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However, this conclusion largely relies on the assumption that participation is compulsory. Here, we examine how zealots affect the evolution of cooperation in a generalized optional public goods game, where individuals can cooperate, defect, or opt out. Non-participants receive an external payoff and may also exert external effects on the public good. Using pairwise comparison dynamics in an infinite well-mixed population, we show that zealots do not necessarily promote cooperation. Cooperation is enhanced only at moderate zealot densities when non-participants negatively affect the public good. Otherwise, higher zealot densities or non-negative effects from non-participants lead zealots to undermine cooperation. These findings reveal a dual role of zealots, determined by their density and the external influence of non-participants on the public good.<\/jats:p>","DOI":"10.1063\/5.0352497","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T13:18:46Z","timestamp":1790083126000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Zealots can both promote and undermine cooperation in the generalized optional public goods game"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-8132-4351","authenticated-orcid":false,"given":"Yuting","family":"Dong","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Yunnan University of Finance and Economics 1 , Kunming, Yunnan 650221,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-8171-945X","authenticated-orcid":false,"given":"Shulan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Accounting and Auditing, Yunnan University of Finance and Economics 2 , Kunming, Yunnan 650221,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1203-9984","authenticated-orcid":false,"given":"Lei","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Yunnan University of Finance and Economics 1 , Kunming, Yunnan 650221,","place":["China"]},{"name":"School of Statistics and Mathematics and Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance 3 , Shanghai 201209,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"issue":"8","key":"2026092209184313300_c1","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.tics.2013.06.003","article-title":"Human cooperation","volume":"17","year":"2013","journal-title":"Trends Cogn. 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