{"id":"https://openalex.org/W4400933895","doi":"https://doi.org/10.3390/e26080624","title":"An Attacker\u2013Defender Game Model with Constrained Strategies","display_name":"An Attacker\u2013Defender Game Model with Constrained Strategies","publication_year":2024,"publication_date":"2024-07-24","ids":{"openalex":"https://openalex.org/W4400933895","doi":"https://doi.org/10.3390/e26080624","pmid":"https://pubmed.ncbi.nlm.nih.gov/39202094"},"language":"en","primary_location":{"id":"doi:10.3390/e26080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080624","pdf_url":"https://www.mdpi.com/1099-4300/26/8/624/pdf?version=1721898507","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/8/624/pdf?version=1721898507","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102129749","display_name":"J. Ren","orcid":"https://orcid.org/0009-0006-9203-5666"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaqi Ren","raw_affiliation_strings":["National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101597404","display_name":"Jin Liu","orcid":"https://orcid.org/0000-0002-5143-2263"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Liu","raw_affiliation_strings":["National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103045063","display_name":"Yibo Dong","orcid":"https://orcid.org/0009-0001-9920-8113"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yibo Dong","raw_affiliation_strings":["National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100356724","display_name":"Zhe Li","orcid":"https://orcid.org/0009-0009-3725-2248"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Li","raw_affiliation_strings":["National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100401806","display_name":"Weili Li","orcid":"https://orcid.org/0000-0003-2317-5121"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weili Li","raw_affiliation_strings":["National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100401806"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2723,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54077918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"26","issue":"8","first_page":"624","last_page":"624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9959999918937683,"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":0.9959999918937683,"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/T10400","display_name":"Network Security and Intrusion Detection","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/computer-science","display_name":"Computer science","score":0.5533405542373657},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.49562060832977295},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.43828362226486206},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33774492144584656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.263704776763916}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5533405542373657},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.49562060832977295},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.43828362226486206},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33774492144584656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.263704776763916}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080624","pdf_url":"https://www.mdpi.com/1099-4300/26/8/624/pdf?version=1721898507","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:39202094","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39202094","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11353961","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11353961","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11353961/pdf/entropy-26-00624.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:ba64e5118c03452f80ac4c958b67560e","is_oa":true,"landing_page_url":"https://doaj.org/article/ba64e5118c03452f80ac4c958b67560e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 8, p 624 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26080624","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080624","pdf_url":"https://www.mdpi.com/1099-4300/26/8/624/pdf?version=1721898507","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400933895.pdf","grobid_xml":"https://content.openalex.org/works/W4400933895.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1966962864","https://openalex.org/W1970913835","https://openalex.org/W1978487619","https://openalex.org/W1986310535","https://openalex.org/W2003858305","https://openalex.org/W2008620264","https://openalex.org/W2043820931","https://openalex.org/W2048063069","https://openalex.org/W2056944867","https://openalex.org/W2060464767","https://openalex.org/W2067050450","https://openalex.org/W2076995980","https://openalex.org/W2080434622","https://openalex.org/W2103446323","https://openalex.org/W2109183665","https://openalex.org/W2112090702","https://openalex.org/W2148534455","https://openalex.org/W2154897810","https://openalex.org/W2162048614","https://openalex.org/W2170617971","https://openalex.org/W2245796072","https://openalex.org/W2289031131","https://openalex.org/W2474649930","https://openalex.org/W2605381169","https://openalex.org/W2732879715","https://openalex.org/W2799532920","https://openalex.org/W2892594120","https://openalex.org/W2903802770","https://openalex.org/W2915032990","https://openalex.org/W2945251363","https://openalex.org/W2970665103","https://openalex.org/W2973501744","https://openalex.org/W2975191991","https://openalex.org/W2996522055","https://openalex.org/W3138773454","https://openalex.org/W3189397825","https://openalex.org/W3195286465","https://openalex.org/W4244750590","https://openalex.org/W4246877238","https://openalex.org/W4308146793","https://openalex.org/W4313327789","https://openalex.org/W4375947652","https://openalex.org/W4381995687","https://openalex.org/W6664702507","https://openalex.org/W6847388455"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W2382290278","https://openalex.org/W4395014643"],"abstract_inverted_index":{"Recently,":[0],"research":[1,207],"interest":[2],"in":[3,38,45,69,220],"the":[4,32,60,75,84,91,95,99,115,124,149,153,169,173,176,189,198,209,237],"field":[5,210],"of":[6,35,62,77,97,126,152,188,200,240],"infrastructure":[7,221,241],"attack":[8,224],"and":[9,28,118,138,175,223],"defense":[10,222],"scenarios":[11],"has":[12,41],"increased.":[13],"Numerous":[14],"methods":[15],"have":[16],"been":[17,43],"proposed":[18],"for":[19,134,216],"studying":[20],"strategy":[21,101,228],"interactions":[22,57,219],"that":[23],"combine":[24],"complex":[25,39],"network":[26],"theory":[27,121],"game":[29,108],"theory.":[30],"However,":[31],"unavoidable":[33],"effect":[34,187],"constrained":[36,63,111,170],"strategies":[37,112,181,193],"situations":[40],"not":[42],"considered":[44],"previous":[46],"studies.":[47],"This":[48,206],"study":[49],"introduces":[50],"a":[51,65,132,143,213,233],"novel":[52,214],"approach":[53],"to":[54,122,179],"analyzing":[55],"these":[56,127,160],"by":[58,211],"including":[59],"effects":[61],"strategies,":[64,80,171],"factor":[66],"often":[67],"neglected":[68],"traditional":[70],"analyses.":[71],"First,":[72],"we":[73,104,130],"introduce":[74],"rule":[76,117],"constraints":[78,161,190],"on":[79,83,114,142,191,236],"which":[81],"depends":[82],"average":[85,92,184],"distance":[86,93],"between":[87],"selected":[88],"nodes.":[89],"As":[90],"increases,":[94],"probability":[96],"choosing":[98],"corresponding":[100],"decreases.":[102],"Second,":[103],"establish":[105],"an":[106],"attacker-defender":[107],"model":[109],"with":[110,182],"based":[113,141],"above":[116],"using":[119],"information":[120],"evaluate":[123],"uncertainty":[125],"strategies.":[128],"Finally,":[129],"present":[131],"method":[133],"solving":[135],"this":[136],"problem":[137],"conduct":[139],"experiments":[140],"target":[144],"network.":[145],"The":[146,186],"results":[147],"highlight":[148],"unique":[150],"characteristics":[151],"Nash":[154,165],"equilibrium":[155],"when":[156],"setting":[157],"constraints,":[158,229],"as":[159,197],"influence":[162],"decision":[163],"makers'":[164],"equilibria.":[166],"When":[167],"considering":[168],"both":[172],"attacker":[174],"defender":[177],"tend":[178],"select":[180],"lower":[183],"distances.":[185],"their":[192],"becomes":[194],"less":[195],"apparent":[196],"number":[199],"attackable":[201],"or":[202],"defendable":[203],"nodes":[204],"increases.":[205],"advances":[208],"introducing":[212],"framework":[215],"examining":[217],"strategic":[218],"scenarios.":[225],"By":[226],"incorporating":[227],"our":[230],"work":[231],"offers":[232],"new":[234],"perspective":[235],"critical":[238],"area":[239],"security.":[242]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}
