On Bertrand duopoly game with differentiated goods

E. Ahmed, A.A. Elsadany and Tonu Puu

Applied Mathematics and Computation, 2015, vol. 251, issue C, 169-179

Abstract: 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.

Keywords: Bertrand game; CES utility function; Nash equilibrium point; Bifurcation; Chaos (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (25)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:169-179

DOI: 10.1016/j.amc.2014.11.051

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