{"id":"https://openalex.org/W4388010015","doi":"https://doi.org/10.1080/23307706.2023.2266697","title":"Equilibrium analysis for multi-defender Stackelberg security games under a logit tie-breaking rule","display_name":"Equilibrium analysis for multi-defender Stackelberg security games under a logit tie-breaking rule","publication_year":2023,"publication_date":"2023-10-29","ids":{"openalex":"https://openalex.org/W4388010015","doi":"https://doi.org/10.1080/23307706.2023.2266697"},"language":"en","primary_location":{"id":"doi:10.1080/23307706.2023.2266697","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23307706.2023.2266697","pdf_url":null,"source":{"id":"https://openalex.org/S2475925340","display_name":"Journal of Control and Decision","issn_l":"2330-7706","issn":["2330-7706","2330-7714"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control and Decision","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/A5021337969","display_name":"Ling Chen","orcid":"https://orcid.org/0000-0003-3382-0948"},"institutions":[{"id":"https://openalex.org/I174104030","display_name":"Taiyuan Normal University","ror":"https://ror.org/051k00p03","country_code":"CN","type":"education","lineage":["https://openalex.org/I174104030"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ling Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Taiyuan Normal University, Taiyuan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Taiyuan Normal University, Taiyuan, People's Republic of China","institution_ids":["https://openalex.org/I174104030"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077829209","display_name":"Mingchu Li","orcid":"https://orcid.org/0000-0001-8280-2936"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingchu Li","raw_affiliation_strings":["School of Software Technology, Dalian University of Technology, Dalian, Liaoning, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Software Technology, Dalian University of Technology, Dalian, Liaoning, People's Republic of China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021337969"],"corresponding_institution_ids":["https://openalex.org/I174104030"],"apc_list":null,"apc_paid":null,"fwci":0.3399,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.52862486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"669","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9697999954223633,"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":0.9697999954223633,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.9472699165344238},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7571079134941101},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.7114385366439819},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.618852436542511},{"id":"https://openalex.org/keywords/logit","display_name":"Logit","score":0.5952473878860474},{"id":"https://openalex.org/keywords/sequential-equilibrium","display_name":"Sequential equilibrium","score":0.5655084848403931},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.5242850184440613},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.501915454864502},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.45927199721336365},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.43335819244384766},{"id":"https://openalex.org/keywords/solution-concept","display_name":"Solution concept","score":0.41749250888824463},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3931538462638855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37146589159965515},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.25651538372039795},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.175998717546463}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.9472699165344238},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7571079134941101},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.7114385366439819},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.618852436542511},{"id":"https://openalex.org/C140331021","wikidata":"https://www.wikidata.org/wiki/Q1868104","display_name":"Logit","level":2,"score":0.5952473878860474},{"id":"https://openalex.org/C201364048","wikidata":"https://www.wikidata.org/wiki/Q2897085","display_name":"Sequential equilibrium","level":5,"score":0.5655084848403931},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.5242850184440613},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.501915454864502},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.45927199721336365},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.43335819244384766},{"id":"https://openalex.org/C11343654","wikidata":"https://www.wikidata.org/wiki/Q780008","display_name":"Solution concept","level":3,"score":0.41749250888824463},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3931538462638855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37146589159965515},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.25651538372039795},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.175998717546463}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/23307706.2023.2266697","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23307706.2023.2266697","pdf_url":null,"source":{"id":"https://openalex.org/S2475925340","display_name":"Journal of Control and Decision","issn_l":"2330-7706","issn":["2330-7706","2330-7714"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Control and Decision","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.5,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G6113137189","display_name":null,"funder_award_id":"61572095, 61877007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7726169887","display_name":null,"funder_award_id":"20210302124303, 202203021222251","funder_id":"https://openalex.org/F4320327913","funder_display_name":"ShanXi Science and Technology Department"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327913","display_name":"ShanXi Science and Technology Department","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2056418346","https://openalex.org/W2058296799","https://openalex.org/W2105308124","https://openalex.org/W2159149982","https://openalex.org/W2159230854","https://openalex.org/W2242906909","https://openalex.org/W2499811908","https://openalex.org/W2565555529","https://openalex.org/W2622408375","https://openalex.org/W2772649202","https://openalex.org/W2807790269","https://openalex.org/W2963982390","https://openalex.org/W2992905780","https://openalex.org/W4206524320","https://openalex.org/W4283797868"],"related_works":["https://openalex.org/W1553185561","https://openalex.org/W2097226409","https://openalex.org/W2953375265","https://openalex.org/W4299590005","https://openalex.org/W4302558842","https://openalex.org/W4221157020","https://openalex.org/W2952611531","https://openalex.org/W2097264194","https://openalex.org/W2408729172","https://openalex.org/W1979147872"],"abstract_inverted_index":{"We":[0,75,104,127],"introduce":[1],"a":[2,14,23,65,70,83,129],"general":[3],"multi-defender":[4],"Stackelberg":[5,30,78,108],"security":[6],"game":[7],"where":[8],"multiple":[9],"independent":[10],"defenders":[11],"jointly":[12],"protect":[13],"same":[15],"set":[16],"of":[17,38],"targets":[18],"from":[19],"being":[20],"attacked":[21],"by":[22,147],"common":[24],"attacker.":[25],"In":[26],"the":[27,36,57,101,135],"game,":[28],"Strong":[29],"Equilibrium":[31,93,110,115,138],"is":[32,44],"fundamentally":[33],"problematic,":[34],"because":[35],"notion":[37],"\u2018breaking":[39],"ties":[40],"in":[41,139],"defender's":[42],"favour\u2019":[43],"no":[45,141],"longer":[46],"well":[47,88],"defined,":[48],"as":[49,87,89],"we":[50,63],"must":[51],"specify":[52],"which":[53,119,140],"defender":[54,142],"will":[55],"receive":[56],"favour.":[58],"To":[59],"address":[60],"this":[61],"issue,":[62],"define":[64],"new":[66],"equilibrium":[67,102],"concept":[68],"under":[69],"newly":[71],"defined":[72],"tie-breaking":[73,85],"rule.":[74],"characterise":[76],"Logit":[77,107],"Multi-Defender":[79,109],"Equilibrium,":[80],"corresponding":[81],"to":[82,122,133],"logit":[84],"rule,":[86],"an":[90,124],"equivalent":[91,113],"Nash":[92,114],"among":[94],"defenders,":[95],"and":[96,111],"exhibit":[97],"algorithms":[98],"for":[99],"computing":[100],"solutions.":[103],"find":[105,123,134],"that":[106],"its'":[112],"may":[116],"not":[117],"exist,":[118],"motivates":[120],"us":[121],"approximate":[125,136],"equilibrium.":[126],"design":[128],"revised":[130],"exclusion":[131],"algorithm":[132],"\u03b5-Nash":[137],"gains":[143],"more":[144],"than":[145],"\u03b5":[146],"deviating.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
