{"id":"https://openalex.org/W1076438846","doi":"https://doi.org/10.1137/140993399","title":"Mean Field Stackelberg Games: Aggregation of Delayed Instructions","display_name":"Mean Field Stackelberg Games: Aggregation of Delayed Instructions","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1076438846","doi":"https://doi.org/10.1137/140993399","mag":"1076438846"},"language":"en","primary_location":{"id":"doi:10.1137/140993399","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140993399","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":"green","oa_url":"https://scholars.cityu.edu.hk/en/publications/mean-field-stackelberg-games-aggregation-of-delayed-instructions","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Bensoussan","raw_affiliation_strings":["University of Texas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas","institution_ids":[]}]},{"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/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":"M. H. M. Chau","raw_affiliation_strings":["Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"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":["Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3609,"has_fulltext":true,"cited_by_count":61,"citation_normalized_percentile":{"value":0.95344962,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"4","first_page":"2237","last_page":"2266"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9923999905586243,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.7255587577819824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7190521359443665},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.5632780194282532},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.4653606712818146},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.45215579867362976},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4305945932865143},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3608829081058502},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.311659038066864}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.7255587577819824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7190521359443665},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.5632780194282532},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.4653606712818146},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.45215579867362976},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4305945932865143},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3608829081058502},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.311659038066864}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140993399","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140993399","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/mean-field-stackelberg-games-aggregation-of-delayed-instructions","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BENSOUSSAN, A, CHAU, M H M & YAM, S C P 2015, 'Mean field Stackelberg games : Aggregation of delayed instructions', SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 2237-2266. https://doi.org/10.1137/140993399","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:publications/3cbc15fb-b90b-41d2-a7f1-7243d2c7c489","is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/3cbc15fb-b90b-41d2-a7f1-7243d2c7c489","pdf_url":"https://scholars.cityu.edu.hk/files/188875950/5448431.pdf","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 & YAM, S C P 2015, 'Mean field Stackelberg games : Aggregation of delayed instructions', SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 2237-2266. https://doi.org/10.1137/140993399","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/mean-field-stackelberg-games-aggregation-of-delayed-instructions","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BENSOUSSAN, A, CHAU, M H M & YAM, S C P 2015, 'Mean field Stackelberg games : Aggregation of delayed instructions', SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 2237-2266. https://doi.org/10.1137/140993399","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6192104829","display_name":"Mean Field Games, Mean Field Type Control and Extensions","funder_award_id":"1303775","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"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320324900","display_name":"Rheinische Friedrich-Wilhelms-Universit\u00e4t Bonn","ror":"https://ror.org/041nas322"},{"id":"https://openalex.org/F4320337180","display_name":"Hausdorff Research Institute for Mathematics","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W76132677","https://openalex.org/W586490843","https://openalex.org/W1515432731","https://openalex.org/W1576577548","https://openalex.org/W1607455690","https://openalex.org/W1821455959","https://openalex.org/W1868220410","https://openalex.org/W1973258650","https://openalex.org/W1978500102","https://openalex.org/W1983997656","https://openalex.org/W1996884126","https://openalex.org/W2007602002","https://openalex.org/W2011000015","https://openalex.org/W2025691158","https://openalex.org/W2026814250","https://openalex.org/W2028316825","https://openalex.org/W2038686546","https://openalex.org/W2040158468","https://openalex.org/W2046241416","https://openalex.org/W2057470999","https://openalex.org/W2075099603","https://openalex.org/W2957010402","https://openalex.org/W3099900433","https://openalex.org/W3103347805","https://openalex.org/W3124687253","https://openalex.org/W3125645766"],"related_works":["https://openalex.org/W2911450788","https://openalex.org/W2342897687","https://openalex.org/W3125766157","https://openalex.org/W1548768505","https://openalex.org/W1546379251","https://openalex.org/W4206804910","https://openalex.org/W2884865466","https://openalex.org/W2946404151","https://openalex.org/W2156423594","https://openalex.org/W2952425247"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,103,143,201],"consider":[4],"an":[5,126,133],"$N$-player":[6,112,140],"interacting":[7],"strategic":[8],"game":[9],"in":[10,31],"the":[11,32,40,61,73,79,119,137,152,169,175,179,183,187,191,194,210,219,225,236,266,270,276,280],"presence":[12],"of":[13,34,66,110,115,159,193,209,221,227,239,249,257,260,269,279],"a":[14,49,57,86,92,98,107,148,165,247,255,258],"(endogenous)":[15],"dominating":[16,62,80,166,176,271],"player,":[17,81],"who":[18],"gives":[19],"direct":[20],"influence":[21],"on":[22,28,39,52,151],"individual":[23,44],"agents,":[24],"through":[25,213],"its":[26],"impact":[27],"their":[29],"control":[30,192,268],"sense":[33],"Stackelberg":[35],"game,":[36],"and":[37,178],"then":[38],"whole":[41,180],"community.":[42],"Each":[43],"agent":[45,196],"is":[46,69,198,243,273],"subject":[47],"to":[48,76,118,189,203],"delay":[50,58,68,83,163],"effect":[51],"collecting":[53],"information,":[54],"specifically":[55],"at":[56],"time,":[59],"from":[60,91,164,173],"player.":[63,167],"The":[64],"size":[65],"his":[67,82,228],"completely":[70],"known":[71],"by":[72,245],"agent,":[74],"while":[75],"others,":[77],"including":[78],"plays":[84],"as":[85,132],"hidden":[87],"random":[88],"variable":[89],"coming":[90],"common":[93,211],"fixed":[94,100],"distribution.":[95],"By":[96],"invoking":[97],"noncanonical":[99],"point":[101],"property,":[102],"show":[104],"that":[105,129],"for":[106,136,218,224,235,285],"general":[108],"class":[109,248,259],"finite":[111,139],"games,":[113],"each":[114],"them":[116],"converges":[117],"mean":[120,156,184,240,282],"field":[121,157,185,241,283],"counterpart":[122],"which":[123,190],"may":[124],"possess":[125],"optimal":[127,229,267],"solution":[128],"can":[130],"serve":[131],"$\\epsilon$-Nash":[134],"equilibrium":[135,242,284],"corresponding":[138,153],"game.":[141],"Second,":[142],"provide,":[144],"with":[145,162],"explicit":[146],"solutions,":[147],"comprehensive":[149],"study":[150,256],"linear":[154],"quadratic":[155],"games":[158],"small":[160,286],"agents":[161],"Given":[168],"information":[170],"flow":[171],"obtained":[172],"both":[174],"player":[177,272],"community":[181],"via":[182,254],"term,":[186],"filtration":[188],"representative":[195],"adapted":[197],"non-Brownian.":[199],"Therefore,":[200],"propose":[202],"utilize":[204],"backward":[205,214],"stochastic":[206,215,262],"dynamics":[207],"(instead":[208],"approach":[212],"differential":[216,264],"equations)":[217],"construction":[220],"adjoint":[222],"process":[223],"resolution":[226],"control.":[230],"A":[231],"simple":[232],"sufficient":[233],"condition":[234],"unique":[237,277],"existence":[238,278],"provided":[244],"tackling":[246],"nonsymmetric":[250],"Riccati":[251],"equations.":[252],"Finally,":[253],"forward-backward":[261],"functional":[263],"equations,":[265],"granted":[274],"given":[275],"mentioned":[281],"players.":[287]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
