{"id":"https://openalex.org/W2752423433","doi":"https://doi.org/10.1137/15m1052937","title":"Linear-Quadratic Mean Field Stackelberg Games with State and Control Delays","display_name":"Linear-Quadratic Mean Field Stackelberg Games with State and Control Delays","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2752423433","doi":"https://doi.org/10.1137/15m1052937","mag":"2752423433"},"language":"en","primary_location":{"id":"doi:10.1137/15m1052937","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1052937","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/linear-quadratic-mean-field-stackelberg-games-with-state-and-cont","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027426452","display_name":"Alain Bensoussan","orcid":"https://orcid.org/0000-0003-2465-1249"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Bensoussan","raw_affiliation_strings":["The University of Texas at Dallas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Dallas","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007823368","display_name":"M. H. M. Chau","orcid":"https://orcid.org/0000-0002-8234-7029"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"M. H. M. Chau","raw_affiliation_strings":["Imperial College London; The University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London; The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055113920","display_name":"Yee Lok Lai","orcid":"https://orcid.org/0009-0004-1002-8805"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Y. Lai","raw_affiliation_strings":["The Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075984844","display_name":"Sheung Chi Phillip Yam","orcid":"https://orcid.org/0000-0002-4380-0919"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"S. C. P. Yam","raw_affiliation_strings":["The Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.392,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.96721169,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"55","issue":"4","first_page":"2748","last_page":"2781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9980000257492065,"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":0.9980000257492065,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9965000152587891,"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/stackelberg-competition","display_name":"Stackelberg competition","score":0.843876838684082},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7890439033508301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.763737678527832},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.6982958912849426},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5939239263534546},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5854807496070862},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.46527454257011414},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46409717202186584},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4567467272281647},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.44715189933776855},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4420813024044037},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43770238757133484},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.41264641284942627},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4071842432022095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21318981051445007},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18566513061523438},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0915001630783081}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.843876838684082},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7890439033508301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.763737678527832},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.6982958912849426},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5939239263534546},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5854807496070862},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.46527454257011414},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46409717202186584},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4567467272281647},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.44715189933776855},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4420813024044037},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43770238757133484},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.41264641284942627},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4071842432022095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21318981051445007},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18566513061523438},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0915001630783081},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1052937","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1052937","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/linear-quadratic-mean-field-stackelberg-games-with-state-and-cont","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/6293da6b-b79a-4d0d-96e6-060b018180b5","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/6293da6b-b79a-4d0d-96e6-060b018180b5","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"BENSOUSSAN, A, CHAU, M H M, LAI, Y & YAM, S C P 2017, 'Linear-Quadratic Mean Field Stackelberg Games WIth State and Control Delays', SIAM Journal on Control and Optimization, vol. 55, no. 4, pp. 2748-2781. https://doi.org/10.1137/15M1052937","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/linear-quadratic-mean-field-stackelberg-games-with-state-and-cont","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3964355217","display_name":null,"funder_award_id":"GRF 