{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T04:54:18Z","timestamp":1778648058082,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,8]],"date-time":"2020-02-08T00:00:00Z","timestamp":1581120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61663046, 61876166"],"award-info":[{"award-number":["61663046, 61876166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Foundation of Key Laboratory of Software Engineering of Yunnan Province","award":["2015SE204"],"award-info":[{"award-number":["2015SE204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The reconnection of broken edges is an effective way to avoid drawback for the commons in past studies. Inspired by this, we proposed a public goods game model under the edges rules, where we evaluate the weight of edges by their nodes\u2019 payoff. The results proved that the game obtains a larger range of cooperation with a small gain factor by this proposed model by consulting Monte Carlo simulations (MCS) and real experiments. Furthermore, as the following the course of game and discussing the reason of cooperation, in the research, we found that the distribution entropy of the excess average degree is able to embody and predict the presence of cooperation.<\/jats:p>","DOI":"10.3390\/e22020199","type":"journal-article","created":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T11:48:51Z","timestamp":1581335331000},"page":"199","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Co-Evolution of Complex Network Public Goods Game under the Edges Rules"],"prefix":"10.3390","volume":"22","author":[{"given":"Xingping","family":"Sun","sequence":"first","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yibing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5466-7092","authenticated-orcid":false,"given":"Hongwei","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoyu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingyi","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software, Yunnan University, Kunming 650000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.econlet.2006.12.031","article-title":"Team competition and the public goods game","volume":"96","author":"Tan","year":"2007","journal-title":"Econ. 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