Change search
ReferencesLink to record
Permanent link

Direct link
On Bertrand duopoly game with differentiated goods
Department of Mathematics, Faculty of Science, Mansoura University, Egypt.
Department of Basic Science, Faculty of Computers and Informatics, Ismailia, Suez Canal University, Egypt; Department of Mathematics, Shanghai University, Shanghai 200444, China.
Umeå University, Faculty of Social Sciences, Centre for Regional Science (CERUM).
2015 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 251, 169-179 p.Article in journal (Refereed) Published
Abstract [en]

The paper investigates a dynamic Bertrand duopoly with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update their price in each period. The demand functions are derived from an underlying CES utility function. We investigate numerically the dynamical properties of the model. We consider two specific parameterizations for the CES function and study the Nash equilibrium and its local stability in the models. The general finding is that the Nash equilibrium becomes unstable as the speed of adjustment increases. The Nash equilibrium loses stability through a period-doubling bifurcation and the system eventually becomes chaotic either through a series of period-doubling bifurcations or after a Neimark–Sacker bifurcation.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 251, 169-179 p.
Keyword [en]
Bertrand game, CES utility function, Nash equilibrium point, Bifurcation, Chaos
National Category
URN: urn:nbn:se:umu:diva-100237DOI: 10.1016/j.amc.2014.11.051ISI: 000347405500016OAI: diva2:790937
Available from: 2015-02-26 Created: 2015-02-26 Last updated: 2015-12-14Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textURL

Search in DiVA

By author/editor
Puu, Tönu
By organisation
Centre for Regional Science (CERUM)
In the same journal
Applied Mathematics and Computation

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 91 hits
ReferencesLink to record
Permanent link

Direct link