{"id":"https://openalex.org/W2025377957","doi":"https://doi.org/10.1109/tac.2015.2423891","title":"An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games","display_name":"An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games","publication_year":2015,"publication_date":"2015-04-17","ids":{"openalex":"https://openalex.org/W2025377957","doi":"https://doi.org/10.1109/tac.2015.2423891","mag":"2025377957"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2423891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2423891","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.0186","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069273068","display_name":"Ankur A. Kulkarni","orcid":"https://orcid.org/0000-0001-8139-5216"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Ankur A. Kulkarni","raw_affiliation_strings":["Systems and Control Engineering group, Indian Insitute of Technology Bombay, Mumbai, India","Syst. & Control Eng. Group, Indian Insitute of Technol. Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Systems and Control Engineering group, Indian Insitute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Syst. & Control Eng. Group, Indian Insitute of Technol. Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047034022","display_name":"Uday V. Shanbhag","orcid":"https://orcid.org/0000-0001-5869-9561"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]},{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Uday V. Shanbhag","raw_affiliation_strings":["Department of Industrial and Manufacturing Engineering, Pennsylvania State University, PA, USA","Syst. & Control Eng. Group, Indian Insitute of Technol. Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Manufacturing Engineering, Pennsylvania State University, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Syst. & Control Eng. Group, Indian Insitute of Technol. Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069273068"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":3.7039,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.92942053,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"12","first_page":"3379","last_page":"3384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9959999918937683,"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":0.9959999918937683,"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/T10424","display_name":"Electric Power System Optimization","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/stackelberg-competition","display_name":"Stackelberg competition","score":0.9719557762145996},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7480366230010986},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.7064368724822998},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5778657793998718},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.5618339776992798},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.5586131811141968},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5440016388893127},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.5365154147148132},{"id":"https://openalex.org/keywords/potential-game","display_name":"Potential game","score":0.5299941897392273},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.483581006526947},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4509260058403015},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44369080662727356},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.419607549905777},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.4076693654060364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3967851400375366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3655853867530823}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.9719557762145996},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7480366230010986},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.7064368724822998},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5778657793998718},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.5618339776992798},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.5586131811141968},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5440016388893127},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.5365154147148132},{"id":"https://openalex.org/C2778079155","wikidata":"https://www.wikidata.org/wiki/Q288500","display_name":"Potential game","level":3,"score":0.5299941897392273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.483581006526947},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4509260058403015},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44369080662727356},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.419607549905777},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.4076693654060364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3967851400375366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3655853867530823},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":2,"locations":[{"id":"doi:10.1109/tac.2015.2423891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2423891","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:arXiv.org:1401.0186","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.0186","pdf_url":"https://arxiv.org/pdf/1401.0186","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.0186","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.0186","pdf_url":"https://arxiv.org/pdf/1401.0186","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":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.800000011920929,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W217831350","https://openalex.org/W290038075","https://openalex.org/W1490458594","https://openalex.org/W1543439990","https://openalex.org/W1578630563","https://openalex.org/W1720757687","https://openalex.org/W1972612549","https://openalex.org/W1994238514","https://openalex.org/W1998667911","https://openalex.org/W2027555061","https://openalex.org/W2045047916","https://openalex.org/W2064518527","https://openalex.org/W2076736386","https://openalex.org/W2117179049","https://openalex.org/W2158898097","https://openalex.org/W2162885967","https://openalex.org/W2165807407","https://openalex.org/W2166063259","https://openalex.org/W3022321359","https://openalex.org/W3101433250","https://openalex.org/W4231147659","https://openalex.org/W4234277722","https://openalex.org/W4236123449","https://openalex.org/W4301791716","https://openalex.org/W6610459132"],"related_works":["https://openalex.org/W1853631319","https://openalex.org/W2013767790","https://openalex.org/W4221157020","https://openalex.org/W4315489088","https://openalex.org/W4299551322","https://openalex.org/W211718035","https://openalex.org/W4302558842","https://openalex.org/W2025767136","https://openalex.org/W3125812435","https://openalex.org/W1554758635"],"abstract_inverted_index":{"In":[0,81,157],"a":[1,7,14,23,41,77,125,128,140],"hierarchical":[2],"Stackelberg":[3,5],"v/s":[4],"game,":[6],"collection":[8],"of":[9,22,31,43,50,64,70,99,110,121,139,154,160,168],"players":[10],"called":[11,33],"leaders":[12,51,123],"play":[13],"Nash":[15,25],"game":[16,26],"constrained":[17],"by":[18,165],"the":[19,47,62,68,89,108,111,116,119,122,134,149,155,166],"equilibrium":[20,109],"conditions":[21,66],"distinct":[24],"played":[27],"amongst":[28],"another":[29],"set":[30],"players,":[32],"followers.":[34],"Generically,":[35],"follower":[36],"equilibria":[37,75,95,153,161],"are":[38,52,145],"non-unique":[39],"as":[40],"function":[42],"leader":[44],"strategies":[45],"and":[46,55,136,151],"decision":[48],"problems":[49],"highly":[53],"nonconvex":[54],"lacking":[56],"in":[57,131,184],"standard":[58],"regularity":[59],"conditions.":[60,176],"Consequently,":[61],"provision":[63],"sufficient":[65],"for":[67,94,96],"existence":[69,92,159],"global":[71,135,150],"or":[72],"even":[73],"local":[74,137,152],"remains":[76],"largely":[78],"open":[79],"question.":[80],"this":[82,97,132],"paper,":[83,133],"we":[84,102],"present":[85],"what":[86],"is":[87],"possibly":[88],"first":[90],"general":[91],"result":[93],"class":[98],"games.":[100],"Importantly,":[101],"impose":[103],"no":[104],"single-valuedness":[105],"assumption":[106,117],"on":[107],"follower-level":[112],"game.":[113,156],"Specifically,":[114],"under":[115,174],"that":[118],"objectives":[120],"admit":[124],"quasi-potential":[126,179],"function,":[127],"notion":[129],"introduced":[130],"minimizers":[138],"suitably":[141],"defined":[142],"optimization":[143,170],"problem":[144,171],"shown":[146],"to":[147],"be":[148,163],"effect,":[158],"can":[162],"guaranteed":[164],"solvability":[167],"an":[169,182],"which":[172],"holds":[173],"mild":[175],"We":[177],"motivate":[178],"games":[180],"through":[181],"application":[183],"communication":[185],"networks.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}