{"id":"https://openalex.org/W4407948499","doi":"https://doi.org/10.1109/tnse.2025.3546295","title":"Large-Scale Group Opinion Evolution With Coexistence of Influential Individuals and Strongly Organized Groups Based on Mean Field Games","display_name":"Large-Scale Group Opinion Evolution With Coexistence of Influential Individuals and Strongly Organized Groups Based on Mean Field Games","publication_year":2025,"publication_date":"2025-02-26","ids":{"openalex":"https://openalex.org/W4407948499","doi":"https://doi.org/10.1109/tnse.2025.3546295"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2025.3546295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2025.3546295","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016954423","display_name":"Lu Ren","orcid":"https://orcid.org/0000-0001-9660-3356"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lu Ren","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","School of Mathematical Sciences, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuxin Jin","orcid":"https://orcid.org/0000-0002-9807-4934"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuxin Jin","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","School of Mathematical Sciences, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030067518","display_name":"Wang Yao","orcid":"https://orcid.org/0000-0002-5316-1962"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang Yao","raw_affiliation_strings":["Institute of Artificial Intelligence, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Artificial Intelligence, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032417256","display_name":"Xiao Zhang","orcid":"https://orcid.org/0000-0003-4927-5016"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","School of Mathematical Sciences, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082686687","display_name":"Guohui Jiao","orcid":"https://orcid.org/0000-0003-4054-6406"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghui Jiao","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","School of Mathematical Sciences, Beihang University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Mathematical Sciences, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5016954423"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":3.7893,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.91989529,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"12","issue":"3","first_page":"2202","last_page":"2216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9718000292778015,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5870817303657532},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5392431616783142},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4673711657524109},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43785661458969116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.346158504486084},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32459157705307007},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.24639835953712463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23896151781082153},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10504856705665588},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.0992230772972107}],"concepts":[{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5870817303657532},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5392431616783142},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4673711657524109},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43785661458969116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.346158504486084},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32459157705307007},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.24639835953712463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23896151781082153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10504856705665588},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0992230772972107},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnse.2025.3546295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2025.3546295","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G352320128","display_name":null,"funder_award_id":"2022ZD0116401","funder_id":"https://openalex.org/F4320329860","funder_display_name":"National Science and Technology Major Project"}],"funders":[{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1607455690","https://openalex.org/W1778162479","https://openalex.org/W1983321045","https://openalex.org/W2011000015","https://openalex.org/W2028316825","https://openalex.org/W2038686546","https://openalex.org/W2055540791","https://openalex.org/W2057470999","https://openalex.org/W2060634340","https://openalex.org/W2090976912","https://openalex.org/W2097730910","https://openalex.org/W2098268497","https://openalex.org/W2129951390","https://openalex.org/W2187721800","https://openalex.org/W2559831931","https://openalex.org/W2743546722","https://openalex.org/W2765755511","https://openalex.org/W2791817315","https://openalex.org/W2883504765","https://openalex.org/W2888559564","https://openalex.org/W2941105224","https://openalex.org/W2948627903","https://openalex.org/W2954311168","https://openalex.org/W2976183074","https://openalex.org/W3003091230","https://openalex.org/W3013880462","https://openalex.org/W3016919015","https://openalex.org/W3046141473","https://openalex.org/W3096809873","https://openalex.org/W3108916953","https://openalex.org/W3111383176","https://openalex.org/W3189082966","https://openalex.org/W3195511071","https://openalex.org/W4223539201","https://openalex.org/W4225767175","https://openalex.org/W4254346901","https://openalex.org/W4288439593","https://openalex.org/W4313646288","https://openalex.org/W4386600208","https://openalex.org/W4387298519","https://openalex.org/W4390952383","https://openalex.org/W4392941752","https://openalex.org/W4396224940","https://openalex.org/W4404921937","https://openalex.org/W6676950571","https://openalex.org/W6756281551"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"With":[0],"the":[1,7,32,40,50,55,74,99,116,122,135,140,147,151,160,175,180],"vigorous":[2],"development":[3],"of":[4,9,21,42,101,139,150,163,179],"online":[5],"media,":[6],"prevalence":[8],"key":[10],"opinion":[11,33,75,161],"leaders":[12],"and":[13,28,45,87,113,125,137,146,167,177],"water":[14],"armies":[15],"has":[16],"led":[17],"to":[18,30,72,173],"unexpected":[19],"evolutions":[20,162],"users'":[22],"opinions.":[23],"Therefore,":[24],"it":[25],"is":[26,154],"valuable":[27],"interesting":[29],"investigate":[31],"evolution":[34,76],"problem":[35],"for":[36,97,134],"large-scale":[37],"groups":[38,90,170],"with":[39],"coexistence":[41],"influential":[43,80,165],"individuals":[44,81,104,166],"strongly":[46,88,102],"organized":[47,89,103],"groups.":[48],"For":[49],"above":[51],"problem,":[52],"based":[53],"on":[54,159],"mean-field":[56],"game":[57,69],"theory,":[58],"this":[59],"article":[60],"innovatively":[61],"proposes":[62],"a":[63],"multi-leader":[64],"multi-population-follower":[65],"Stackelberg":[66,141],"mean":[67],"field":[68],"(MLMPF-SMFG)":[70],"model":[71],"describe":[73],"scenario,":[77],"in":[78],"which":[79],"are":[82,91,105,119,144,171],"regarded":[83,92],"as":[84,93],"leaders,":[85],"normal":[86],"follower":[94],"populations.":[95],"Moreover,":[96],"generality,":[98],"types":[100],"classified":[106],"into":[107],"three":[108],"typical":[109],"types:":[110],"propagandists,":[111],"spies,":[112],"neutrals.":[114],"Then,":[115],"optimal":[117],"strategies":[118],"derived":[120],"via":[121],"adjoint":[123],"method":[124],"solved":[126],"by":[127],"forward\u2013backward":[128],"stochastic":[129],"differential":[130],"equations.":[131],"Sufficient":[132],"conditions":[133],"existence":[136],"uniqueness":[138],"equilibrium":[142],"(SE)":[143],"given,":[145],"approximate":[148],"SE":[149],"finite":[152],"system":[153],"proven.":[155],"Finally,":[156],"simulation":[157],"experiments":[158],"two":[164,168],"ordinary":[169],"performed":[172],"demonstrate":[174],"feasibility":[176],"effectiveness":[178],"proposed":[181],"MLMPF-SMFG":[182],"model.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}