{"id":"https://openalex.org/W7123360546","doi":"https://doi.org/10.1109/cdc57313.2025.11312467","title":"Nonlinear Mean Field Games with Multiple Major Agents and Multiple Populations of Minor Agents","display_name":"Nonlinear Mean Field Games with Multiple Major Agents and Multiple Populations of Minor Agents","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W7123360546","doi":"https://doi.org/10.1109/cdc57313.2025.11312467"},"language":null,"primary_location":{"id":"doi:10.1109/cdc57313.2025.11312467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5122860836","display_name":"Xuanping Zhang","orcid":null},"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":"Xuanping Zhang","raw_affiliation_strings":["Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","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":false,"raw_author_name":"Lu Ren","raw_affiliation_strings":["Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191","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/I4210100255","display_name":"Beijing Academy of Artificial Intelligence","ror":"https://ror.org/016a74861","country_code":"CN","type":"other","lineage":["https://openalex.org/I4210100255"]},{"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":["Beihang University,School of Artificial Intelligence and LMIB,Beijing,China,100191"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University,School of Artificial Intelligence and LMIB,Beijing,China,100191","institution_ids":["https://openalex.org/I4210100255","https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122905566","display_name":"Xiao Zhang","orcid":null},"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":["Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University,School of Mathematical Sciences and LMIB,Beijing,China,100191","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"6330","last_page":"6337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.12890000641345978,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.12890000641345978,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.12229999899864197,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.11349999904632568,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5679000020027161},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5178999900817871},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4986000061035156},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4844000041484833},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4819999933242798},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4740000069141388},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4438000023365021},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.3950999975204468},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.38989999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7811999917030334},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5679000020027161},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5178999900817871},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4986000061035156},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45829999446868896},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4438000023365021},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3481000065803528},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.319599986076355},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.3190999925136566},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.2799000144004822},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.27090001106262207},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C42246873","wikidata":"https://www.wikidata.org/wiki/Q6045167","display_name":"Interacting particle system","level":4,"score":0.2648000121116638},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc57313.2025.11312467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321125","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56"},{"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":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"paper":[1],"studies":[2],"a":[3,67,160],"nonlinear":[4],"mean":[5,63],"field":[6,64],"game":[7],"(MFG)":[8],"model":[9],"based":[10,98],"on":[11,70,99],"McKean-Vlasov":[12],"(MV)":[13],"approximation,":[14],"which":[15,126,149],"involves":[16],"multiple":[17,21],"major":[18],"agents":[19,34,39],"and":[20,40,159],"populations":[22],"of":[23,55,83,90,121,134],"minor":[24],"agents.":[25],"Since":[26],"the":[27,50,62,71,88,93,106,119,144],"interactions":[28],"occur":[29],"not":[30],"only":[31],"between":[32],"major\u2013minor":[33],"but":[35],"also":[36],"among":[37],"major\u2013major":[38],"minor\u2013minor":[41],"populations,":[42],"complicating":[43],"equilibrium":[44,122,140],"existence":[45,89,120],"analysis,":[46],"we":[47],"first":[48],"cast":[49],"MFG":[51],"as":[52,129],"two":[53,132],"sets":[54,133],"adjoint":[56],"stochastic":[57,101],"McKean\u2013Vlasov":[58],"equations":[59,84],"coupled":[60,135],"via":[61],"behavior.":[65],"Subsequently,":[66],"new":[68],"norm":[69],"product":[72,108],"probability":[73],"measure":[74],"space":[75],"is":[76,96,115,127,141,166],"constructed":[77],"to":[78,92,117,131,157],"prove":[79,118],"that":[80],"one":[81],"set":[82,95],"exists":[85],"solutions,":[86],"while":[87,152],"solutions":[91,130],"other":[94],"proved":[97,142],"Pontryagin":[100],"maximum":[102],"principle.":[103],"Then,":[104],"within":[105],"established":[107],"normed":[109],"space,":[110],"Banach\u2019s":[111],"fixed":[112],"point":[113],"theorem":[114],"utilized":[116],"for":[123,143],"this":[124],"MFG,":[125],"manifested":[128],"equations.":[136],"Finally,":[137],"an":[138],"\u03f5-Nash":[139],"finite":[145],"agent":[146],"situation,":[147],"in":[148],"\u03f5":[150],"\u21920":[151],"all":[153],"population":[154],"sizes":[155],"go":[156],"\u221e,":[158],"numerical":[161],"experiment":[162],"under":[163],"certain":[164],"settings":[165],"carried":[167],"out.":[168]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2026-01-14T00:00:00"}