{"id":"https://openalex.org/W7127044485","doi":"https://doi.org/10.1038/s41598-025-32002-0","title":"Strategic enforcement of linear payoff relations in a three-player strictly alternating prisoner\u2019s dilemma game","display_name":"Strategic enforcement of linear payoff relations in a three-player strictly alternating prisoner\u2019s dilemma game","publication_year":2026,"publication_date":"2026-02-01","ids":{"openalex":"https://openalex.org/W7127044485","doi":"https://doi.org/10.1038/s41598-025-32002-0","pmid":"https://pubmed.ncbi.nlm.nih.gov/41622217"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-025-32002-0","doi":"https://doi.org/10.1038/s41598-025-32002-0","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-025-32002-0","pdf_url":"https://www.nature.com/articles/s41598-025-32002-0.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-025-32002-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014697945","display_name":"Mohammad A. Taha","orcid":"https://orcid.org/0000-0002-3250-8605","observed_orcids":["https://orcid.org/0000-0002-3250-8605"]},"institutions":[{"id":"https://openalex.org/I114794399","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074","country_code":"EG","type":"education","lineage":["https://openalex.org/I114794399"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Mohammad A. Taha","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, 41522, Egypt. mohammed_taha@science.suez.edu.eg"],"raw_orcid":"https://orcid.org/0000-0002-3250-8605","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, 41522, Egypt. mohammed_taha@science.suez.edu.eg","institution_ids":["https://openalex.org/I114794399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024881772","display_name":"Samira S. Mersal","orcid":"https://orcid.org/0000-0003-3696-4488","observed_orcids":["https://orcid.org/0000-0003-3696-4488"]},"institutions":[{"id":"https://openalex.org/I114794399","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074","country_code":"EG","type":"education","lineage":["https://openalex.org/I114794399"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Samira S. Mersal","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, 41522, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, 41522, Egypt","institution_ids":["https://openalex.org/I114794399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091760294","display_name":"M. G. Brikaa","orcid":"https://orcid.org/0000-0002-6788-6446","observed_orcids":["https://orcid.org/0000-0002-6788-6446"]},"institutions":[{"id":"https://openalex.org/I114794399","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074","country_code":"EG","type":"education","lineage":["https://openalex.org/I114794399"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"M. G. Brikaa","raw_affiliation_strings":["Department of Basic Sciences, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt","institution_ids":["https://openalex.org/I114794399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014697945"],"corresponding_institution_ids":["https://openalex.org/I114794399"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":12.152,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.95658832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"16","issue":"1","first_page":"4539","last_page":"4539"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.8901000022888184,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.8901000022888184,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.09969999641180038,"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"}},{"id":"https://openalex.org/T10646","display_name":"Experimental Behavioral Economics Studies","score":0.004000000189989805,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prisoner-s-dilemma","display_name":"prisoner's dilemma","score":0.8640000224113464},{"id":"https://openalex.org/keywords/zero-determinant-strategies","display_name":"zero-determinant strategies","score":0.8479999899864197},{"id":"https://openalex.org/keywords/three-player-games","display_name":"three-player games","score":0.7670000195503235},{"id":"https://openalex.org/keywords/repeated-games","display_name":"repeated games","score":0.8330000042915344},{"id":"https://openalex.org/keywords/cooperation","display_name":"cooperation","score":0.7559999823570251},{"id":"https://openalex.org/keywords/feasible-region","display_name":"feasible region","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C2778496695","wikidata":"https://www.wikidata.org/wiki/Q254128","display_name":"Dilemma","level":2,"score":0.9147999882698059},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.6215000152587891},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.592199981212616},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.571399986743927},{"id":"https://openalex.org/C2779066997","wikidata":"https://www.wikidata.org/wiki/Q6452087","display_name":"Extortion","level":2,"score":0.5626999735832214},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.5583999752998352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5507000088691711},{"id":"https://openalex.org/C113494165","wikidata":"https://www.wikidata.org/wiki/Q41693","display_name":"Prisoner's dilemma","level":3,"score":0.5360000133514404},{"id":"https://openalex.org/C90659851","wikidata":"https://www.wikidata.org/wiki/Q1300745","display_name":"Superrationality","level":4,"score":0.49300000071525574},{"id":"https://openalex.org/C2779777834","wikidata":"https://www.wikidata.org/wiki/Q4202277","display_name":"Enforcement","level":2,"score":0.4812000095844269},{"id":"https://openalex.org/C47993264","wikidata":"https://www.wikidata.org/wiki/Q1518456","display_name":"Traveler's