500113","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G4356538801","display_name":null,"funder_award_id":"DMS 1612880","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G650832913","display_name":null,"funder_award_id":"DMS 1303775","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7085319725","display_name":null,"funder_award_id":"GRF 11303316","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G8328215554","display_name":null,"funder_award_id":"GRF 14301015","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1076438846","https://openalex.org/W1480180679","https://openalex.org/W1607455690","https://openalex.org/W1808956822","https://openalex.org/W1821455959","https://openalex.org/W1970319238","https://openalex.org/W1973258650","https://openalex.org/W1983997656","https://openalex.org/W1984960279","https://openalex.org/W1986314707","https://openalex.org/W1997965124","https://openalex.org/W2011435133","https://openalex.org/W2016775936","https://openalex.org/W2017903822","https://openalex.org/W2019740115","https://openalex.org/W2023461927","https://openalex.org/W2026814250","https://openalex.org/W2028316825","https://openalex.org/W2037152246","https://openalex.org/W2038686546","https://openalex.org/W2040050197","https://openalex.org/W2040666728","https://openalex.org/W2042086201","https://openalex.org/W2046654819","https://openalex.org/W2057470999","https://openalex.org/W2075099603","https://openalex.org/W2091265977","https://openalex.org/W2103714988","https://openalex.org/W2952444919","https://openalex.org/W3106272087","https://openalex.org/W4240527760"],"related_works":["https://openalex.org/W1987562536","https://openalex.org/W4383533535","https://openalex.org/W1988922213","https://openalex.org/W2364446825","https://openalex.org/W1564190868","https://openalex.org/W2022702275","https://openalex.org/W3041410939","https://openalex.org/W3122364233","https://openalex.org/W1983902399","https://openalex.org/W2767031889"],"abstract_inverted_index":{"In":[0,152],"this":[1],"article,":[2],"we":[3,106,170,185,200,214,303],"consider":[4],"a":[5,11,16,202,244,283,307,311],"linear-quadratic":[6],"mean":[7,158,195],"field":[8,159,196],"game":[9,24,75],"between":[10],"leader":[12,167,221],"(dominating":[13],"player)":[14],"and":[15,33,62,92,122,133,143,161,211,222,258,278,349],"group":[17],"of":[18,47,69,89,94,97,165,181,219,234,237,287,300,310,320,327,335],"followers":[19],"(agents)":[20],"under":[21],"the":[22,45,70,87,90,95,110,157,162,166,172,178,187,193,216,220,231,235,238,251,271,297,301,317,321,325,333],"Stackelberg":[23,74],"setting":[25,242],"as":[26,65,67,114,168],"proposed":[27],"in":[28,250,282,344],"[A.":[29,254,345],"Bensoussan,":[30,255,346],"M.":[31,256,347],"Chau,":[32,257,348],"S.":[34,123,259,350],"Yam,":[35,260,351],"Appl.":[36,261,352],"Math.":[37,262,353],"Optim.,":[38,263,354],"74":[39,264,355],"(2016),":[40,265,356],"pp.":[41,131,266,357],"91-128],":[42,267],"so":[43],"that":[44,207,224,249],"evolution":[46],"each":[48,182,275,328],"individual":[49],"follower":[50],"is":[51,76],"now":[52],"also":[53],"subjected":[54],"to":[55,86,145,176,191,305],"delay":[56,163,272,318],"effects":[57,273,319],"from":[58,270,274,316],"both":[59],"his/her":[60],"state":[61,277],"control":[63,180,218,299,323],"variables,":[64],"well":[66],"those":[68],"leader.":[71],"The":[72],"overall":[73],"solved":[77],"by":[78,108,154],"tackling":[79],"three":[80,98],"subproblems":[81],"hierarchically.":[82],"Their":[83],"resolution":[84],"corresponds":[85],"establishment":[88],"existence":[91,210,233],"uniqueness":[93],"solutions":[96],"different":[99,246],"forward-backward":[100,290],"stochastic":[101,291],"functional":[102,292,338],"differential":[103,293],"equations,":[104],"which":[105,199,268,280,330],"manage":[107],"applying":[109],"unified":[111],"continuation":[112],"method":[113],"first":[115,155],"developed":[116],"in,":[117],"for":[118],"example,":[119],"[Y.":[120],"Hu":[121],"Peng,":[124],"Probab.":[125],"Theory":[126],"Related":[127],"Fields,":[128],"103":[129],"(1995),":[130],"273-283]":[132],"[X.":[134],"Xu,":[135],"Fully":[136],"Coupled":[137],"Forward-Backward":[138],"Stochastic":[139],"Functional":[140],"Differential":[141],"Equations":[142],"Applications":[144],"Quadratic":[146],"Optimal":[147],"Control,":[148],"preprint,":[149],"arXiv:1310.6846,":[150],"2013].":[151],"particular,":[153],"regarding":[156],"term":[160],"influence":[164],"exogenous,":[169],"use":[171],"adjoint":[173],"equation":[174],"approach":[175],"solve":[177,215],"optimal":[179,217,298],"follower.":[183],"Next,":[184],"utilize":[186],"fixed":[188],"point":[189],"property":[190],"get":[192],"desired":[194],"equilibrium,":[197],"with":[198,230],"propose":[201],"time":[203],"independent":[204],"sufficient":[205],"condition":[206],"warrants":[208],"its":[209,225],"uniqueness.":[212],"Finally,":[213],"conclude":[223],"presence":[226],"would":[227],"not":[228,342],"interfere":[229],"original":[232],"equilibrium":[236],"community.":[239],"Our":[240],"present":[241],"introduces":[243],"much":[245],"challenge":[247],"than":[248],"former":[252],"work":[253],"stems":[269],"follower's":[276],"control,":[279],"result":[281],"more":[284],"complicated":[285],"system":[286],"infinite":[288],"dimensional":[289],"equations.":[294],"To":[295],"find":[296],"leader,":[302],"need":[304],"develop":[306],"thorough":[308],"understanding":[309],"special":[312],"linear":[313],"operator":[314],"resulting":[315],"leader's":[322],"on":[324,332],"dynamics":[326],"follower,":[329],"hinges":[331],"invertibility":[334],"another":[336],"certain":[337],"operator.":[339],"This":[340],"was":[341],"considered":[343],"91-128].":[358]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}