{"id":"https://openalex.org/W4403730532","doi":"https://doi.org/10.3390/g15060035","title":"On Isaac\u2019s War Game of Attrition and Attack Using Dynamic Programming Approach","display_name":"On Isaac\u2019s War Game of Attrition and Attack Using Dynamic Programming Approach","publication_year":2024,"publication_date":"2024-10-24","ids":{"openalex":"https://openalex.org/W4403730532","doi":"https://doi.org/10.3390/g15060035"},"language":"en","primary_location":{"id":"doi:10.3390/g15060035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15060035","pdf_url":null,"source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"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":"Games","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/g15060035","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114394225","display_name":"Benghebrid Safa","orcid":null},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Benghebrid Safa","raw_affiliation_strings":["Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas Setif-1, Setif 19000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas Setif-1, Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055601273","display_name":"Touffik Bouremani","orcid":"https://orcid.org/0000-0001-7600-0638"},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Bouremani Touffik","raw_affiliation_strings":["Laboratory of Applied Mathematics, Faculty of Technology, University of Ferhat Abbas Setif-1, Setif 19000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Applied Mathematics, Faculty of Technology, University of Ferhat Abbas Setif-1, Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075788164","display_name":"Djamel Benterki","orcid":null},"institutions":[{"id":"https://openalex.org/I40193446","display_name":"University Ferhat Abbas of Setif","ror":"https://ror.org/02rzqza52","country_code":"DZ","type":"education","lineage":["https://openalex.org/I40193446"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Benterki Djamel","raw_affiliation_strings":["Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas Setif-1, Setif 19000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, University of Ferhat Abbas Setif-1, Setif 19000, Algeria","institution_ids":["https://openalex.org/I40193446"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114394225"],"corresponding_institution_ids":["https://openalex.org/I40193446"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24655695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"6","first_page":"35","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12158","display_name":"Guidance and Control Systems","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T13371","display_name":"Military Defense Systems Analysis","score":0.9700000286102295,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9370999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/attrition","display_name":"Attrition","score":0.6589657068252563},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.5483678579330444},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.49289608001708984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46515923738479614},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.46168771386146545},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.37687596678733826},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.3535136580467224},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.33664876222610474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10941687226295471},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07639497518539429}],"concepts":[{"id":"https://openalex.org/C2780553607","wikidata":"https://www.wikidata.org/wiki/Q684868","display_name":"Attrition","level":2,"score":0.6589657068252563},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.5483678579330444},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.49289608001708984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46515923738479614},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.46168771386146545},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.37687596678733826},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.3535136580467224},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.33664876222610474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10941687226295471},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07639497518539429},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/g15060035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15060035","pdf_url":null,"source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"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":"Games","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/330104","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/330104","pdf_url":"https://www.econstor.eu/bitstream/10419/330104/1/games-15-00035.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:gam:jgames:v:15:y:2024:i:6:p:35-:d:1505876","is_oa":false,"landing_page_url":"https://www.mdpi.com/2073-4336/15/6/35/","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"},{"id":"pmh:oai:doaj.org/article:24c5e3039b694258bef186468c7d3c15","is_oa":true,"landing_page_url":"https://doaj.org/article/24c5e3039b694258bef186468c7d3c15","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Games, Vol 15, Iss 6, p 35 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/g15060035","is_oa":true,"landing_page_url":"https://doi.org/10.3390/g15060035","pdf_url":null,"source":{"id":"https://openalex.org/S6552842","display_name":"Games","issn_l":"2073-4336","issn":["2073-4336"],"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":"Games","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1522683408","https://openalex.org/W1527244075","https://openalex.org/W1968070254","https://openalex.org/W2056207177","https://openalex.org/W2057462050","https://openalex.org/W2064833155","https://openalex.org/W2147504449","https://openalex.org/W4210718478","https://openalex.org/W4244358025","https://openalex.org/W4247262579","https://openalex.org/W4385764510","https://openalex.org/W6666788669"],"related_works":["https://openalex.org/W2071306797","https://openalex.org/W3125663232","https://openalex.org/W2414265698","https://openalex.org/W2764180893","https://openalex.org/W2405803446","https://openalex.org/W2892355632","https://openalex.org/W3122286720","https://openalex.org/W2374666693","https://openalex.org/W3022762175","https://openalex.org/W1999522139"],"abstract_inverted_index":{"In":[0],"this":[1,30],"study,":[2],"we":[3,33],"use":[4],"the":[5,15,35,43,56,80,84,100,107,114,129,159],"dynamic":[6],"programming":[7],"method":[8],"introduced":[9],"by":[10,25],"Miric\u0103":[11],"(2004)":[12],"to":[13,38,79],"solve":[14],"well-known":[16],"war":[17],"game":[18,45,73,103],"of":[19,83,102,109,117,139,142],"attrition":[20],"and":[21,51,59,112,128],"attack":[22],"as":[23,163],"formulated":[24],"Isaacs":[26],"(1965).":[27],"By":[28],"using":[29,152],"modern":[31],"approach,":[32],"extend":[34],"classical":[36],"framework":[37],"explore":[39],"optimal":[40],"strategies":[41,76,127],"within":[42],"differential":[44],"setting,":[46],"offering":[47],"a":[48,65,136,153],"complete,":[49],"comprehensive":[50],"theoretically":[52],"robust":[53,88],"solution.":[54],"Additionally,":[55],"study":[57],"identifies":[58],"analyzes":[60],"feedback":[61,119,126],"strategies,":[62],"which":[63],"represent":[64],"significant":[66],"advancement":[67],"over":[68],"other":[69],"strategy":[70],"types":[71],"in":[72,93,106],"theory.":[74],"These":[75],"dynamically":[77],"adapt":[78],"evolving":[81],"state":[82],"system,":[85],"providing":[86],"more":[87],"solutions":[89],"for":[90,144,158,166],"real-time":[91],"decision-making":[92],"conflict":[94],"scenarios.":[95],"This":[96],"novel":[97],"contribution":[98],"enhances":[99],"application":[101,138],"theory,":[104],"particularly":[105],"context":[108],"warfare":[110],"models,":[111],"illustrates":[113],"practical":[115],"advantages":[116],"incorporating":[118],"mechanisms":[120],"into":[121],"strategic":[122],"decision-making.":[123],"The":[124],"admissible":[125],"corresponding":[130],"value":[131,161],"function":[132,162],"are":[133],"constructed":[134],"through":[135],"refined":[137],"Cauchy\u2019s":[140],"Method":[141],"characteristics":[143],"stratified":[145],"Hamilton\u2013Jacobi":[146],"equations.":[147],"Their":[148],"optimality":[149,168],"is":[150],"proved":[151],"suitable":[154],"Elementary":[155],"Verification":[156],"Theorem":[157],"associated":[160],"an":[164],"argument":[165],"sufficient":[167],"conditions.":[169]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2024-10-25T00:00:00"}