{"id":"https://openalex.org/W4396667789","doi":"https://doi.org/10.1109/tifs.2024.3397196","title":"Consistency of Stackelberg and Nash Equilibria in Three-Player Leader-Follower Games","display_name":"Consistency of Stackelberg and Nash Equilibria in Three-Player Leader-Follower Games","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4396667789","doi":"https://doi.org/10.1109/tifs.2024.3397196"},"language":"en","primary_location":{"id":"doi:10.1109/tifs.2024.3397196","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2024.3397196","pdf_url":null,"source":{"id":"https://openalex.org/S61310614","display_name":"IEEE Transactions on Information Forensics and Security","issn_l":"1556-6013","issn":["1556-6013","1556-6021"],"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 Information Forensics and Security","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038764715","display_name":"Gehui Xu","orcid":"https://orcid.org/0000-0002-4134-8455"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gehui Xu","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-4134-8455","affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008412836","display_name":"Guanpu Chen","orcid":"https://orcid.org/0000-0003-0698-7910"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Guanpu Chen","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-0698-7910","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047031115","display_name":"Zhaoyang Cheng","orcid":"https://orcid.org/0000-0001-5729-9558"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaoyang Cheng","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-5729-9558","affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359415","display_name":"Yiguang Hong","orcid":"https://orcid.org/0000-0001-9505-8739"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiguang Hong","raw_affiliation_strings":["Department of Control Science and Engineering, Tongji University, Shanghai, China","Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0001-9505-8739","affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076197013","display_name":"Hongsheng Qi","orcid":"https://orcid.org/0000-0002-1698-7570"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongsheng Qi","raw_affiliation_strings":["Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1698-7570","affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, China","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9566,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.90456572,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"19","issue":null,"first_page":"5330","last_page":"5344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.8705530166625977},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.8290698528289795},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7700250148773193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7259769439697266},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.6051623225212097},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.551192045211792},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48409926891326904},{"id":"https://openalex.org/keywords/strategy","display_name":"Strategy","score":0.47282183170318604},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.45171406865119934},{"id":"https://openalex.org/keywords/dilemma","display_name":"Dilemma","score":0.4477260410785675},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4434582591056824},{"id":"https://openalex.org/keywords/sequential-equilibrium","display_name":"Sequential equilibrium","score":0.4162445664405823},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4104294776916504},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.40256989002227783},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3593434989452362},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.3536490201950073},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.3324583172798157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18263542652130127},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1015465259552002}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.8705530166625977},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.8290698528289795},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7700250148773193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7259769439697266},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.6051623225212097},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.551192045211792},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48409926891326904},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.47282183170318604},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.45171406865119934},{"id":"https://openalex.org/C2778496695","wikidata":"https://www.wikidata.org/wiki/Q254128","display_name":"Dilemma","level":2,"score":0.4477260410785675},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4434582591056824},{"id":"https://openalex.org/C201364048","wikidata":"https://www.wikidata.org/wiki/Q2897085","display_name":"Sequential