{"id":"https://openalex.org/W3006625832","doi":"https://doi.org/10.1142/s0218127420500959","title":"A Dynamic Duopoly Game with Content Providers\u2019 Bounded Rationality","display_name":"A Dynamic Duopoly Game with Content Providers\u2019 Bounded Rationality","publication_year":2020,"publication_date":"2020-06-15","ids":{"openalex":"https://openalex.org/W3006625832","doi":"https://doi.org/10.1142/s0218127420500959","mag":"3006625832"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420500959","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500959","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5048048913","display_name":"Hamid Garmani","orcid":"https://orcid.org/0000-0002-7294-6722"},"institutions":[{"id":"https://openalex.org/I4210119856","display_name":"Universit\u00e9 Sultan Moulay Slimane","ror":"https://ror.org/02m8tb249","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210119856"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Hamid Garmani","raw_affiliation_strings":["Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"],"raw_orcid":"https://orcid.org/0000-0002-7294-6722","affiliations":[{"raw_affiliation_string":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco","institution_ids":["https://openalex.org/I4210119856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055642737","display_name":"Driss Ait Omar","orcid":"https://orcid.org/0000-0002-4096-8273"},"institutions":[{"id":"https://openalex.org/I4210119856","display_name":"Universit\u00e9 Sultan Moulay Slimane","ror":"https://ror.org/02m8tb249","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210119856"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Driss Ait Omar","raw_affiliation_strings":["Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco","institution_ids":["https://openalex.org/I4210119856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049008500","display_name":"Mohamed El Amrani","orcid":"https://orcid.org/0000-0003-4884-9663"},"institutions":[{"id":"https://openalex.org/I4210119856","display_name":"Universit\u00e9 Sultan Moulay Slimane","ror":"https://ror.org/02m8tb249","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210119856"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohamed El Amrani","raw_affiliation_strings":["Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco","institution_ids":["https://openalex.org/I4210119856"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088714836","display_name":"Mohamed Baslam","orcid":"https://orcid.org/0000-0003-4819-533X"},"institutions":[{"id":"https://openalex.org/I4210119856","display_name":"Universit\u00e9 Sultan Moulay Slimane","ror":"https://ror.org/02m8tb249","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210119856"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohamed Baslam","raw_affiliation_strings":["Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco","institution_ids":["https://openalex.org/I4210119856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022610843","display_name":"Mostafa Jourhmane","orcid":"https://orcid.org/0000-0002-6606-5945"},"institutions":[{"id":"https://openalex.org/I4210119856","display_name":"Universit\u00e9 Sultan Moulay Slimane","ror":"https://ror.org/02m8tb249","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210119856"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mostafa Jourhmane","raw_affiliation_strings":["Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco","institution_ids":["https://openalex.org/I4210119856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5048048913"],"corresponding_institution_ids":["https://openalex.org/I4210119856"],"apc_list":null,"apc_paid":null,"fwci":2.4446,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.92699181,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"07","first_page":"2050095","last_page":"2050095"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11043","display_name":"Merger and Competition Analysis","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11043","display_name":"Merger and Competition Analysis","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.991100013256073,"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/T11182","display_name":"Auction Theory and Applications","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-rationality","display_name":"Bounded rationality","score":0.7427728176116943},{"id":"https://openalex.org/keywords/duopoly","display_name":"Duopoly","score":0.7299901247024536},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.575507402420044},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5676620602607727},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5589724183082581},{"id":"https://openalex.org/keywords/rationality","display_name":"Rationality","score":0.5444700121879578},{"id":"https://openalex.org/keywords/credibility","display_name":"Credibility","score":0.5156039595603943},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47692057490348816},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.45810365676879883},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.4370948076248169},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4365026354789734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39611539244651794},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3645561933517456},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3393744230270386},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.24914991855621338},{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.18851953744888306},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09141913056373596},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08367112278938293}],"concepts":[{"id":"https://openalex.org/C58694771","wikidata":"https://www.wikidata.org/wiki/Q814385","display_name":"Bounded