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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 universitet, Samhällsvetenskapliga fakulteten, Centrum för regionalvetenskap (CERUM).
2015 (Engelska)Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 251, s. 169-179Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Elsevier, 2015. Vol. 251, s. 169-179
Nyckelord [en]
Bertrand game, CES utility function, Nash equilibrium point, Bifurcation, Chaos
Nationell ämneskategori
Nationalekonomi
Identifikatorer
URN: urn:nbn:se:umu:diva-100237DOI: 10.1016/j.amc.2014.11.051ISI: 000347405500016OAI: oai:DiVA.org:umu-100237DiVA, id: diva2:790937
Tillgänglig från: 2015-02-26 Skapad: 2015-02-26 Senast uppdaterad: 2018-06-07Bibliografiskt granskad

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