A., and Highfield, R. (2011). Super Cooperators, Free Press."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bowls, S., and Gintis, H. (2011). A Cooperative Species, Princeton University Press.","DOI":"10.23943\/princeton\/9780691151250.003.0001"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yamagishi, T. (2011). Trust: The Evolutionary Game of Mind and Society, Springer.","DOI":"10.1007\/978-4-431-53936-0"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.05.004","article-title":"Statistical physics of human cooperation","volume":"68","author":"Perc","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Uchida, S., Yamamoto, H., Okada, I., and Sasaki, T. (2019). Evolution of Cooperation with Peer Punishment under Prospect Theory. Games, 10.","DOI":"10.3390\/g10010011"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1914185","article-title":"Prospect theory: Analysis of decision under risk","volume":"47","author":"Kahneman","year":"1979","journal-title":"Econometrica"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.2307\/2937956","article-title":"Loss aversion in riskless choice: A reference-dependent model","volume":"106","author":"Tversky","year":"1991","journal-title":"Q. J. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wakker, P.P. (2010). Prospect Theory: For Risk and Ambiguity, Cambridge University Press.","DOI":"10.1017\/CBO9780511779329"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gilboa, I. (2009). Theory of Decision under Uncertainty, Cambridge University Press.","DOI":"10.1017\/CBO9780511840203"},{"key":"ref_16","unstructured":"Gilboa, I. (2010). Making Better Decisions: Decision Theory in Practice, John Wiley and Sons."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1126\/science.185.4157.1124","article-title":"Judgement under uncertainty: Heuristics and biases","volume":"185","author":"Tversky","year":"1974","journal-title":"Science"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"277","DOI":"10.2307\/1912631","article-title":"Expected utility analysis without the independence axiom","volume":"50","author":"Machina","year":"1982","journal-title":"Econometrica"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1037\/0033-295X.90.4.293","article-title":"Extensional vs. intuitive reasoning: The conjunction fallacy in probability judging","volume":"90","author":"Tversky","year":"1983","journal-title":"Psychol. Rev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"571","DOI":"10.2307\/1911053","article-title":"Subjective probability and expected utility without additivity","volume":"57","author":"Schmeidler","year":"1989","journal-title":"Econometrica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0304-4068(89)90018-9","article-title":"Maxmin expected utility with a non-unique prior","volume":"18","author":"Gilboa","year":"1989","journal-title":"J. Math. Econ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1257\/jel.38.2.332","article-title":"Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk","volume":"38","author":"Starmer","year":"2000","journal-title":"J. Econ. Lit."},{"key":"ref_23","first-page":"57","article-title":"Research on Enterprise Radical Technology Innovation Behavior\u2014Evolutionary Game Analysis Based on Prospect Theory","volume":"39","author":"Yang","year":"2020","journal-title":"J. Ind. Technol. Econ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"13357","DOI":"10.1007\/s00500-022-07527-5","article-title":"Evolutionary Game Analysis of Enterprise Carbon Emission Regulation Based on Prospect Theory","volume":"26","author":"Sun","year":"2022","journal-title":"Soft Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"125929","DOI":"10.1016\/j.jclepro.2021.125929","article-title":"Prospect Theory in an Evolutionary Game: Construction of Watershed Ecological Compensation System in Taihu Lake Basin","volume":"291","author":"Shen","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Li, Y., and Zhang, J. (2024). Evolutionary Game Analysis of Low-Carbon Incentive Behaviour of Power Battery Recycling Based on Prospect Theory. Sustainability, 16.","DOI":"10.3390\/su16072793"},{"key":"ref_27","unstructured":"Sigmund, K. (2017). Games of Life, Dover Publications."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ferreira, P.L., Santos, F.C., and Pequito, S. (2021). Risk sensitivity and theory of mind in human coordination. PLoS Comput. Biol., 17.","DOI":"10.1371\/journal.pcbi.1009167"},{"key":"ref_29","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_30","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1038\/nature04131","article-title":"Evolution of indirect reciprocity","volume":"437","author":"Nowak","year":"2005","journal-title":"Nature"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1006\/jtbi.1998.0775","article-title":"The dynamics of indirect reciprocity","volume":"194","author":"Nowak","year":"1998","journal-title":"J. Theor. Biol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1098\/rspb.2000.1573","article-title":"Evolution of cooperation through indirect reciprocity","volume":"268","author":"Leimar","year":"2001","journal-title":"Proc. R. Soc. B"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.jtbi.2004.06.005","article-title":"How should we define goodness?