{"id":"https://openalex.org/W2958264303","doi":"https://doi.org/10.1080/01605682.2019.1630332","title":"Optimal defence-attack strategies between one defender and two attackers","display_name":"Optimal defence-attack strategies between one defender and two attackers","publication_year":2019,"publication_date":"2019-07-13","ids":{"openalex":"https://openalex.org/W2958264303","doi":"https://doi.org/10.1080/01605682.2019.1630332","mag":"2958264303"},"language":"en","primary_location":{"id":"doi:10.1080/01605682.2019.1630332","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01605682.2019.1630332","pdf_url":null,"source":{"id":"https://openalex.org/S169988927","display_name":"Journal of the Operational Research Society","issn_l":"0160-5682","issn":["0160-5682","1476-9360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319703","host_organization_name":"Palgrave Macmillan","host_organization_lineage":["https://openalex.org/P4310319703","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Palgrave Macmillan","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Operational Research Society","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/A5034200305","display_name":"Di Wu","orcid":"https://orcid.org/0000-0002-4996-587X"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Di Wu","raw_affiliation_strings":["School of Management, The State Key Lab for Manufacturing Systems Engineering, The Key Lab of the Ministry of Education for Process Control & Efficiency Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China;"],"raw_orcid":"https://orcid.org/0000-0002-4996-587X","affiliations":[{"raw_affiliation_string":"School of Management, The State Key Lab for Manufacturing Systems Engineering, The Key Lab of the Ministry of Education for Process Control & Efficiency Engineering, Xi\u2019an Jiaotong University, Xi\u2019an, China;","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058377213","display_name":"Xiangbin Yan","orcid":"https://orcid.org/0000-0001-7442-1244"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangbin Yan","raw_affiliation_strings":["Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, China;"],"raw_orcid":"https://orcid.org/0000-0001-7442-1244","affiliations":[{"raw_affiliation_string":"Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, China;","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081036659","display_name":"Rui Peng","orcid":"https://orcid.org/0000-0001-6596-0334"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rui Peng","raw_affiliation_strings":["Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, China;","School of Economics and Management, Beijing University of Technology, Beijing, China;"],"raw_orcid":"https://orcid.org/0000-0001-6596-0334","affiliations":[{"raw_affiliation_string":"Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, China;","institution_ids":["https://openalex.org/I92403157"]},{"raw_affiliation_string":"School of Economics and Management, Beijing University of Technology, Beijing, China;","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022122025","display_name":"Shaomin Wu","orcid":"https://orcid.org/0000-0001-9786-3213"},"institutions":[{"id":"https://openalex.org/I20581793","display_name":"University of Kent","ror":"https://ror.org/00xkeyj56","country_code":"GB","type":"education","lineage":["https://openalex.org/I20581793"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Shaomin Wu","raw_affiliation_strings":["Kent Business School, University of Kent, Canterbury, Kent, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kent Business School, University of Kent, Canterbury, Kent, United Kingdom","institution_ids":["https://openalex.org/I20581793"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081036659"],"corresponding_institution_ids":["https://openalex.org/I37796252","https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":2.2788,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86744619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"71","issue":"11","first_page":"1830","last_page":"1846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11807","display_name":"Infrastructure Resilience and Vulnerability Analysis","score":0.9972000122070312,"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":0.9972000122070312,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9394000172615051,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.9110999703407288,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"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/computer-science","display_name":"Computer science","score":0.6036099195480347},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.59141606092453},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5391228199005127},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.49354469776153564},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.4652681350708008},{"id":"https://openalex.org/keywords/risk-analysis","display_name":"Risk analysis (engineering)","score":0.39221271872520447},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.27729082107543945},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.250810831785202},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.24372190237045288},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12135151028633118}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6036099195480347},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.59141606092453},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5391228199005127},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.49354469776153564},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.4652681350708008},{"id":"https://openalex.org/C112930515","wikidata":"https://www.wikidata.org/wiki/Q4389547","display_name":"Risk analysis (engineering)","level":1,"score":0.39221271872520447},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.27729082107543945},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.250810831785202},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.24372190237045288},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12135151028633118},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/01605682.2019.1630332","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01605682.2019.1630332","pdf_url":null,"source":{"id":"https://openalex.org/S169988927","display_name":"Journal of the Operational Research Society","issn_l":"0160-5682","issn":["0160-5682","1476-9360"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319703","host_organization_name":"Palgrave Macmillan","host_organization_lineage":["https://openalex.org/P4310319703","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Palgrave Macmillan","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Operational Research Society","raw_type":"journal-article"},{"id":"pmh:oai:kar.kent.ac.uk:75325","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01605682.2019.1630332>)","pdf_url":null,"source":{"id":"https://openalex.org/S4377196264","display_name":"Kent Academic Repository (University of Kent)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20581793","host_organization_name":"University of Kent","host_organization_lineage":["https://openalex.org/I20581793"],"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":"PeerReviewed"},{"id":"pmh:oai:RePEc:taf:tjorxx:v:71:y:2020:i:11:p:1830-1846","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/01605682.2019.1630332","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2414310148","display_name":null,"funder_award_id":"71832011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5096515670","display_name":null,"funder_award_id":"71671016","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W48523275","https://openalex.org/W117655037","https://openalex.org/W170486074","https://openalex.org/W1593741082","https://openalex.org/W1846144622","https://openalex.org/W1969674217","https://openalex.org/W1973977385","https://openalex.org/W1979249228","https://openalex.org/W1980339486","https://openalex.org/W1996400815","https://openalex.org/W2002803140","https://openalex.org/W2012848440","https://openalex.org/W2014181466","https://openalex.org/W2015127657","https://openalex.org/W2015632107","https://openalex.org/W2019592007","https://openalex.org/W2039397642","https://openalex.org/W2041946752","https://openalex.org/W2047256245","https://openalex.org/W2047736339","https://openalex.org/W2057936272","https://openalex.org/W2077389155","https://openalex.org/W2083410951","https://openalex.org/W2084801753","https://openalex.org/W2090472855","https://openalex.org/W2109492877","https://openalex.org/W2110509986","https://openalex.org/W2116070369","https://openalex.org/W2119240992","https://openalex.org/W2160006859","https://openalex.org/W2205836349","https://openalex.org/W2269749770","https://openalex.org/W2467898204","https://openalex.org/W2506828386","https://openalex.org/W2621501304","https://openalex.org/W2743826488","https://openalex.org/W2744151781","https://openalex.org/W2792796684","https://openalex.org/W2811130173","https://openalex.org/W2906483748","https://openalex.org/W2915262231","https://openalex.org/W3123316650","https://openalex.org/W4397012138"],"related_works":["https://openalex.org/W2049150502","https://openalex.org/W1967500081","https://openalex.org/W2365751862","https://openalex.org/W2172599225","https://openalex.org/W3190778120","https://openalex.org/W3095114358","https://openalex.org/W4323341852","https://openalex.org/W2945191958","https://openalex.org/W4285411252","https://openalex.org/W4214943875"],"abstract_inverted_index":{"This":[0],"paper":[1],"analyses":[2],"the":[3,18,28,33,38,41,51,67,71,78,87,99,119,128,137,152,155,165,170,175,189,196],"optimal":[4,138],"strategies":[5,142,167,173],"for":[6,64,96,143,174,188],"one":[7],"defender":[8,19,120],"and":[9,26,31,48,140,168,183],"two":[10,29,34,72,161,178],"attackers":[11,73],"in":[12],"a":[13,55,61,93],"defence-attack":[14],"game,":[15],"where":[16],"a)":[17],"allocates":[20],"its":[21,122],"resource":[22],"into":[23,46],"defending":[24,49],"against":[25,50],"attacking":[27,47],"attackers,":[30,35],"b)":[32],"after":[36],"observing":[37],"action":[39],"of":[40,66,80,98,154,172],"defender,":[42,52],"allocate":[43],"their":[44,81,111],"resources":[45],"on":[53],"either":[54],"cooperative":[56,62],"or":[57],"non-cooperative":[58,94],"basis.":[59],"On":[60,92],"basis,":[63,95],"each":[65,97,103],"defender\u2019s":[68,100],"given":[69,101],"strategies,":[70,102],"work":[74],"together":[75],"to":[76,109,135,150,194],"maximise":[77,110],"sum":[79],"cumulative":[82,113,123],"prospect":[83,114,124],"values":[84],"while":[85,126],"anticipating":[86,127],"eight":[88],"possible":[89],"game":[90],"outcomes.":[91],"attacker":[104],"simultaneously":[105],"yet":[106],"independently":[107],"tries":[108],"own":[112],"value.":[115],"In":[116,157],"both":[117],"cases,":[118],"maximises":[121],"value":[125],"attackers\u2019":[129,166],"actions.":[130],"Backward":[131],"induction":[132],"is":[133],"employed":[134],"obtain":[136],"defence":[139],"attack":[141],"all":[144],"scenarios.":[145],"Numerical":[146],"examples":[147],"are":[148,191],"performed":[149,193],"illustrate":[151,195],"applications":[153],"strategies.":[156],"general,":[158],"we":[159],"find":[160],"opposing":[162],"effects":[163],"considering":[164],"analyse":[169],"alteration":[171,190],"participants":[176],"under":[177],"different":[179],"risk":[180,184],"preferences:":[181],"risk-averse":[182],"seeking.":[185],"The":[186],"reasons":[187],"also":[192],"practical":[197],"applications.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
