{"id":"https://openalex.org/W2789382902","doi":"https://doi.org/10.1109/tac.2018.2798807","title":"Linear\u2013Quadratic Mean-Field Game for Stochastic Delayed Systems","display_name":"Linear\u2013Quadratic Mean-Field Game for Stochastic Delayed Systems","publication_year":2018,"publication_date":"2018-01-26","ids":{"openalex":"https://openalex.org/W2789382902","doi":"https://doi.org/10.1109/tac.2018.2798807","mag":"2789382902"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2798807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2798807","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/A5075552347","display_name":"Jianhui Huang","orcid":"https://orcid.org/0000-0003-3315-6549"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Jianhui Huang","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100368113","display_name":"Na Li","orcid":"https://orcid.org/0000-0002-4293-515X"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Na Li","raw_affiliation_strings":["School of Statistics, Shandong University of Finance and Economics, Jinan"],"affiliations":[{"raw_affiliation_string":"School of Statistics, Shandong University of Finance and Economics, Jinan","institution_ids":["https://openalex.org/I59483232"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075552347"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":4.9696,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.95037802,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"63","issue":"8","first_page":"2722","last_page":"2729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.991599977016449,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.989300012588501,"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/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.7052214741706848},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.55260169506073},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5312737226486206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202330350875854},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45390358567237854},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.44455254077911377},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4435368776321411},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.41328245401382446},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4016307592391968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3385957181453705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14458930492401123},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1399434506893158}],"concepts":[{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.7052214741706848},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.55260169506073},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5312737226486206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202330350875854},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45390358567237854},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.44455254077911377},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4435368776321411},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.41328245401382446},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4016307592391968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3385957181453705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14458930492401123},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1399434506893158},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2018.2798807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2798807","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/78301","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/78301","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1069189080","display_name":null,"funder_award_id":"G-YL04","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G7998669502","display_name":null,"funder_award_id":"11626142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8923561122","display_name":null,"funder_award_id":"ZR2016AB08","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1275718198","https://openalex.org/W1808956822","https://openalex.org/W1821455959","https://openalex.org/W1969717343","https://openalex.org/W1973258650","https://openalex.org/W1983321045","https://openalex.org/W1985050062","https://openalex.org/W1989886421","https://openalex.org/W2011000015","https://openalex.org/W2011435133","https://openalex.org/W2037152246","https://openalex.org/W2037743307","https://openalex.org/W2038686546","https://openalex.org/W2046241416","https://openalex.org/W2062611968","https://openalex.org/W2067437055","https://openalex.org/W2091265977","https://openalex.org/W2094305067","https://openalex.org/W2097730910","https://openalex.org/W2129951390","https://openalex.org/W3099900433","https://openalex.org/W6638427445"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4210910892","https://openalex.org/W2228513190","https://openalex.org/W4283371013","https://openalex.org/W4386821009","https://openalex.org/W2962927879"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,21,69,95,102,119],"linear-quadratic":[4],"mean-field":[5],"game":[6],"(MFG)":[7],"for":[8,117],"a":[9,17,29,65,83,88],"class":[10],"of":[11,23,56,111],"stochastic":[12,30,48],"delayed":[13,32,112],"systems.":[14],"We":[15],"consider":[16],"large-population":[18],"system,":[19,42],"where":[20],"dynamics":[22],"each":[24],"agent":[25],"is":[26,37,44],"modeled":[27],"by":[28,87],"differential":[31,49],"equation.":[33],"The":[34,54],"consistency":[35],"condition":[36],"derived":[38],"through":[39],"an":[40,45,58,76],"auxiliary":[41],"which":[43,118],"anticipated":[46],"forward-backward":[47],"equation":[50],"with":[51],"delay":[52],"(AFBSDDE).":[53],"wellposedness":[55],"such":[57],"AFBSDDE":[59],"system":[60],"can":[61,72],"be":[62,73],"obtained":[63],"using":[64],"continuation":[66],"method.":[67,93],"Thus,":[68],"MFG":[70,123],"strategies":[71,97,124],"defined":[74],"on":[75,82],"arbitrary":[77],"time":[78,85],"horizon,":[79],"not":[80],"necessary":[81],"small":[84],"horizon":[86],"commonly":[89],"used":[90],"contraction":[91],"mapping":[92],"Moreover,":[94],"decentralized":[96],"are":[98,114,125],"verified":[99],"to":[100],"satisfy":[101],"\u03b5-Nash":[103],"equilibrium":[104],"property.":[105],"For":[106],"illustration,":[107],"three":[108],"special":[109],"cases":[110],"systems":[113],"further":[115],"explored,":[116],"closed-loop":[120],"and":[121],"open-loop":[122],"derived,":[126],"respectively.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}