rationality","level":2,"score":0.7427728176116943},{"id":"https://openalex.org/C180456769","wikidata":"https://www.wikidata.org/wiki/Q750207","display_name":"Duopoly","level":3,"score":0.7299901247024536},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.575507402420044},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5676620602607727},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5589724183082581},{"id":"https://openalex.org/C201717286","wikidata":"https://www.wikidata.org/wiki/Q938185","display_name":"Rationality","level":2,"score":0.5444700121879578},{"id":"https://openalex.org/C2780224610","wikidata":"https://www.wikidata.org/wiki/Q1530061","display_name":"Credibility","level":2,"score":0.5156039595603943},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47692057490348816},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.45810365676879883},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4370948076248169},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4365026354789734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39611539244651794},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3645561933517456},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3393744230270386},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.24914991855621338},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.18851953744888306},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09141913056373596},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08367112278938293},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420500959","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420500959","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W184217447","https://openalex.org/W1581775889","https://openalex.org/W1977596607","https://openalex.org/W1980348039","https://openalex.org/W1982636489","https://openalex.org/W1985131349","https://openalex.org/W1986243632","https://openalex.org/W2014221334","https://openalex.org/W2049645248","https://openalex.org/W2067729019","https://openalex.org/W2071125069","https://openalex.org/W2092665479","https://openalex.org/W2094086312","https://openalex.org/W2138910010","https://openalex.org/W2161137744","https://openalex.org/W2165616869","https://openalex.org/W2283191420","https://openalex.org/W2612372339","https://openalex.org/W2782167235","https://openalex.org/W2791919259","https://openalex.org/W2802443662","https://openalex.org/W2811502688","https://openalex.org/W2896276795","https://openalex.org/W2907782043","https://openalex.org/W2907987700","https://openalex.org/W2912644043","https://openalex.org/W4243456132"],"related_works":["https://openalex.org/W2388687352","https://openalex.org/W2535743999","https://openalex.org/W2370187191","https://openalex.org/W1990162851","https://openalex.org/W2369854048","https://openalex.org/W2374291020","https://openalex.org/W2355907197","https://openalex.org/W3171042291","https://openalex.org/W2390961115","https://openalex.org/W2388138913"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,31,39,59,64,74,78,107,111,114,120,131,136],"dynamical":[4,79],"behaviors":[5],"of":[6,26,33,77,94,106,113,130],"a":[7,45,87],"duopoly":[8],"model":[9,108],"with":[10],"two":[11,17],"content":[12,34],"providers":[13],"(CPs).":[14],"Competition":[15],"between":[16],"CPs":[18,49],"is":[19,117,133],"assumed":[20],"to":[21,38,67],"take":[22],"place":[23],"in":[24,55],"terms":[25],"their":[27],"pricing":[28],"decisions":[29],"and":[30,85,89,119],"credibility":[32],"they":[35],"offer.":[36],"According":[37],"CPs\u2019":[40],"rationality":[41],"level,":[42],"we":[43],"consider":[44],"scenario":[46],"where":[47],"both":[48],"are":[50,109],"bounded":[51,83],"rational.":[52],"Each":[53],"CP":[54],"any":[56],"period":[57,66],"uses":[58],"marginal":[60],"profit":[61],"observed":[62],"from":[63],"previous":[65],"choose":[68],"its":[69,95],"strategies.":[70],"We":[71],"compute":[72],"explicitly":[73],"steady":[75],"states":[76],"system":[80,132],"induced":[81],"by":[82,139],"rationality,":[84],"establish":[86],"necessary":[88],"sufficient":[90],"condition":[91],"for":[92],"stability":[93,112],"Nash":[96],"equilibrium":[97],"(NE).":[98],"Numerical":[99],"simulations":[100],"show":[101],"that":[102],"if":[103],"some":[104],"parameters":[105],"varied,":[110],"NE":[115,137],"point":[116,138],"lost":[118],"complex":[121],"(periodic":[122],"or":[123],"chaotic)":[124],"behavior":[125,129],"occurs.":[126],"The":[127],"chaotic":[128],"stabilized":[134],"on":[135],"applying":[140],"control.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}