{"id":"https://openalex.org/W2950156793","doi":"https://doi.org/10.1137/140958906","title":"The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games","display_name":"The Maximum Principle for Global Solutions of Stochastic Stackelberg Differential Games","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2950156793","doi":"https://doi.org/10.1137/140958906","mag":"2950156793"},"language":"en","primary_location":{"id":"doi:10.1137/140958906","doi":"https://doi.org/10.1137/140958906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958906","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2139/ssrn.2413990","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","observed_orcids":["https://orcid.org/0000-0003-2465-1249"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alain 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/A5081520995","display_name":"Shaokuan Chen","orcid":"https://orcid.org/0000-0002-2097-9936","observed_orcids":["https://orcid.org/0000-0002-2097-9936"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shaokuan Chen","raw_affiliation_strings":["(University of Texas)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(University of Texas)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088868657","display_name":"SURESH P. SETHI","orcid":"https://orcid.org/0000-0001-9590-5627","observed_orcids":["https://orcid.org/0000-0001-9590-5627"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suresh P. Sethi","raw_affiliation_strings":["(University of Texas)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(University of Texas)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.8289,"has_fulltext":true,"cited_by_count":144,"citation_normalized_percentile":{"value":0.98328275,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"53","issue":"4","first_page":"1956","last_page":"1981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9082000255584717,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9082000255584717,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.03280000016093254,"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/T12158","display_name":"Guidance and Control Systems","score":0.019099999219179153,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.9800000190734863},{"id":"https://openalex.org/keywords/stackelberg-game","display_name":"Stackelberg game","score":0.9309999942779541},{"id":"https://openalex.org/keywords/linear-quadratic-differential-games","display_name":"linear-quadratic games","score":0.8040000200271606},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8859999775886536},{"id":"https://openalex.org/keywords/stochastic-optimal-control","display_name":"stochastic optimal control","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.9029170870780945},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.762702226638794},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6966334581375122},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6647669076919556},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.6585474610328674},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6457637548446655},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.6119754314422607},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5071673393249512},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.5021817684173584},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46829667687416077},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.452729195356369},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.430172860622406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4189125895500183},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3599613606929779},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.331448495388031},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31730005145072937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23901787400245667}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/140958906","doi":"https://doi.org/10.1137/140958906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958906","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,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-1","norway-2","poland-100","russia-white-list-1","vabb-shw"],"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":"doi:10.2139/ssrn.2413990","doi":"https://doi.org/10.2139/ssrn.2413990","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.2413990","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:arXiv.org:1210.3124","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.3124","pdf_url":"https://arxiv.org/pdf/1210.3124","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"mag:2950156793","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1210.3124","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.762.3852","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.3852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1210.3124.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/dd9ee89c-aaab-4e72-956b-4b47749ddf0e","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/dd9ee89c-aaab-4e72-956b-4b47749ddf0e","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,"listed_in":[],"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, CHEN, S & SETHI, S P 2015, 'The maximum principle for global solutions of stochastic Stackelberg differential games', SIAM Journal on Control and Optimization, vol. 53, no. 4, pp. 1956-1981. https://doi.org/10.1137/140958906","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1210.3124","doi":"https://doi.org/10.48550/arxiv.1210.3124","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1210.3124","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.2139/ssrn.2413990","doi":"https://doi.org/10.2139/ssrn.2413990","is_oa":true,"landing_page_url":"https://doi.org/10.2139/ssrn.2413990","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4476238879","display_name":null,"funder_award_id":"20007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G962589265","display_name":"\u5e26\u8df3\u7684\u5012\u5411\u968f\u673a\u53d1\u5c55\u65b9\u7a0b\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"11101140","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W318136472","https://openalex.org/W620096566","https://openalex.org/W659339155","https://openalex.org/W1489605740","https://openalex.org/W1526282600","https://openalex.org/W1578630563","https://openalex.org/W1653619892","https://openalex.org/W1659904137","https://openalex.org/W1826160640","https://openalex.org/W1965138785","https://openalex.org/W1975595259","https://openalex.org/W1980404349","https://openalex.org/W1983902399","https://openalex.org/W1985050062","https://openalex.org/W2005176287","https://openalex.org/W2012841422","https://openalex.org/W2029794338","https://openalex.org/W2031072241","https://openalex.org/W2032085216","https://openalex.org/W2044979772","https://openalex.org/W2046553535","https://openalex.org/W2069321330","https://openalex.org/W2076038719","https://openalex.org/W2078895915","https://openalex.org/W2081458347","https://openalex.org/W2086139156","https://openalex.org/W2099958618","https://openalex.org/W2113678542","https://openalex.org/W2117183166","https://openalex.org/W2145546590","https://openalex.org/W2157883119","https://openalex.org/W2171879346","https://openalex.org/W2187721800","https://openalex.org/W2963565702","https://openalex.org/W3123057635","https://openalex.org/W3139794508","https://openalex.org/W3146585103","https://openalex.org/W3147553541","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W3197736597","https://openalex.org/W2470903094","https://openalex.org/W3004700137","https://openalex.org/W1967591506","https://openalex.org/W2181123679","https://openalex.org/W2516672776","https://openalex.org/W3210191061","https://openalex.org/W2755034378","https://openalex.org/W3196800410","https://openalex.org/W2611580843"],"abstract_inverted_index":{"For":[0],"stochastic":[1],"Stackelberg":[2,36,65],"differential":[3],"games":[4,66],"played":[5],"by":[6],"a":[7,10],"leader":[8],"and":[9,71],"follower,":[11],"there":[12],"are":[13],"several":[14],"solution":[15,37],"concepts":[16],"in":[17],"terms":[18],"of":[19],"the":[20,29,33,39,46,50,54,80],"players'":[21],"information":[22,43,75],"sets.":[23],"In":[24],"this":[25],"paper":[26],"we":[27,61],"derive":[28],"maximum":[30],"principle":[31],"for":[32],"leader's":[34,51],"global":[35,48],"under":[38,67],"adapted":[40,69,72],"closed-loop":[41,73],"memoryless":[42,74],"structure,":[44],"where":[45],"term":[47],"signifies":[49],"domination":[52],"over":[53],"entire":[55],"game":[56],"duration.":[57],"As":[58],"special":[59],"cases,":[60],"study":[62],"linear":[63],"quadratic":[64],"both":[68],"open-loop":[70],"structures,":[76],"as":[77,79],"well":[78],"resulting":[81],"Riccati":[82],"equations.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-24T09:50:30.924529","created_date":"2019-06-27T00:00:00"}
