{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:49Z","timestamp":1760236969637,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T00:00:00Z","timestamp":1580688000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011665","name":"Deanship of Scientific Research, King Saud University","doi-asserted-by":"publisher","award":["RG-1435-054"],"award-info":[{"award-number":["RG-1435-054"]}],"id":[{"id":"10.13039\/501100011665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb\u2013Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game\u2019s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game\u2019s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game\u2019s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.<\/jats:p>","DOI":"10.3390\/e22020173","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T11:28:31Z","timestamp":1580729311000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Dynamic Effects Arise Due to Consumers\u2019 Preferences Depending on Past Choices"],"prefix":"10.3390","volume":"22","author":[{"given":"Sameh S.","family":"Askar","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5242-0280","authenticated-orcid":false,"given":"A.","family":"Al-khedhairi","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1561\/105.00000058","article-title":"A new approach to modeling Bertrand duopoly","volume":"4","author":"Puu","year":"2017","journal-title":"Rev. Behav. 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