equilibrium","level":5,"score":0.4162445664405823},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4104294776916504},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.40256989002227783},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3593434989452362},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.3536490201950073},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.3324583172798157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18263542652130127},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1015465259552002},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tifs.2024.3397196","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tifs.2024.3397196","pdf_url":null,"source":{"id":"https://openalex.org/S61310614","display_name":"IEEE Transactions on Information Forensics and Security","issn_l":"1556-6013","issn":["1556-6013","1556-6021"],"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 Information Forensics and Security","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5977796052","display_name":null,"funder_award_id":"62173250","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7879707153","display_name":null,"funder_award_id":"61873262","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1533945010","https://openalex.org/W1968226644","https://openalex.org/W1979527786","https://openalex.org/W2006109604","https://openalex.org/W2034992769","https://openalex.org/W2045051323","https://openalex.org/W2047071794","https://openalex.org/W2047399268","https://openalex.org/W2067064328","https://openalex.org/W2088562872","https://openalex.org/W2122311135","https://openalex.org/W2126879264","https://openalex.org/W2153644609","https://openalex.org/W2155740782","https://openalex.org/W2209091760","https://openalex.org/W2319530283","https://openalex.org/W2492629073","https://openalex.org/W2544056523","https://openalex.org/W2560309904","https://openalex.org/W2560934771","https://openalex.org/W2566316543","https://openalex.org/W2601675742","https://openalex.org/W2751212131","https://openalex.org/W2792119783","https://openalex.org/W2794050488","https://openalex.org/W2808595754","https://openalex.org/W2891044362","https://openalex.org/W2945487542","https://openalex.org/W2963294138","https://openalex.org/W2964300354","https://openalex.org/W2981452619","https://openalex.org/W2995398033","https://openalex.org/W3025606635","https://openalex.org/W3092345110","https://openalex.org/W3093749735","https://openalex.org/W3101069223","https://openalex.org/W3101557870","https://openalex.org/W3137920819","https://openalex.org/W3162486746","https://openalex.org/W3190954595","https://openalex.org/W3197710054","https://openalex.org/W4234761190","https://openalex.org/W4301791716","https://openalex.org/W4366367078","https://openalex.org/W4377001565","https://openalex.org/W4384024694","https://openalex.org/W4386634581","https://openalex.org/W4387415129","https://openalex.org/W4389885612","https://openalex.org/W6605000091","https://openalex.org/W6676131375","https://openalex.org/W6679567685","https://openalex.org/W6779984877"],"related_works":["https://openalex.org/W211718035","https://openalex.org/W4221157020","https://openalex.org/W4302558842","https://openalex.org/W4299551322","https://openalex.org/W2953375265","https://openalex.org/W3125812435","https://openalex.org/W1151949413","https://openalex.org/W4299590005","https://openalex.org/W2025767136","https://openalex.org/W2612802384"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"significant":[3],"recent":[4],"interest":[5],"in":[6,14,73],"a":[7,21,25,30,44,87,96,115,121,136],"class":[8],"of":[9,160],"three-player":[10,75],"leader-follower":[11,45],"game":[12],"models":[13],"many":[15],"important":[16],"cybersecurity":[17],"scenarios.":[18],"In":[19],"such":[20,43,101],"tri-level":[22],"hierarchical":[23],"structure,":[24],"defender":[26],"usually":[27],"serves":[28],"as":[29],"leader,":[31],"dominating":[32],"the":[33,37,52,67,74,79,130,150,161,169],"decision":[34],"process":[35],"by":[36],"Stackelberg":[38],"equilibrium":[39,54],"(SE)":[40],"strategy.":[41,175],"However,":[42],"scheme":[46],"may":[47,57],"not":[48,109],"always":[49],"work,":[50],"and":[51,71,85,98,165,189],"Nash":[53],"(NE)":[55],"strategy":[56,83],"provide":[58,95],"an":[59,106,124,146,157,173],"alternative":[60],"choice.":[61],"Thus,":[62],"we":[63,93,128,155,177],"need":[64],"to":[65,77,113,167,182],"reveal":[66],"consistency":[68,151,180],"between":[69,163],"SE":[70,104,117,138,144,164,174],"NE":[72,166],"model":[76],"help":[78,168],"leader":[80,170],"evaluate":[81],"its":[82],"impact":[84],"avoid":[86],"choice":[88],"dilemma.":[89],"To":[90],"this":[91],"end,":[92],"first":[94],"necessary":[97],"sufficient":[99],"condition":[100,152],"that":[102],"each":[103],"is":[105],"NE,":[107],"which":[108],"only":[110],"provides":[111],"access":[112],"seek":[114],"satisfactory":[116],"but":[118],"also":[119],"makes":[120],"criterion":[122],"for":[123,132],"obtained":[125],"SE.":[126],"Then,":[127],"apply":[129,178],"results":[131],"case":[133],"studies":[134],"with":[135,140],"unique":[137],"or":[139],"at":[141],"least":[142],"one":[143],"being":[145],"NE.":[147],"Moreover,":[148],"when":[149],"falls":[153],"short,":[154],"give":[156],"upper":[158],"bound":[159],"deviation":[162],"tolerably":[171],"adopt":[172],"Finally,":[176],"our":[179],"analysis":[181],"practical":[183],"scenarios,":[184],"including":[185],"secure":[186],"wireless":[187],"transmission":[188],"advanced":[190],"persistent":[191],"threat":[192],"defense.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}