{"id":"https://openalex.org/W3204022810","doi":"https://doi.org/10.1137/21m1450458","title":"Zero-Sum Stackelberg Stochastic Linear-Quadratic Differential Games","display_name":"Zero-Sum Stackelberg Stochastic Linear-Quadratic Differential Games","publication_year":2023,"publication_date":"2023-02-22","ids":{"openalex":"https://openalex.org/W3204022810","doi":"https://doi.org/10.1137/21m1450458","mag":"3204022810"},"language":"en","primary_location":{"id":"doi:10.1137/21m1450458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450458","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2109.14893","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046249714","display_name":"Jingrui Sun","orcid":"https://orcid.org/0000-0002-7101-9169"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingrui Sun","raw_affiliation_strings":["Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China"],"raw_orcid":"https://orcid.org/0000-0002-7101-9169","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101454802","display_name":"Hanxiao Wang","orcid":"https://orcid.org/0000-0003-2439-1280"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hanxiao Wang","raw_affiliation_strings":["Corresponding author. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China"],"raw_orcid":"https://orcid.org/0000-0003-2439-1280","affiliations":[{"raw_affiliation_string":"Corresponding author. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042328688","display_name":"Jiaqiang Wen","orcid":"https://orcid.org/0000-0001-7790-8453"},"institutions":[{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaqiang Wen","raw_affiliation_strings":["Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, China"],"raw_orcid":"https://orcid.org/0000-0001-7790-8453","affiliations":[{"raw_affiliation_string":"Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen 518055, China","institution_ids":["https://openalex.org/I3045169105"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.2606,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.96847704,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"61","issue":"1","first_page":"252","last_page":"284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9965999722480774,"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":0.9965999722480774,"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/T12137","display_name":"Economic theories and models","score":0.9846000075340271,"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/T10471","display_name":"Climate Change Policy and Economics","score":0.9829999804496765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.9530314207077026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8126554489135742},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6578619480133057},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.6356561183929443},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.584134042263031},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5701417922973633},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.5063413381576538},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45762500166893005},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.43526026606559753},{"id":"https://openalex.org/keywords/backward-induction","display_name":"Backward induction","score":0.43380600214004517},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4266689419746399},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38255631923675537},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.36511439085006714},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.2604254484176636},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18465277552604675}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.9530314207077026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8126554489135742},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6578619480133057},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.6356561183929443},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.584134042263031},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5701417922973633},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.5063413381576538},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45762500166893005},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.43526026606559753},{"id":"https://openalex.org/C160343169","wikidata":"https://www.wikidata.org/wiki/Q968642","display_name":"Backward induction","level":3,"score":0.43380600214004517},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4266689419746399},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38255631923675537},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.36511439085006714},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.2604254484176636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18465277552604675},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1450458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1450458","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:arXiv.org:2109.14893","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.14893","pdf_url":"https://arxiv.org/pdf/2109.14893","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2109.14893","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.14893","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2109.14893","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.14893","pdf_url":"https://arxiv.org/pdf/2109.14893","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3420297265","display_name":null,"funder_award_id":"11901280","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3568702072","display_name":null,"funder_award_id":"Y01286233","funder_id":"https://openalex.org/F4320327605","funder_display_name":"Southern University of Science and Technology"},{"id":"https://openalex.org/G7299993470","display_name":null,"funder_award_id":"2021A1515010031","funder_id":"https://openalex.org/F4320321586","funder_display_name":"Government of Guangdong Province"},{"id":"https://openalex.org/G7594298208","display_name":null,"funder_award_id":"R-146-000-271-112","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321586","display_name":"Government of Guangdong Province","ror":"https://ror.org/050m0b055"},{"id":"https://openalex.org/F4320327605","display_name":"Southern University of Science and Technology","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W644361365","https://openalex.org/W941869882","https://openalex.org/W1525883337","https://openalex.org/W1566322288","https://openalex.org/W1965138785","https://openalex.org/W1988097234","https://openalex.org/W1994999662","https://openalex.org/W2029794338","https://openalex.org/W2054973458","https://openalex.org/W2055504162","https://openalex.org/W2059859243","https://openalex.org/W2067437055","https://openalex.org/W2070866329","https://openalex.org/W2098696428","https://openalex.org/W2102316513","https://openalex.org/W2148753127","https://openalex.org/W2157047632","https://openalex.org/W2173931892","https://openalex.org/W2181123679","https://openalex.org/W2531372032","https://openalex.org/W2752423433","https://openalex.org/W2804631621","https://openalex.org/W2891171846","https://openalex.org/W2898256821","https://openalex.org/W2900971135","https://openalex.org/W2902287998","https://openalex.org/W2963197062","https://openalex.org/W2963349698","https://openalex.org/W2997572556","https://openalex.org/W3009228455","https://openalex.org/W3039880972","https://openalex.org/W3040080951","https://openalex.org/W3104162674","https://openalex.org/W3125172959","https://openalex.org/W3133589444","https://openalex.org/W3152681045","https://openalex.org/W3157127717","https://openalex.org/W3157446626","https://openalex.org/W3158664135","https://openalex.org/W3166860115","https://openalex.org/W3202505006","https://openalex.org/W4212780424","https://openalex.org/W4221149767","https://openalex.org/W4287231927"],"related_works":["https://openalex.org/W1511033389","https://openalex.org/W1988922213","https://openalex.org/W2091923150","https://openalex.org/W2364446825","https://openalex.org/W1564190868","https://openalex.org/W2022702275","https://openalex.org/W3041410939","https://openalex.org/W2081462673","https://openalex.org/W3122364233","https://openalex.org/W1983902399"],"abstract_inverted_index":{"The":[0],"paper":[1],"is":[2,26,62],"concerned":[3],"with":[4,72,77],"a":[5,19,32,45,103,116],"zero-sum":[6,79],"Stackelberg":[7,24,57,89,100],"stochastic":[8,34,81],"linear-quadratic":[9],"(LQ,":[10],"for":[11,41],"short)":[12,42],"differential":[13,83],"game":[14,111],"over":[15],"finite":[16],"horizons.":[17],"Under":[18],"fairly":[20],"weak":[21],"condition,":[22],"the":[23,56,64,73,78,88,92,99,109],"equilibrium":[25,90,94,101],"explicitly":[27],"obtained":[28],"by":[29],"first":[30],"solving":[31],"forward":[33],"LQ":[35,82],"optimal":[36],"control":[37],"problem":[38],"(SLQ":[39],"problem,":[40],"and":[43,91,108],"then":[44],"backward":[46],"SLQ":[47],"problem.":[48],"Two":[49],"Riccati":[50,69,74],"equations":[51,70],"are":[52,95],"derived":[53],"in":[54,115],"constructing":[55],"equilibrium.":[58],"An":[59],"interesting":[60],"finding":[61],"that":[63,87],"difference":[65],"of":[66],"these":[67],"two":[68],"coincides":[71],"equation":[75],"associated":[76],"Nash":[80,93,110],"game,":[84],"which":[85],"implies":[86],"actually":[96],"identical.":[97],"Consequently,":[98],"admits":[102],"linear":[104],"state":[105],"feedback":[106],"representation,":[107],"can":[112],"be":[113],"solved":[114],"leader-follower":[117],"manner.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2021-10-11T00:00:00"}