\u2014Reputation dynamics in indirect reciprocity","volume":"231","author":"Ohtsuki","year":"2004","journal-title":"J. Theor. Biol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.jtbi.2005.08.008","article-title":"The leading eight: Social norms that can maintain cooperation by indirect reciprocity","volume":"239","author":"Ohtsuki","year":"2006","journal-title":"J. Theor. Biol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"41870","DOI":"10.1038\/srep41870","article-title":"The evolution of conditional moral assessment in indirect reciprocity","volume":"7","author":"Sasaki","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"14","DOI":"10.3389\/fphy.2018.00014","article-title":"A theoretical approach to norm ecosystems: Two adaptive architectures of indirect reciprocity show different paths to the evolution of cooperation","volume":"6","author":"Uchida","year":"2018","journal-title":"Front. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1019422","DOI":"10.3389\/fphy.2022.1019422","article-title":"Exploring norms indispensable for both emergence and maintenance of cooperation in indirect reciprocity","volume":"10","author":"Yamamoto","year":"2022","journal-title":"Front. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"e2300544120","DOI":"10.1073\/pnas.2300544120","article-title":"Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment","volume":"120","author":"Fujimoto","year":"2023","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.jtbi.2010.05.010","article-title":"Upstream reciprocity in heterogeneous networks","volume":"265","author":"Iwagami","year":"2010","journal-title":"J. Theor. Biol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1098\/rspb.2004.2988","article-title":"Evolution of cooperation by generalized reciprocity","volume":"272","author":"Pfeiffer","year":"2005","journal-title":"Proc. R. Soc. B"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Okada, I. (2020). A review of theoretical studies on indirect reciprocity. Games, 11.","DOI":"10.3390\/g11030027"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1016\/j.jtbi.2006.08.018","article-title":"Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation","volume":"244","author":"Ohtsuki","year":"2007","journal-title":"J. Theor. Biol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jtbi.2009.11.013","article-title":"The competition of assessment rules for indirect reciprocity","volume":"263","author":"Uchida","year":"2010","journal-title":"J. Theor. Biol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1038\/s41598-021-04033-w","article-title":"Social norms in indirect reciprocity with ternary reputations","volume":"12","author":"Murase","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1037\/0022-3514.51.1.110","article-title":"The provision of a sanctioning system as a public good","volume":"51","author":"Yamagishi","year":"1986","journal-title":"J. Personal. Soc. Psychol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0162-3095(92)90032-Y","article-title":"Punishment allows the evolution of cooperation (or anything else) in sizable groups","volume":"13","author":"Boyd","year":"1992","journal-title":"Ethol. Sociobiol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1038\/452297a","article-title":"Human behaviour: Punisher pays","volume":"452","author":"Milinski","year":"2008","journal-title":"Nature"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.jebo.2009.03.022","article-title":"Cooperation under alternative punishment institutions: An experiment","volume":"71","author":"Casari","year":"2009","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1257\/aer.99.4.1335","article-title":"Institution formation in public goods games","volume":"99","author":"Kosfeld","year":"2009","journal-title":"Am. Econ. Rev."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1038\/nature09203","article-title":"Social learning promotes institutions for governing the commons","volume":"466","author":"Sigmund","year":"2010","journal-title":"Nature"},{"key":"ref_51","first-page":"3716","article-title":"An economic experiment reveals that humans prefer pool punishment to maintain the commons","volume":"279","author":"Traulsen","year":"2012","journal-title":"Proc. Biol. Sci."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/3\/16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:33:05Z","timestamp":1760106785000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/15\/3\/16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,25]]},"references-count":51,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["g15030016"],"URL":"https:\/\/doi.org\/10.3390\/g15030016","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2024,4,25]]}}}