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We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control. <\/jats:p>","DOI":"10.1142\/s0218127420500959","type":"journal-article","created":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T09:25:33Z","timestamp":1593595533000},"page":"2050095","source":"Crossref","is-referenced-by-count":15,"title":["A Dynamic Duopoly Game with Content Providers\u2019 Bounded Rationality"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7294-6722","authenticated-orcid":false,"given":"Hamid","family":"Garmani","sequence":"first","affiliation":[{"name":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"}]},{"given":"Driss Ait","family":"Omar","sequence":"additional","affiliation":[{"name":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"}]},{"given":"Mohamed","family":"El Amrani","sequence":"additional","affiliation":[{"name":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"}]},{"given":"Mohamed","family":"Baslam","sequence":"additional","affiliation":[{"name":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"}]},{"given":"Mostafa","family":"Jourhmane","sequence":"additional","affiliation":[{"name":"Information Processing and Decision Support Laboratory, Faculty of Sciences and Technics, University of Sultan Moulay Slimane, Beni Mellal, Morocco"}]}],"member":"219","published-online":{"date-parts":[[2020,7,1]]},"reference":[{"key":"S0218127420500959BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(98)00322-1"},{"key":"S0218127420500959BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-59647-1_33"},{"key":"S0218127420500959BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-05529-5_18"},{"key":"S0218127420500959BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-018-0642-5"},{"key":"S0218127420500959BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20798-3_6"},{"key":"S0218127420500959BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.02.032"},{"key":"S0218127420500959BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417502066"},{"key":"S0218127420500959BIB008","first-page":"642","volume-title":"Game Theory for Networks","author":"Baslam M.","year":"2011"},{"key":"S0218127420500959BIB009","doi-asserted-by":"publisher","DOI":"10.4108\/valuetools.2012.250410"},{"key":"S0218127420500959BIB010","doi-asserted-by":"publisher","DOI":"10.5772\/54380"},{"key":"S0218127420500959BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1336-9_20"},{"key":"S0218127420500959BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2006.07.022"},{"key":"S0218127420500959BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2011.2119327"},{"key":"S0218127420500959BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2014.02.030"},{"key":"S0218127420500959BIB015","first-page":"369","volume-title":"Teletraffic Science and Engineering","author":"El Azouzi R.","year":"2003"},{"key":"S0218127420500959BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.06.011"},{"key":"S0218127420500959BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.joems.2014.01.006"},{"key":"S0218127420500959BIB018","doi-asserted-by":"publisher","DOI":"10.14257\/ijca.2018.11.4.12"},{"key":"S0218127420500959BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-05529-5_19"},{"key":"S0218127420500959BIB020","volume-title":"A Primer in Game Theory","author":"Gibbons R.","year":"1992"},{"key":"S0218127420500959BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(00)00395-2"},{"key":"S0218127420500959BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s11786-011-0096-z"},{"key":"S0218127420500959BIB023","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/29207"},{"key":"S0218127420500959BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-09683-4_12"},{"key":"S0218127420500959BIB026","doi-asserted-by":"publisher","DOI":"10.4018\/IJBDCN.2019010106"},{"key":"S0218127420500959BIB027","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2016.01.024"},{"key":"S0218127420500959BIB028","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741850027X"},{"key":"S0218127420500959BIB029","volume-title":"Stability and Predictability of Dynamical Economic Systems with Memory","author":"Stiefenhofer A.","year":"1997"},{"key":"S0218127420500959BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(02)00143-1"},{"key":"S0218127420500959BIB031","first-page":"1","volume":"2016","author":"Zhao L.","year":"2016","journal-title":"Discr. 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