dilemma","level":5,"score":0.45410001277923584},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4318999946117401},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.40459999442100525},{"id":"https://openalex.org/C93733245","wikidata":"https://www.wikidata.org/wiki/Q3770642","display_name":"Symmetric game","level":5,"score":0.38929998874664307},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3610999882221222},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.3513000011444092},{"id":"https://openalex.org/C95940807","wikidata":"https://www.wikidata.org/wiki/Q12237274","display_name":"Simultaneous game","level":4,"score":0.299699991941452},{"id":"https://openalex.org/C187206662","wikidata":"https://www.wikidata.org/wiki/Q55607920","display_name":"Social dilemma","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C47175762","wikidata":"https://www.wikidata.org/wiki/Q13422573","display_name":"Non-cooperative game","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.2872999906539917},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.2619999945163727},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.25760000944137573}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1038/s41598-025-32002-0","doi":"https://doi.org/10.1038/s41598-025-32002-0","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-025-32002-0","pdf_url":"https://www.nature.com/articles/s41598-025-32002-0.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},{"id":"pmid:41622217","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41622217","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,"listed_in":[],"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":"Scientific reports","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:11676563","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12868688","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":"Text"},{"id":"pmh:oai:doaj.org/article:552f664b2c134075a3984729faad5bf7","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/552f664b2c134075a3984729faad5bf7","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,"listed_in":[],"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":"Scientific Reports, Vol 16, Iss 1, Pp 1-13 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1038/s41598-025-32002-0","doi":"https://doi.org/10.1038/s41598-025-32002-0","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-025-32002-0","pdf_url":"https://www.nature.com/articles/s41598-025-32002-0.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6601999998092651,"display_name":"Peace, justice, and strong institutions"}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F6896549162","display_name":"Suez Canal University","ror":"https://ror.org/02m82p074"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127044485.pdf","grobid_xml":"https://content.openalex.org/works/W7127044485.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1976450472","https://openalex.org/W2001846609","https://openalex.org/W2007759681","https://openalex.org/W2017045031","https://openalex.org/W2033601694","https://openalex.org/W2042252765","https://openalex.org/W2058674890","https://openalex.org/W2062663664","https://openalex.org/W2070095606","https://openalex.org/W2077453922","https://openalex.org/W2119667990","https://openalex.org/W2270436655","https://openalex.org/W2611060343","https://openalex.org/W2771663519","https://openalex.org/W2911964379","https://openalex.org/W2976152462","https://openalex.org/W2981587494","https://openalex.org/W3004890069","https://openalex.org/W3198215647","https://openalex.org/W3205844153","https://openalex.org/W4210886181"],"related_works":[],"abstract_inverted_index":{"The":[0],"prisoner\u2019s":[1,56,95],"dilemma":[2,57,96],"game":[3,9],"is":[4],"a":[5,48],"fundamental":[6],"model":[7,53,86],"in":[8,47,82,91,129],"theory":[10],"for":[11],"studying":[12],"the":[13,28,42,55,67,79,83,92,101,123],"emergence":[14],"of":[15,44,54,70,106],"cooperation":[16,127],"among":[17],"self-interested":[18],"individuals":[19],"with":[20],"conflicting":[21],"incentives.":[22],"Most":[23],"existing":[24],"studies":[25],"have":[26],"examined":[27],"simultaneous":[29,93],"two-player":[30],"version,":[31],"where":[32,59],"both":[33],"players":[34,60],"act":[35],"simultaneously.":[36],"In":[37],"contrast,":[38],"this":[39,115],"paper":[40],"investigates":[41],"impact":[43],"Zero-Determinant":[45,80,107],"strategies":[46,81,108],"strictly":[49,84],"alternating":[50,85,131],"three-player":[51,94],"repeated":[52],"game,":[58],"take":[61],"turns":[62],"making":[63],"decisions":[64],"based":[65],"on":[66],"previous":[68],"actions":[69],"their":[71,111],"opponents":[72],"(one-memory":[73],"strategy).":[74],"Analytical":[75],"results":[76],"reveal":[77],"that":[78],"differ":[87],"significantly":[88],"from":[89],"those":[90],"game.":[97],"We":[98],"further":[99],"examine":[100],"equalizer":[102],"and":[103,109,126],"extortion":[104],"subsets":[105],"derive":[110],"feasible":[112],"regions":[113],"within":[114],"framework.":[116],"These":[117],"findings":[118],"provide":[119],"new":[120],"insights":[121],"into":[122],"strategic":[124],"control":[125],"mechanisms":[128],"multi-player":[130],"interactions.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2026-02-03T00:00:00"}
