{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T01:40:20Z","timestamp":1769823620899,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,12,17]],"date-time":"2023-12-17T00:00:00Z","timestamp":1702771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["72131003"],"award-info":[{"award-number":["72131003"]}]},{"name":"National Science Foundation of China","award":["72103021"],"award-info":[{"award-number":["72103021"]}]},{"name":"National Science Foundation of China","award":["72091511"],"award-info":[{"award-number":["72091511"]}]},{"name":"National Science Foundation of China","award":["Z220001"],"award-info":[{"award-number":["Z220001"]}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["72131003"],"award-info":[{"award-number":["72131003"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["72103021"],"award-info":[{"award-number":["72103021"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["72091511"],"award-info":[{"award-number":["72091511"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["Z220001"],"award-info":[{"award-number":["Z220001"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Scholarship Council","award":["72131003"],"award-info":[{"award-number":["72131003"]}]},{"name":"China Scholarship Council","award":["72103021"],"award-info":[{"award-number":["72103021"]}]},{"name":"China Scholarship Council","award":["72091511"],"award-info":[{"award-number":["72091511"]}]},{"name":"China Scholarship Council","award":["Z220001"],"award-info":[{"award-number":["Z220001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group\u2019s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people\u2019s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).<\/jats:p>","DOI":"10.3390\/g14060076","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T10:04:47Z","timestamp":1702893887000},"page":"76","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Cooperation and Coordination in Threshold Public Goods Games with Asymmetric Players"],"prefix":"10.3390","volume":"14","author":[{"given":"Xinmiao","family":"An","sequence":"first","affiliation":[{"name":"Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yali","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Systems Science, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5820-7256","authenticated-orcid":false,"given":"Xiaomin","family":"Wang","sequence":"additional","affiliation":[{"name":"Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0972-3240","authenticated-orcid":false,"given":"Boyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jebo.2003.11.010","article-title":"The impact of endowment heterogeneity and origin on public good contributions: Evidence from the lab","volume":"57","author":"Cherry","year":"2005","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.econlet.2016.07.015","article-title":"Endowment inequality in public goods games: A re-examination","volume":"146","author":"Heap","year":"2016","journal-title":"Econ. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.jebo.2020.07.013","article-title":"We, the rich: Inequality, identity and cooperation","volume":"178","author":"Martinangeli","year":"2020","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF01048198","article-title":"Heterogenous demand for public goods: Behavior in the voluntary contributions mechanism","volume":"85","author":"Fisher","year":"1995","journal-title":"Public Choice"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1007\/s00355-012-0658-2","article-title":"Public goods provision by asymmetric agents: Experimental evidence","volume":"40","author":"McGinty","year":"2013","journal-title":"Soc. Choice Welf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.geb.2012.10.001","article-title":"Enforcement of contribution norms in public good games with heterogeneous populations","volume":"77","author":"Reuben","year":"2013","journal-title":"Games Econ. Behav."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jebo.2014.11.009","article-title":"Heterogeneity and cooperation: The role of capability and valuation on public goods provision","volume":"109","year":"2015","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1038\/s41586-019-1488-5","article-title":"Social dilemmas among unequals","volume":"572","author":"Hauser","year":"2019","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0047-2727(84)90023-9","article-title":"Participation and the provision of discrete public goods: A strategic analysis","volume":"24","author":"Palfrey","year":"1984","journal-title":"J. Public Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s13235-015-0172-0","article-title":"Option fund market dynamics for threshold public goods","volume":"7","author":"Dragicevic","year":"2017","journal-title":"Dyn. Games Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"20210504","DOI":"10.1098\/rstb.2021.0504","article-title":"Cooperation and coordination in heterogeneous populations","volume":"378","author":"Wang","year":"2023","journal-title":"Philos. Trans. R. Soc. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1006\/obhd.1993.1029","article-title":"Incremental contribution in step-level public goods games with asymmetric players","volume":"55","author":"Rapoport","year":"1993","journal-title":"Organ. Behav. Hum. Decis. Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s11127-016-0321-z","article-title":"Full agreement and the provision of threshold public goods","volume":"166","author":"Alberti","year":"2016","journal-title":"Public Choice"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2291","DOI":"10.1073\/pnas.0709546105","article-title":"The collective-risk social dilemma and the prevention of simulated dangerous climate change","volume":"105","author":"Milinski","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1007\/s10584-011-0319-y","article-title":"Cooperative interaction of rich and poor can be catalysed by intermediate climate targets","volume":"109","author":"Milinski","year":"2011","journal-title":"Clim. Change"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11825","DOI":"10.1073\/pnas.1102493108","article-title":"Inequality, communication, and the avoidance of disastrous climate change in a public goods game","volume":"108","author":"Tavoni","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s10640-017-0123-x","article-title":"Climate negotiations in the lab: A threshold public goods game with heterogeneous contributions costs and non-binding voting","volume":"70","author":"Feige","year":"2018","journal-title":"Environ. Resour. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1038\/s41562-018-0418-0","article-title":"Differentiated responsibilities and prosocial behavior in climate change mitigation","volume":"2","author":"Kline","year":"2018","journal-title":"Nat. Hum. Behav."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.oneear.2021.07.006","article-title":"Financial incentives to poor countries promote net emissions reductions in multilateral climate agreements","volume":"4","author":"Dong","year":"2021","journal-title":"One Earth"},{"key":"ref_20","first-page":"806","article-title":"Global emission reduction problem with heterogenous agents","volume":"59","author":"Huang","year":"2023","journal-title":"J. Beijing Norm. Univ. Nat. Sci."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/14\/6\/76\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:40:27Z","timestamp":1760132427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/14\/6\/76"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,17]]},"references-count":20,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["g14060076"],"URL":"https:\/\/doi.org\/10.3390\/g14060076","relation":{},"ISSN":["2073-4336"],"issn-type":[{"value":"2073-4336","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,17]]}}}