{"id":"https://openalex.org/W2780400403","doi":"https://doi.org/10.3390/e20010015","title":"Robust Consensus of Networked Evolutionary Games with Attackers and Forbidden Profiles \u2020","display_name":"Robust Consensus of Networked Evolutionary Games with Attackers and Forbidden Profiles \u2020","publication_year":2017,"publication_date":"2017-12-29","ids":{"openalex":"https://openalex.org/W2780400403","doi":"https://doi.org/10.3390/e20010015","mag":"2780400403","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265105"},"language":"en","primary_location":{"id":"doi:10.3390/e20010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20010015","pdf_url":"https://www.mdpi.com/1099-4300/20/1/15/pdf?version=1514889283","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/1/15/pdf?version=1514889283","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087490419","display_name":"Yalu Li","orcid":"https://orcid.org/0000-0003-2886-8736"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yalu Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089351894","display_name":"Xueying Ding","orcid":"https://orcid.org/0000-0003-3685-5855"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xueying Ding","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100453276","display_name":"Haitao Li","orcid":"https://orcid.org/0000-0001-5322-5375"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haitao Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China;","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100453276"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.2412,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91850156,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"1","first_page":"15","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9528785943984985},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.7222479581832886},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6993893980979919},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5998035669326782},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5960745215415955},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5593546628952026},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.471116304397583},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4601789712905884},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.43993908166885376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.370635986328125},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24813702702522278},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.2364327311515808},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16523540019989014},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.10317623615264893}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9528785943984985},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7222479581832886},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6993893980979919},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5998035669326782},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5960745215415955},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5593546628952026},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.471116304397583},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4601789712905884},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.43993908166885376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.370635986328125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24813702702522278},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.2364327311515808},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16523540019989014},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.10317623615264893},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e20010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20010015","pdf_url":"https://www.mdpi.com/1099-4300/20/1/15/pdf?version=1514889283","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33265105","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265105","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:78be1541c1d64c3db453911ebe8717eb","is_oa":true,"landing_page_url":"https://doaj.org/article/78be1541c1d64c3db453911ebe8717eb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 20, Iss 1, p 15 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/1/15/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e20010015","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 20; Issue 1; Pages: 15","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7512187","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512187","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e20010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20010015","pdf_url":"https://www.mdpi.com/1099-4300/20/1/15/pdf?version=1514889283","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1840156515","display_name":null,"funder_award_id":"JQ201613","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G242850823","display_name":null,"funder_award_id":"JQ201613","funder_id":"https://openalex.org/F4320334121","funder_display_name":"Natural Science Fund for Distinguished Young Scholars of Shandong Province"},{"id":"https://openalex.org/G2802911279","display_name":null,"funder_award_id":"Young","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3020716557","display_name":null,"funder_award_id":"61503225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3203987162","display_name":null,"funder_award_id":"6150322","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5897711184","display_name":null,"funder_award_id":"61374065, 61503225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7742015313","display_name":null,"funder_award_id":"JQ201613","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G8795705117","display_name":null,"funder_award_id":"61374065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320334121","display_name":"Natural Science Fund for Distinguished Young Scholars of Shandong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2780400403.pdf","grobid_xml":"https://content.openalex.org/works/W2780400403.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W150105584","https://openalex.org/W567151721","https://openalex.org/W821019010","https://openalex.org/W1498617765","https://openalex.org/W1910803460","https://openalex.org/W1967829443","https://openalex.org/W1968994121","https://openalex.org/W1970601741","https://openalex.org/W1971318969","https://openalex.org/W1981094067","https://openalex.org/W1993183252","https://openalex.org/W1998278502","https://openalex.org/W1999160177","https://openalex.org/W2000929155","https://openalex.org/W2003127754","https://openalex.org/W2004239486","https://openalex.org/W2025490132","https://openalex.org/W2030235975","https://openalex.org/W2031177601","https://openalex.org/W2033041501","https://openalex.org/W2043307254","https://openalex.org/W2044787085","https://openalex.org/W2045077417","https://openalex.org/W2071953091","https://openalex.org/W2073458555","https://openalex.org/W2073599364","https://openalex.org/W2090408760","https://openalex.org/W2099540651","https://openalex.org/W2106309139","https://openalex.org/W2111250529","https://openalex.org/W2131885414","https://openalex.org/W2147037042","https://openalex.org/W2149869214","https://openalex.org/W2153020797","https://openalex.org/W2202757959","https://openalex.org/W2297307567","https://openalex.org/W2339651028","https://openalex.org/W2375265599","https://openalex.org/W2397970027","https://openalex.org/W2486512961","https://openalex.org/W2582548704","https://openalex.org/W2591095277","https://openalex.org/W2610723735","https://openalex.org/W2618208446","https://openalex.org/W2754558971","https://openalex.org/W2766894369","https://openalex.org/W2774059279","https://openalex.org/W2774673689","https://openalex.org/W3098354597","https://openalex.org/W3104180001","https://openalex.org/W6606218254","https://openalex.org/W6645554118"],"related_works":["https://openalex.org/W2136512912","https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W149700981","https://openalex.org/W2513478072"],"abstract_inverted_index":{"Using":[0],"the":[1,9,38,49,66,84,103],"algebraic":[2,24,39],"state":[3,80],"space":[4],"representation,":[5],"this":[6],"paper":[7],"studies":[8],"robust":[10,50,59,67,85],"consensus":[11,86],"of":[12,53,58,87],"networked":[13],"evolutionary":[14],"games":[15],"(NEGs)":[16],"with":[17,30,89],"attackers":[18,31,90],"and":[19,32,43,91],"forbidden":[20,33,92],"profiles.":[21,34,93],"Firstly,":[22],"an":[23,95],"form":[25],"is":[26,46,62,76,98],"established":[27],"for":[28,48,83],"NEGs":[29,88],"Secondly,":[35],"based":[36,70],"on":[37,71],"form,":[40],"a":[41,56,73],"necessary":[42],"sufficient":[44],"condition":[45],"presented":[47],"constrained":[51,68],"reachability":[52],"NEGs.":[54],"Thirdly,":[55],"series":[57],"reachable":[60],"sets":[61],"constructed":[63],"by":[64],"using":[65],"reachability,":[69],"which":[72],"constructive":[74],"procedure":[75],"proposed":[77],"to":[78,100],"design":[79],"feedback":[81],"controls":[82],"Finally,":[94],"illustrative":[96],"example":[97],"given":[99],"show":[101],"that":[102],"main":[104],"results":[105],"are":[106],"effective.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
