{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:26:26Z","timestamp":1754155586887,"version":"3.41.2"},"reference-count":54,"publisher":"Emerald","issue":"8","license":[{"start":{"date-parts":[[2018,3,13]],"date-time":"2018-03-13T00:00:00Z","timestamp":1520899200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["K"],"published-print":{"date-parts":[[2018,9,26]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>The purpose of this paper is to investigate the impact of price adjustment speed on the stability of Bertrand\u2013Nash equilibrium in the context of a dual-channel supply chain competition.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>The paper considers a dual-channel supply chain comprising a manufacturer, a traditional retailer and an online retailer. A two-dimensional discrete dynamical system is used to examine the Bertrand competition between the retailers. The retailers are assumed to follow bounded rational expectations. Local stability of Bertrand\u2013Nash equilibrium is investigated with respect to the price adjustment speed.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>As the price adjustment speed increases, the stability of Bertrand\u2013Nash equilibrium is lost, leading to complex chaotic dynamics. The results showed that chaotic dynamics deteriorates the profit of the retailers. The authors also found that the chaos can be controlled using an adaptive adjustment mechanism and the retailers enjoy higher profit when the chaos is controlled.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Practical implications<\/jats:title>\n<jats:p>This study helps retail managers to choose an appropriate price adjustment speed to maximize profit.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>The heterogeneity of the retailers is not considered in the studies involving dynamics of retailer competition. This paper contributes to the literature by considering the operational difference between a traditional retailer and an online retailer, i.e. price adjustment speed. In addition, the study establishes a link between price adjustment speed and profit.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/k-08-2017-0301","type":"journal-article","created":{"date-parts":[[2018,3,13]],"date-time":"2018-03-13T10:57:25Z","timestamp":1520938645000},"page":"1494-1523","source":"Crossref","is-referenced-by-count":6,"title":["Impact of price adjustment speed on the stability of Bertrand\u2013Nash equilibrium and profit of the retailers"],"prefix":"10.1108","volume":"47","author":[{"given":"Rofin","family":"T.M.","sequence":"first","affiliation":[]},{"given":"Biswajit","family":"Mahanty","sequence":"additional","affiliation":[]}],"member":"140","published-online":{"date-parts":[[2018,3,13]]},"reference":[{"issue":"12","key":"key2021041509184293000_ref001","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1016\/S0960-0779(98)00006-X","article-title":"Explicit stability zones for cournot game with 3 and 4 competitors","volume":"9","year":"1998","journal-title":"Chaos, Solitons & Fractals"},{"issue":"3","key":"key2021041509184293000_ref002","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/S0096-3003(03)00190-5","article-title":"Chaotic dynamics in nonlinear duopoly game with heterogeneous players","volume":"149","year":"2004","journal-title":"Applied Mathematics and Computation"},{"issue":"9","key":"key2021041509184293000_ref003","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1016\/S0960-0779(00)00021-7","article-title":"The dynamics of Bowley\u2019s model with bounded rationality","volume":"12","year":"2001","journal-title":"Chaos, Solitons and Fractals"},{"article-title":"A cournot duopoly with bounded inverse demand function","volume-title":"Complex Oligopoly Dynamics","year":"2002","key":"key2021041509184293000_ref004"},{"issue":"15","key":"key2021041509184293000_ref005","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1016\/S0960-0779(99)00160-5","article-title":"The dynamics of a triopoly cournot game","volume":"11","year":"2000","journal-title":"Chaos, Solitons and Fractals"},{"issue":"4","key":"key2021041509184293000_ref006","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1287\/mnsc.46.4.563.12061","article-title":"Frictionless commerce? 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